Robust estimation and hypothesis testing

Cover
......Page 1
Preface
......Page 8
Contents
......Page 12
1.2 Robustness of Sample Mean and Variance
......Page 18
1.4 Comparing Several Means
......Page 21
1.5 Robustness of t and F for small Samples
......Page 22
1.6 Distribution of F Under Non-Normality
......Page 23
1.7 Distribution of the one-way Classification Variance Ratio......Page 24
1.8 Non-Normal Power Function......Page 29
1.9 Effect of Non-Normality on the t Statistic......Page 30
1.10 Testing Equality of two Variances......Page 32
Appendix 1A......Page 35
Appendix 1B......Page 36
Appendix 1C......Page 38
2.2 Maximum Likelihood......Page 39
2.3 Modifield Likelihood......Page 42
2.4  Estimating Location and Scale......Page 45
2.5 Generalized Logistic......Page 48
2.6 Extreme Value Distribution......Page 50
2.7 Best Linear Unbiased Estimators......Page 52
2.8 Numerical Examples......Page 54
2.9 Asymptotic Distributions of the MML Estimators......Page 57
2.10 Hypothesis Testing......Page 60
2.11 Huber M-Estimators......Page 62
Appendix 2A : Asymptotic Equivalence......Page 67
Appendix 2B : Numerical Comparison......Page 68
Appendix 2D : The PSI-function......Page 70
Appendix 2E : Estimators Based on Censored Samples......Page 71
3.2 Linear Regression......Page 73
3.3 The Weibull Distribution
......Page 76
3.4 Modified Likelihood......Page 77
3.5 Least Squares for the Weibull......Page 80
3.6 Short-Tailed Symmetric Family
......Page 83
3.7 MML estimators for short-tailed family......Page 85
3.8 Le estimators for Short-tailed family
......Page 87
3.9 Long-tailed symmetric family......Page 88
3.10 General Linear model......Page 91
3.11 Stochastic Linear Regression......Page 92
3.12 MML estimators for the bivariate distribution
......Page 94
3.13 Hypothesis testing
......Page 96
3.14 Numerical examples
......Page 99
Appendix 3A: Information matrix
......Page 101
Appendix 3B: Value of E(Z)
......Page 102
4.2 Link Functions......Page 104
4.3 Modified Likelihood estimators......Page 106
4.4 Variances and Covariances......Page 107
4.5 Hypothesis Testing......Page 108
4.7 Comparison of the ML and MML estimates......Page 109
4.8 Non Logistic Density Functions......Page 110
4.9 Quadratic Model......Page 112
4.10 Multiple Covariates......Page 114
4.11 Stochastic Covariates......Page 116
4.12 Modified Likelihood......Page 117
4.13 The MML estimators......Page 118
4.14 Asymptotic Properties
......Page 119
4.15 Symmetric family......Page 120
Appendix 4A : Density and Cumulative Density functions
......Page 122
Appendix 4C......Page 123
Appendix 4D: Elements of the information matrix
......Page 124
5.1 Introduction......Page 125
5.3 Gamma Distribution......Page 126
5.4 Modified Likelihood......Page 127
5.5 Asymptotic Covariance Matrix......Page 129
5.6 Least Squares......Page 130
5.7 Hypothesis Testing for Gamma......Page 131
5.8 Short-tailed Symmetric Distributions
......Page 133
5.9 Asymptotic Covariance Matrix......Page 134
5.10 Hypothesis testing for STS Distributions......Page 135
5.11 Long-tailed Symmetric Distributions
......Page 137
5.12 Hypothesis testing for LTS Distubutions......Page 140
5.13 Time Series Model......Page 141
5.14 Asymptotic Properties......Page 142
5.15 Unit root Problem......Page 145
5.16 Unknown Location......Page 147
5.17 Generalization to AR(q) Models......Page 149
Appendix : Expected value and Variance of Yt......Page 150
6.2 One-Way Classification......Page 151
6.3 Generalized Logistic......Page 153
6.4 Modified Likelihood......Page 154
6.5 Testing Block Effects
......Page 156
6.6 The Weibull Family......Page 157
6.7 Two-Way Classification and Interaction......Page 158
6.8 Effects Under Non-Normality......Page 159
6.9 Variance Ratio Statistics......Page 160
6.10 Box-Cox Data......Page 161
6.11 Linear Contrasts......Page 163
6.12 Non-Normal Distributions......Page 165
6.13 Non-Identical Error Distributions......Page 166
6.14 Linear Contrast with Non-Identical Distributions......Page 167
6.15 Normal Theory Test With Non-Identical Blocks
......Page 169
7.2 Estimation of Parameters
......Page 172
7.3 Censored Samples from Normal Distribution
......Page 176
7.4 Symmetric Censoring
......Page 179
7.5 Censored Samples in Experimental Design
......Page 184
7.6 Inliers in Normal Samples
......Page 186
7.7 Rayleigh Distribution
......Page 190
7. 8 Censored Samples From LTS Distributions
......Page 193
7.9 Variances and Covariances
......Page 196
7.10 Hypothesis Testing
......Page 198
7.11 Type I Censoring
......Page 199
7.12 Progressively Censored Samples
......Page 201
7.13 Truncated Normal Distribution
......Page 203
7.14 Experimental Design With Truncated Normal
......Page 206
Appendix 7A Exponential Sample Spacings
......Page 209
Appendix 7B
......Page 210
Appendix 7C The Coefficients for Censored Normal Samples
......Page 211
8.2 Robust Estimators of Location and Scale
......Page 212
8.3 Comparison for Skew Distributions
......Page 216
8.5 Hypothesis Testing
......Page 217
8.6 Robustness for STS Distributions
......Page 219
8.7 Robustness of Regression Estimators
......Page 221
8.8 Robustness of Estimators in Binary Regression
......Page 226
8.9 Robustness of Autoregression Estimators
......Page 229
8.10 Robustness in Experimental Design
......Page 234
Appendix 8A Simulated Means, Variances and Efficiencies
......Page 237
9.2 Q-Q Plots
......Page 242
9.3 Goodness of Fit Tests
......Page 246
9.4 Directional Test for Any Distribution
......Page 249
9.5 Omnibus Tests
......Page 255
9.6 Shapiro-Wilk Test
......Page 257
9.8 Tiku Statistics Based on Spacings
......Page 258
9.9 Extension to Non-Exponential Distributions
......Page 260
9.10 The Omnibus U and U* Tests
......Page 262
9.11 Extreme Value Distribution
......Page 264
9.12 Multisample Situations
......Page 265
9.14 Censored Samples
......Page 267
9.15 Outlier Detection
......Page 269
9.16 Testing for Outliers
......Page 270
9.17 Tiku Approach to 
Outlier Detection......Page 272
9.18 Power of the Outlier Tests
......Page 275
9.19 Testing the Sample for Outliers
......Page 278
Appendix 9A
......Page 281
Appendix 9B
......Page 282
10.2. Super-Population Model
......Page 283
10.3 Symmetric Family
......Page 284
10.4 Finite Population Model
......Page 286
10.5 Sample Size Determination
......Page 288
10.6 Stratified Sampling
......Page 289
10.7 Skew Distributions in Sample Survey
......Page 290
10.8 Estimating the Mean 
......Page 295
Appendix 10 A
......Page 297
11.2 Estimators of Location and Scale Parameters
......Page 298
11.3 Determination of Shape Parameters
......Page 305
11.4 Estimation in Linear Regression Models
......Page 306
11.5. Multiple Linear Regression
......Page 311
11.6 Autoregression
......Page 314
11.7 Experimental Design
......Page 316
Appendix 11A MMLE for the Beta Distribution
......Page 320
Appendix 11B
......Page 322
Appendix 11C
......Page 323
Bibliography
......Page 325
Index
......Page 348