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E-raamat: Nonparametric Statistical Inference

  • Formaat: 694 pages
  • Ilmumisaeg: 21-Dec-2020
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351616164
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  • Formaat: 694 pages
  • Ilmumisaeg: 21-Dec-2020
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351616164

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Praise for previous editions:

"… a classic with a long history."

Statistical Papers

"The fact that the first edition of this book was published in 1971 … [ is] testimony to the book’s success over a long period."

ISI Short Book Reviews

"… one of the best books available for a theory course on nonparametric statistics. … very well written and organized … recommended for teachers and graduate students."

Biometrics

"… There is no competitor for this book and its comprehensive development and application of nonparametric methods. Users of one of the earlier editions should certainly consider upgrading to this new edition."Technometrics

"… Useful to students and research workers … a good textbook for a beginning graduate-level course in nonparametric statistics."

Journal of the American Statistical Association

Since its first publication in 1971, Nonparametric Statistical Inference has been widely regarded as the source for learning about nonparametrics. The Sixth Edition carries on this tradition and incorporates computer solutions based on R.

Features

  • Covers the most commonly used nonparametric procedures
  • States the assumptions, develops the theory behind the procedures, and illustrates the techniques using realistic examples from the social, behavioral, and life sciences
  • Presents tests of hypotheses, confidence-interval estimation, sample size determination, power, and comparisons of competing procedures
  • Includes an Appendix of user-friendly tables needed for solutions to all data-oriented examples
  • Gives examples of computer applications based on R, MINITAB, STATXACT, and SAS
    • Lists over 100 new references
  • Nonparametric Statistical Inference, Sixth Edition

    ,

    has been thoroughly revised and rewritten to make it more readable and reader-friendly. All of the R solutions are new and make this book much more useful for applications in modern times. It has been updated throughout and contains 100 new citations, including some of the most recent, to make it more current and useful for researchers.

    Arvustused

    a classic with a long history. Statistical Papers

    The fact that the first edition of this book was published in 1971 [ is]ntestimony to the books success over a long period. ISI Short Book Reviews

    one of the best books available for a theory course on nonparametric statistics. very well written and organized recommended for teachers and graduate students. Biometrics

    There is no competitor for this book and its comprehensive development and application of nonparametric methods. Users of one of the earlier editions should certainly consider upgrading to this new edition. Technometrics

    Useful to students and research workers a good textbook for a beginning graduate-level course in nonparametric statistics. Journal of the American Statistical Association

    Preface to the Sixth Edition xv
    Author Biographies xix
    1 Introduction and Fundamentals 1(28)
    1.1 Introduction
    1(6)
    1.2 Fundamental Statistical Concepts
    7(20)
    1.2.1 Basic Definitions
    8(2)
    1.2.2 Moments of Linear Combinations of Random Variables
    10(1)
    1.2.3 Probability Functions
    10(4)
    1.2.4 Distributions of Functions of Random Variables Using the Method of Jacobians
    14(1)
    1.2.5 Chebyshev's Inequality
    15(1)
    1.2.6 Central Limit Theorem
    15(1)
    1.2.7 Point and Interval Estimation
    16(1)
    1.2.8 Hypothesis Testing
    17(3)
    1.2.9 P Value
    20(1)
    1.2.10 Consistency
    21(1)
    1.2.11 Pitman Efficiency
    22(2)
    1.2.12 Randomized Tests
    24(1)
    1.2.13 Continuity Correction
    25(2)
    1.3 Computers and Nonparametrics
    27(2)
    2 Order Statistics, Quantiles, and Coverages 29(52)
    2.1 Introduction
    29(1)
    2.2 Quantile Function
    30(3)
    2.3 Empirical Distribution Function
    33(4)
    2.3.1 Empirical Quantile Function
    36(1)
    2.4 Statistical Properties of Order Statistics
    37(2)
    2.4.1 Cumulative Distribution Function of X(r)
    37(1)
    2.4.2 Probability Density Function of X(r)
    37(2)
    2.5 Probability Integral Transformation
    39(2)
    2.6 Joint Distribution of Order Statistics
    41(6)
    2.7 Distributions of the Median and Range
    47(4)
    2.7.1 Distribution of the Median
    47(2)
    2.7.2 Distribution of the Range
    49(2)
    2.8 Exact Moments of Order Statistics
    51(5)
    2.8.1 kth Moment about the Origin
    51(1)
    2.8.2 Covariance between X(r) and X(s)
    52(4)
    2.9 Large-Sample Approximations to the Moments of Order Statistics
    56(3)
    2.10 Asymptotic Distribution of Order Statistics
    59(4)
    2.11 Tolerance Intervals, Prediction Intervals, and Coverages
    63(9)
    2.11.1 Tolerance Intervals
    63(3)
    2.11.2 Prediction Intervals
    66(3)
    2.11.3 One-Sample Coverages
    69(1)
    2.11.4 Two-Sample Coverages
    70(1)
    2.11.5 Ranks, Block Frequencies, and Placements
    71(1)
    2.12 Summary
    72(1)
    Problems
    72(9)
    3 Tests of Randomness 81(26)
    3.1 Introduction
    81(1)
    3.2 Tests Based on the Total Number of Runs
    82(9)
    3.2.1 Exact Null Distribution of R
    82(3)
    3.2.2 Moments of the Null Distribution of R
    85(3)
    3.2.3 Asymptotic Null Distribution
    88(1)
    3.2.4 Discussion
    89(1)
    3.2.5 Applications
    89(2)
    3.3 Tests Based on the Length of the Longest Run
    91(3)
    3.4 Runs Up and Down
    94(6)
    3.4.1 Applications
    98(2)
    3.5 A Test Based on Ranks
    100(2)
    3.6 Summary
    102(1)
    Problems
    103(4)
    4 Tests of Goodness of Fit 107(60)
    4.1 Introduction
    107(1)
    4.2 The Chi-Square Goodness-of-Fit Test
    108(9)
    4.3 The Kolmogorov-Smirnov (K-S) One-Sample Statistic
    117(8)
    4.4 Applications of the Kolmogorov-Smirnov (K-S) One-Sample Statistics
    125(10)
    4.4.1 One-Sided Tests
    131(2)
    4.4.2 Confidence Bands
    133(1)
    4.4.3 Determination of Sample Size
    134(1)
    4.5 Lilliefors's Test for Normality
    135(5)
    4.6 Lilliefors's Test for the Exponential Distribution
    140(4)
    4.7 Anderson-Darling (A-D) Test
    144(8)
    4.8 Visual Analysis of Goodness of Fit
    152(4)
    4.9 Summary
    156(3)
    Problems
    159(8)
    5 One-Sample and Paired-Sample Procedures 167(80)
    5.1 Introduction
    167(1)
    5.2 Confidence Interval for a Population Quantile
    168(6)
    5.3 Hypothesis Testing for a Population Quantile
    174(5)
    5.4 The Sign Test and Confidence Interval for the Median
    179(24)
    5.4.1 P Value
    181(1)
    5.4.2 Normal Approximations
    181(1)
    5.4.3 Zero Differences
    182(1)
    5.4.4 Power Function
    182(4)
    5.4.5 Simulated Power
    186(3)
    5.4.6 Sample Size Determination
    189(3)
    5.4.7 Confidence Interval for the Median
    192(1)
    5.4.8 Problem of Zeros
    193(1)
    5.4.9 Paired-Sample Procedures
    193(1)
    5.4.10 Applications
    194(9)
    5.5 Rank Order Statistics
    203(4)
    5.6 Treatment of Ties in Rank Tests
    207(2)
    5.6.1 Randomization
    207(1)
    5.6.2 Midranks
    208(1)
    5.6.3 Average Statistic
    208(1)
    5.6.4 Average Probability
    208(1)
    5.6.5 Least Favorable Statistic
    208(1)
    5.6.6 Range of Probability
    208(1)
    5.6.7 Omission of Tied Observations
    209(1)
    5.7 The Wilcoxon Signed-Rank Test and Confidence Interval
    209(25)
    5.7.1 The Problem of Zero and Tied Differences
    216(1)
    5.7.2 Power Function
    217(1)
    5.7.3 Simulated Power
    218(1)
    5.7.4 Sample Size Determination
    219(2)
    5.7.5 Confidence Interval Procedures
    221(4)
    5.7.6 Paired-Sample Procedures
    225(1)
    5.7.7 Use of Wilcoxon Statistics to Test for Symmetry
    225(1)
    5.7.8 Applications
    226(8)
    5.8 Summary
    234(2)
    Problems
    236(8)
    Appendix 5.A
    244(3)
    6 The General Two-Sample Problem 247(54)
    6.1 Introduction
    247(5)
    6.2 The Wald-Wolfowitz Runs Test
    252(5)
    6.2.1 The Problem of Ties
    256(1)
    6.2.2 Discussion
    256(1)
    6.3 The Kolmogorov-Smirnov (K-S) Two-Sample Test
    257(7)
    6.3.1 One-Sided Alternatives
    261(1)
    6.3.2 Ties
    262(1)
    6.3.3 Discussion
    262(1)
    6.3.4 Applications
    263(1)
    6.4 The Median Test
    264(15)
    6.4.1 Applications
    271(3)
    6.4.2 Confidence Interval Procedure
    274(3)
    6.4.3 Power of the Median Test
    277(2)
    6.5 The Control Median Test
    279(5)
    6.5.1 Curtailed Sampling
    281(1)
    6.5.2 Power of the Control Median Test
    282(1)
    6.5.3 Discussion
    282(1)
    6.5.4 Applications
    283(1)
    6.6 The Mann-Whitney U Test and Confidence Interval
    284(12)
    6.6.1 The Problem of Ties
    290(1)
    6.6.2 Confidence Interval Procedure
    291(2)
    6.6.3 Sample Size Determination
    293(2)
    6.6.4 Discussion
    295(1)
    6.7 Summary
    296(1)
    Problems
    297(4)
    7 Linear Rank Statistics and the General Two-Sample Problem 301(14)
    7.1 Introduction
    301(1)
    7.2 Definition of Linear Rank Statistics
    301(2)
    7.3 Distribution Properties of Linear Rank Statistics
    303(9)
    7.4 Usefulness in Inference
    312(1)
    Problems
    313(2)
    8 Linear Rank Tests for the Location Problem 315(24)
    8.1 Introduction
    315(1)
    8.2 The Wilcoxon Rank-Sum Test and Confidence Interval
    316(11)
    8.2.1 Applications
    319(8)
    8.3 Other Location Tests
    327(6)
    8.3.1 Terry-Hoeffding (Normal Scores) Test
    327(1)
    8.3.2 van der Waerden Test
    328(4)
    8.3.3 Percentile-Modified Rank Tests
    332(1)
    8.4 Summary
    333(1)
    Problems
    334(5)
    9 Linear Rank Tests for the Scale Problem 339(34)
    9.1 Introduction
    339(3)
    9.2 The Mood Test
    342(3)
    9.3 The Freund-Ansari-Bradley-David-Barton Tests
    345(3)
    9.4 The Siegel-Tukey Test
    348(2)
    9.5 The Klotz Normal-Scores Test
    350(1)
    9.6 The Percentile-Modified Rank Tests for Scale
    351(1)
    9.7 The Sukhatme Test
    351(4)
    9.8 Confidence Interval Procedures
    355(1)
    9.9 Other Tests for the Scale Problem
    356(3)
    9.10 Applications
    359(8)
    9.11 Summary
    367(2)
    Problems
    369(4)
    10 Tests of the Equality of k Distributions 373(46)
    10.1 Introduction
    373(1)
    10.2 Extension of the Median Test
    374(7)
    10.3 Extension of the Control Median Test
    381(3)
    10.4 The Kruskal-Wallis One-Way ANOVA Test and Multiple Comparisons
    384(10)
    10.4.1 Applications
    388(6)
    10.5 Other Rank Test Statistics
    394(3)
    10.6 Tests against Ordered Alternatives
    397(8)
    10.6.1 Applications
    401(4)
    10.7 Comparisons with a Control
    405(6)
    10.7.1 Case I: θ1 Known
    406(2)
    10.7.2 Case II: θ1 Unknown
    408(2)
    10.7.3 Applications
    410(1)
    10.8 Summary
    411(1)
    Problems
    412(7)
    11 Measures of Association for Bivariate Samples 419(52)
    11.1 Introduction: Definition of Measures of Association in a Bivariate Population
    419(4)
    11.2 Kendall's Tau Coefficient
    423(18)
    11.2.1 Null Distribution of T
    430(3)
    11.2.2 The Large-Sample Nonnull Distribution of Kendall's Statistic
    433(4)
    11.2.3 Tied Observations
    437(2)
    11.2.4 A Related Measure of Association for Discrete Populations
    439(1)
    11.2.5 Use of Kendall's Statistic to Test against Trend
    440(1)
    11.3 Spearman's Coefficient of Rank Correlation
    441(9)
    11.3.1 Exact Null Distribution of R
    444(3)
    11.3.2 Asymptotic Null Distribution of R
    447(1)
    11.3.3 Testing the Null Hypothesis
    447(1)
    11.3.4 Tied Observations
    448(2)
    11.3.5 Use of Spearman's R to Test against Trend
    450(1)
    11.4 The Relations between R and T; E(R), &taj;, and ρ
    450(6)
    11.5 Another Measure of Association
    456(1)
    11.6 Applications
    457(5)
    11.7 Summary
    462(2)
    Problems
    464(7)
    12 Measures of Association in Multiple Classifications 471(44)
    12.1 Introduction
    471(2)
    12.2 Friedman's Two-Way Analysis of Variance by Ranks in a kxn Table and Multiple Comparisons
    473(10)
    12.2.1 Applications
    478(5)
    12.3 Page's Test for Ordered Alternatives
    483(4)
    12.4 The Coefficient of Concordance for k Sets of Rankings of n Objects
    487(9)
    12.4.1 Relationship between W and Rank Correlation
    489(1)
    12.4.2 Tests of Significance Based on W
    490(2)
    12.4.3 Estimation of the True Preferential Order of Objects
    492(1)
    12.4.4 Tied Observations
    493(1)
    12.4.5 Applications
    493(3)
    12.5 The Coefficient of Concordance for k Sets of Incomplete Rankings
    496(6)
    12.5.1 Tests of Significance Based on W
    499(2)
    12.5.2 Tied Observations
    501(1)
    12.5.3 Applications
    501(1)
    12.6 Kendall's Tau Coefficient for Partial Correlation
    502(4)
    12.6.1 Applications
    505(1)
    12.7 Summary
    506(1)
    Problems
    507(8)
    13 Asymptotic Relative Efficiency 515(26)
    13.1 Introduction
    515(3)
    13.2 Theoretical Bases for Calculating the ARE
    518(5)
    13.3 Examples of the Calculation of Efficacy and ARE
    523(15)
    13.3.1 One-Sample and Paired-Sample Problems
    523(6)
    13.3.2 Two-Sample Location Problems
    529(5)
    13.3.3 Two-Sample Scale Problems
    534(4)
    13.4 Summary
    538(1)
    Problems
    539(2)
    14 Analysis of Count Data 541(34)
    14.1 Introduction
    541(1)
    14.2 Contingency Tables
    541(8)
    14.2.1 Contingency Coefficient
    546(3)
    14.3 Some Special Results for 2xk Contingency Tables
    549(4)
    14.4 Fisher's Exact Test
    553(5)
    14.5 McNemar's Test
    558(7)
    14.6 Analysis of Multinomial Data
    565(4)
    14.6.1 Ordered Categories
    567(2)
    14.7 Summary
    569(1)
    Problems
    569(6)
    15 Summary 575(6)
    15.1 Outline
    575(2)
    15.2 Self-Test
    577(4)
    Appendix of Tables 581(58)
    Table A Normal Distribution
    582(1)
    Table B Chi-Square Distribution
    583(1)
    Table C Cumulative Binomial Distribution
    584(13)
    Table D Total Number of Runs Distribution
    597(5)
    Table E Runs Up and Down Distribution
    602(3)
    Table F Kolmogorov-Smirnov One-Sample Statistic
    605(1)
    Table G Binomial Distribution for θ = 0.5
    606(1)
    Table H Probabilities for the Wilcoxon Signed-Rank Statistic
    607(4)
    Table I Kolmogorov-Smirnov Two-Sample Statistic
    611(3)
    Table J Probabilities for the Wilcoxon Rank Sum Statistic
    614(8)
    Table K Kruskal-Wallis Test Statistic
    622(1)
    Table L Kendall's Tau Statistic
    623(2)
    Table M Spearman's Coefficient of Rank Correlation
    625(3)
    Table N Friedman's Analysis-of-Variance Statistic and Kendall's Coefficient of Concordance
    628(1)
    Table O Lilliefors's Test for Normal Distribution Critical Values
    629(1)
    Table P Significance Points of Txy, for Kendall's Partial Rank Correlation Coefficient
    630(1)
    Table Q Page's L Statistic
    631(1)
    Table R Critical Values and Associated Probabilities for the Jonckheere-Terpstra Test
    632(3)
    Table S Rank von Neumann Statistic
    635(3)
    Table T Lilliefors's Test for Exponential Distribution Critical Values
    638(1)
    Answers to Selected Problems 639(8)
    References 647(18)
    Index 665
    Jean Dickinson Gibbons is Russell Professor Emerita of Applied Statistics at the University of Alabama, where she also served as Chair for 20 years. She is a life member of the American Statistical Association, serving three terms on their Board of Directors; she was elected a Fellow in 1972. She earned the B.A. (1958) and M.A. (1959) in mathematics from Duke University and the Ph.D. (1962) in statistics from Virginia Tech, which recently named their graduate program after her. In addition to Alabama, she taught at the Wharton School of the University of Pennsylvania, the University of Cincinnati and Mercer University and offered short courses for the U.S. Army, the Naval Postgraduate School and the American Statistical Association. She currently lives in Vero Beach, Florida, where she is a peer leader in the Fielden Institute for Lifelong Learning at Indian River State College.

    Subhabrata Chakraborti is Professor of Statistics and Morrow Faculty Fellow at the University of Alabama. He is a Fellow of the American Statistical Association and an Elected Member of the International Statistical Institute. In 2019, he received the Burnum Distinguished Faculty Award and the SEC Professor of the Year Award at the University of Alabama. Professor Chakraborti has authored or co-authored over one hundred publications. He is the co-author of Nonparametric Statistical Process Control (2019) published by John Wiley. His research interests include applications of statistical methods, including nonparametric methods in industrial statistics and allied areas. Professor Chakraborti has been a Fulbright Scholar and a visiting professor in several countries including South Africa, India and Brazil; he is recognized for his work with students and scholars from around the world. He serves as an Associate Editor of Communications in Statistics and Quality Engineering.