Preface |
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ix | |
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1 | (8) |
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9 | (42) |
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9 | (1) |
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Exact Moments: Normal Case |
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9 | (9) |
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Exact Moments: Nonnormal Case |
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18 | (6) |
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18 | (1) |
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19 | (1) |
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19 | (1) |
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20 | (1) |
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K-Parameter Exponential Density |
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21 | (1) |
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Mixtures of Distributions |
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22 | (1) |
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Edgeworth Density or Gram-Charlier Density |
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23 | (1) |
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Exact Moments: General Case |
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24 | (2) |
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Approximations of Moments |
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26 | (22) |
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Large Sample Approximations: Normal and Nonnormal |
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27 | (9) |
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Small-σ Approximations: Normal and Nonnormal |
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36 | (8) |
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Results for Non-i.i.d Cases |
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44 | (1) |
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The Laplace Approximation: Normal and Nonnormal |
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45 | (3) |
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48 | (3) |
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Finite Sample Distributions |
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51 | (24) |
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51 | (1) |
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51 | (4) |
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Distribution of Ratio of Quadratic Forms |
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52 | (3) |
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Approximations of the Distribution of Quadratic Forms |
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55 | (1) |
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56 | (1) |
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57 | (1) |
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Large-n Edgeworth Expansion |
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57 | (10) |
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Small-σ Edgeworth Expansion of h(y) (Normal and Nonnormal) |
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67 | (2) |
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Remarks on the Edgeworth Expansion |
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69 | (6) |
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75 | (22) |
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75 | (1) |
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Model Specification and Least Squares Estimation |
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75 | (2) |
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77 | (20) |
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77 | (3) |
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Residuals and Residual Sum of Squares |
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80 | (3) |
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83 | (3) |
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86 | (1) |
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87 | (2) |
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Exact Moments Under Nonnormal |
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89 | (1) |
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90 | (4) |
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94 | (2) |
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Nonlinear Regression Models |
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96 | (1) |
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Models with Nonscalar Covariance Matrix of Errors |
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97 | (32) |
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97 | (1) |
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General Model with Nonscalar Covariance Matrix |
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97 | (10) |
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97 | (3) |
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Approximate Distribution and Moments |
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100 | (4) |
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104 | (3) |
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107 | (22) |
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107 | (5) |
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Heteroskedasticity Testing |
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112 | (1) |
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Model with Autocorrelation |
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113 | (3) |
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Seemingly Unrelated Regressions |
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116 | (4) |
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Limited Dependent Variable Models |
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120 | (3) |
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123 | (6) |
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Dynamic Time Series Model |
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129 | (24) |
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129 | (1) |
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Model and Least-Squares Estimator |
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129 | (4) |
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Finite Sample Results for Dynamic Model |
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133 | (18) |
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133 | (4) |
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Exact Results for AR(1) model |
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137 | (2) |
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139 | (6) |
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Probability Distributions |
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145 | (2) |
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147 | (1) |
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148 | (1) |
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149 | (2) |
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151 | (2) |
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Simultaneous Equations Model |
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153 | (26) |
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153 | (1) |
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Simultaneous Equations Model |
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154 | (17) |
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154 | (1) |
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Moments of the Single Equation Estimators |
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155 | (7) |
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Moments of the IV Estimators of β |
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162 | (1) |
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General Case of m Endogenous Variables |
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162 | (2) |
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164 | (1) |
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Nonlinear Simultaneous Equations Model |
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164 | (2) |
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Density Function of IV Estimator |
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166 | (2) |
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Further Finite Sample Results |
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168 | (2) |
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170 | (1) |
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Analysis of Weak Instruments |
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171 | (8) |
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Effects on the Moments and Distribution |
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171 | (4) |
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Issue of Optimal Instruments |
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175 | (4) |
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Appendix A Statistical Methods |
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179 | (20) |
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A.1 Moments and Cumulants |
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179 | (1) |
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A.2 Gram-Charlier and Edgeworth Series |
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180 | (2) |
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A.3 Asymptotic Expansion and Asymptotic Approximation |
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182 | (3) |
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A.3.1 Asymptotic Expansion (Stochastic) |
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184 | (1) |
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A.4 Moments of the Quadratic Forms Under Normality |
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185 | (2) |
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A.5 Moments of Quadratic Forms Under Nonnormality |
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187 | (1) |
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A.6 Moment of Quadratic Form of a Vector of Squared Nonnormal Random Variables |
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188 | (1) |
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A.7 Moments of Quadratic Forms in Random Matrices |
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189 | (3) |
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A.8 Distribution of Quadratic Forms |
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192 | (4) |
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A.8.1 Density and Moments of a Noncentral Chi-square Variable |
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193 | (1) |
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A.8.2 Moment Generating Function and Characteristic Function |
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194 | (1) |
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A.8.3 Density Function Based on Characteristic Function |
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195 | (1) |
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A.9 Hypergeometric Functions |
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196 | (1) |
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A.9.1 Asymptotic Expansion |
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197 | (1) |
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A.10 Order of Magnitudes (Small o and Large O) |
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197 | (2) |
References |
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199 | (28) |
Index |
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227 | |