Robust inference / M.L. Tiku, W.Y. Tan, N. Balakrishnan.

Format:

Book

Author/Creator:

Tiku, Moti Lal.

Contributor:

Tan, W. Y., 1934-

Balakrishnan, N., 1956-

Class of 1932 Fund.

Series:

Statistics, textbooks and monographs ; v. 71.

Statistics, textbooks and monographs ; vol. 71

Language:

English

Subjects (All):

Robust statistics.

Nonparametric statistics.

Estimation theory.

Physical Description:

ix, 321 pages ; 24 cm.

Place of Publication:

New York : M. Dekker, [1986]

Summary:

This authoritative new volume treats a wide class of distributions that constitute plausible alternatives to normality -- such as short- and long-tailed symmetric distributions and moderately skewed distributions -- all having finite mean and variance. Robust Inference illustrates the appropriateness of various robust methods for solving both one-sample and multisample statistical inference problems ... develops Laguerre series expansions for Student's t and variance-ratio F statistic distributions ... analyzes normal and nonnormal distribution efficiencies ... works out modified maximum likelihood (MML) estimators based on type II censored samples for log-normal, logistic, exponential, and Rayleigh distributions ... uses MML estimators in constructing robust hypothesis-testing procedures ... considers the specialized topics of regression, analysis of variance, classification, and sample survey ... discusses goodness-of-fit tests ... describes Q-Q plots in a special appendix ... and much more. An outstanding, time-saving reference for theoreticians and practitioners of statistics, Robust Inference is also an excellent auxiliary text for an undergraduate- or graduate-level course on robustness.

Contents:

1 Robustness of Some Classical Tests 1

1.2 Student's t test 2

1.3 Asymptotic robustness of the t test 2

1.4 Variance-ratio test for comparing several means 3

1.5 Asymptotic robustness of the variance-ratio test 4

1.6 Small-sample distributions of t and F under nonnormal distributions and robustness 5

1.7 Small-sample null distribution of F and type I robustness 5

1.8 Small-sample power of the t test and the F test 12

1.9 Testing equality of two variances 12

Appendix A Laguerre polynomial expansion of nonnegative random variables 18

2 Estimation Procedures for Censored Samples 21

2.2 Type II censoring 21

2.3 Truncated distributions and their cumulants 22

2.4 Estimation of parameters from type II censored samples 25

2.5 Least-squares estimators (BLUEs) 26

2.6 Maximum likelihood estimators (MLEs) 32

2.7 MMLEs for the normal 34

2.8 Robust estimators and comparisons with the MMLEs 50

2.9 Random choice of the proportion of censoring 62

2.10 Adaptive estimators of location 63

Appendix B Order statistics 66

3 MMLEs for Other Distributions 76

3.2 MMLE for log-normal distribution 76

3.3 MMLE for the logistic distribution 84

3.4 Estimation of parameters of exponential distribution 86

3.5 MML estimation of parameters for Rayleigh distribution 93

3.6 MML estimation in progressively censored samples 98

3.7 MML estimation for truncated distributions 102

4 Robust Tests 111

4.2 Robust Studentized one-sample tests 112

4.3 Testing equality of two location parameters when scale parameters are equal 120

4.4 Testing equality of location parameters of extreme skew distributions 130

4.5 Comparison of two location parameters when the scale parameters are unequal 134

4.6 Comparison of two variances 141

4.7 Sprott approach to robust tests 147

4.8 Robust confidence intervals 151

4.9 The Bayesian approach 153

5 Other Important Robust Procedures 159

5.2 Robust regression via MMLEs 159

5.3 General linear models based on type II censored samples 174

5.4 Testing data anomaly in linear models 178

5.5 Huber's robust regression procedure 180

5.6 Robust analysis of variances via MMLEs 182

5.7 Robust two-way classification 189

5.8 Efficiency of the MML estimator in sample survey 199

6 Goodness-of-Fit Tests 215

6.2 Model discrimination 215

6.3 Directional tests 219

6.4 Omnibus tests 235

7 Tests for Outliers 258

7.2 Testing outliers 259

7.3 Estimation of r[subscript 1] and r[subscript 2] 270

7.4 Testing the sample for outliers 273

7.5 Multisample generalization 275

Special Appendix C Graphical Display of Data 277.

Notes:

Includes index.

Bibliography: pages 284-313.

Local Notes:

Acquired for the Penn Libraries with assistance from the Class of 1932 Fund.

ISBN:

0824775325

OCLC:

13700697