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1 | (14) |
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1 | (1) |
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2 | (1) |
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3 | (1) |
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1.4 Why this book is relevant |
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3 | (1) |
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4 | (3) |
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4 | (1) |
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5 | (1) |
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1.5.3 Hedonic price function |
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6 | (1) |
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7 | (2) |
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8 | (1) |
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9 | (1) |
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1.7 Outline of the remainder of the book |
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9 | (2) |
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1.8 Supplemental materials |
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11 | (1) |
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12 | (3) |
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2 Univariate density estimation |
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15 | (44) |
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2.1 Smoothing preliminaries |
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16 | (3) |
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19 | (9) |
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19 | (3) |
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22 | (2) |
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24 | (4) |
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28 | (1) |
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29 | (1) |
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30 | (15) |
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30 | (3) |
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2.5.2 Data-driven methods |
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33 | (10) |
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2.5.3 Plug-in or cross-validation? |
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43 | (2) |
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45 | (5) |
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47 | (1) |
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2.6.2 Bandwidth selection |
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48 | (2) |
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2.6.3 Relative efficiency |
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50 | (1) |
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50 | (9) |
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51 | (1) |
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52 | (7) |
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3 Multivariate density estimation |
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59 | (24) |
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59 | (3) |
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3.2 Bias, variance, and AMISE |
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62 | (2) |
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3.3 The curse of dimensionality |
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64 | (4) |
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68 | (4) |
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3.4.1 Rule-of-thumb bandwidth selection |
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70 | (1) |
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3.4.2 Cross-validation bandwidth selection |
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70 | (2) |
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3.5 Conditional density estimation |
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72 | (4) |
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3.5.1 Bias, variance, and AMSE |
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73 | (1) |
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3.5.2 Bandwidth selection |
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74 | (1) |
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3.5.3 Inclusion of irrelevant variables |
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75 | (1) |
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76 | (7) |
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4 Inference about the density |
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83 | (30) |
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84 | (8) |
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86 | (1) |
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87 | (2) |
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89 | (1) |
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4.1.4 Degenerate U-statistics |
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89 | (2) |
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91 | (1) |
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92 | (5) |
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4.3 Parametric specification |
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97 | (2) |
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99 | (2) |
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101 | (1) |
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4.6 Silverman test for multimodality |
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102 | (3) |
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105 | (3) |
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4.7.1 Bootstrap versus asymptotic distribution |
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106 | (1) |
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4.7.2 Role of bandwidth selection on reliability of tests |
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106 | (2) |
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108 | (5) |
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108 | (1) |
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4.8.2 Correct parametric specification |
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109 | (1) |
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110 | (1) |
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111 | (1) |
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112 | (1) |
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113 | (46) |
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5.1 Smoothing preliminaries |
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114 | (3) |
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5.2 Local-constant estimator |
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117 | (3) |
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5.2.1 Derivation from density estimators |
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117 | (1) |
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5.2.2 An indicator approach |
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118 | (1) |
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5.2.3 Kernel regression on a constant |
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118 | (2) |
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5.3 Bias, variance, and AMISE of the LCLS estimator |
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120 | (1) |
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121 | (6) |
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5.4.1 Univariate digression |
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121 | (2) |
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5.4.2 Optimal bandwidths in higher dimensions |
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123 | (1) |
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5.4.3 Least-squares cross-validation |
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124 | (1) |
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5.4.4 Cross-validation based on Akaike information criteria |
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125 | (1) |
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5.4.5 Interpretation of bandwidths for LCLS |
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126 | (1) |
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127 | (1) |
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128 | (2) |
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5.7 Local-linear estimation |
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130 | (3) |
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5.7.1 Choosing LLLS over LCLS |
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131 | (1) |
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5.7.2 Efficiency of the local-linear estimator |
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132 | (1) |
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5.8 Local-polynomial estimation |
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133 | (2) |
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5.9 Gradient-based bandwidth selection |
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135 | (2) |
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5.10 Standard errors and confidence bounds |
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137 | (2) |
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137 | (1) |
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5.10.2 Residual bootstrap |
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138 | (1) |
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139 | (1) |
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5.11 Displaying estimates |
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139 | (2) |
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141 | (1) |
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141 | (1) |
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142 | (17) |
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143 | (1) |
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144 | (15) |
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159 | (28) |
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6.1 Testing preliminaries |
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160 | (2) |
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6.1.1 Goodness-of-fit tests |
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160 | (1) |
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6.1.2 Conditional-moment test |
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161 | (1) |
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6.2 Correct parametric specification |
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162 | (6) |
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6.2.1 Goodness-of-fit test |
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163 | (3) |
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6.2.2 Conditional-moment test |
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166 | (2) |
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6.3 Irrelevant regressors |
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168 | (3) |
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6.3.1 Goodness-of-fit test |
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168 | (1) |
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6.3.2 Conditional-moment test |
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169 | (2) |
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171 | (3) |
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174 | (3) |
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6.5.1 Bootstrap versus asymptotic distribution |
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174 | (1) |
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6.5.2 Role of bandwidth selection on reliability of tests |
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175 | (2) |
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177 | (10) |
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6.6.1 Correct functional form |
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177 | (3) |
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180 | (1) |
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180 | (2) |
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182 | (5) |
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7 Smoothing discrete variables |
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187 | (18) |
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7.1 Estimation of a density |
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188 | (3) |
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7.1.1 Kernels for smoothing discrete variables |
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188 | (2) |
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7.1.2 Generalized product kernel |
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190 | (1) |
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7.2 Finite sample properties |
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191 | (3) |
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191 | (1) |
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7.2.2 Discrete-only variance |
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192 | (1) |
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192 | (1) |
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193 | (1) |
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7.2.5 Mixed-data variance |
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193 | (1) |
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193 | (1) |
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194 | (3) |
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195 | (1) |
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196 | (1) |
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7.4 Why the faster rate of convergence? |
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197 | (1) |
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7.5 Alternative discrete kernels |
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198 | (1) |
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199 | (2) |
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201 | (4) |
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8 Regression with discrete covariates |
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205 | (22) |
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8.1 Estimation of the conditional mean |
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206 | (3) |
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8.1.1 Local-constant least-squares |
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206 | (2) |
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8.1.2 Local-linear least-squares |
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208 | (1) |
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8.2 Estimation of gradients |
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209 | (3) |
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8.2.1 Continuous covariates |
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209 | (1) |
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8.2.2 Discrete covariates |
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210 | (2) |
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212 | (3) |
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8.3.1 Automatic bandwidth selection |
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213 | (1) |
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8.3.2 Upper and lower bounds for discrete bandwidths |
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214 | (1) |
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215 | (5) |
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8.4.1 Correct parametric specification |
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215 | (1) |
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8.4.2 Significance of continuous regressors |
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216 | (1) |
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8.4.3 Significance of discrete regressors |
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217 | (3) |
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8.5 All discrete regressors |
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220 | (2) |
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222 | (5) |
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222 | (1) |
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223 | (1) |
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8.6.3 Numerical gradients |
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223 | (2) |
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225 | (2) |
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227 | (40) |
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9.1 Semiparametric efficiency |
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228 | (1) |
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9.2 Partially linear models |
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228 | (10) |
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229 | (3) |
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9.2.2 Bandwidth selection |
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232 | (1) |
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233 | (5) |
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238 | (9) |
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239 | (5) |
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9.3.2 Bandwidth selection |
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244 | (1) |
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245 | (2) |
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9.4 Semiparametric smooth coefficient models |
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247 | (7) |
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249 | (3) |
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9.4.2 Bandwidth selection |
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252 | (1) |
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252 | (2) |
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254 | (7) |
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255 | (3) |
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9.5.2 Bandwidth selection |
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258 | (1) |
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259 | (2) |
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261 | (6) |
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261 | (2) |
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263 | (1) |
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9.6.3 Specification testing |
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264 | (3) |
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10 Instrumental variables |
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267 | (26) |
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10.1 The ill-posed inverse problem |
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268 | (2) |
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10.2 Tackling the ill-posed inverse |
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270 | (2) |
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10.3 Local-polynomial estimation of the control-function model |
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272 | (8) |
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10.3.1 Multiple endogenous regressors |
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274 | (1) |
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10.3.2 Bandwidth selection |
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275 | (1) |
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10.3.3 Choice of polynomial order |
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276 | (2) |
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10.3.4 Simulated evidence of the counterfactual simplification |
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278 | (1) |
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10.3.5 A valid bootstrap procedure |
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279 | (1) |
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280 | (6) |
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10.4.1 Weak identification |
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282 | (2) |
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10.4.2 Estimation in the presence of weak instruments |
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284 | (2) |
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10.4.3 Importance of nonlinearity in the first stage |
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286 | (1) |
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10.5 Discrete endogenous regressor |
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286 | (1) |
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287 | (1) |
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288 | (5) |
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293 | (28) |
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294 | (1) |
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295 | (6) |
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11.2.1 Local-linear weighted least-squares |
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297 | (1) |
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11.2.2 Wang's iterative estimator |
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298 | (3) |
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301 | (5) |
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11.3.1 Additive individual effects |
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302 | (3) |
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11.3.2 Discrete individual effects |
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305 | (1) |
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11.4 Dynamic panel estimation |
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306 | (2) |
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11.5 Semiparametric estimators |
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308 | (1) |
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309 | (1) |
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309 | (2) |
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310 | (1) |
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11.7.2 Residual bootstrap |
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310 | (1) |
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311 | (5) |
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311 | (2) |
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11.8.2 Functional form specification |
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313 | (2) |
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11.8.3 Nonparametric Hausman test |
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315 | (1) |
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316 | (5) |
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317 | (1) |
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318 | (1) |
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318 | (3) |
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12 Constrained estimation and inference |
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321 | (22) |
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322 | (4) |
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12.1.1 Imposing convexity |
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324 | (1) |
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12.1.2 Existing literature |
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325 | (1) |
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12.2 Motivating alternative shape-constrained estimators |
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326 | (4) |
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12.3 Implementation methods via reweighting |
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330 | (1) |
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12.3.1 Constraint-weighted bootstrapping |
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330 | (1) |
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330 | (1) |
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331 | (6) |
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12.4.1 Selecting the distance metric |
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331 | (1) |
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12.4.2 Choice of smoothing parameter |
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332 | (1) |
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12.4.3 Linear in p implementation issues |
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333 | (3) |
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12.4.4 Imposing additive separability |
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336 | (1) |
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12.5 Hypothesis testing on shape constraints |
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337 | (1) |
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338 | (1) |
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339 | (4) |
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12.7.1 Imposing positive marginal product |
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339 | (1) |
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12.7.2 Imposing constant returns to scale |
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340 | (3) |
Bibliography |
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343 | (16) |
Index |
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359 | |