Record:   Prev Next
作者 Tiku, Moti L
書名 Robust Estimation and Hypothesis Testing
出版項 Daryaganj : New Age International Ltd, 2004
©2004
國際標準書號 9788122425376 (electronic bk.)
9788122415568
book jacket
版本 1st ed
說明 1 online resource (354 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
附註 Cover -- Preface -- Contents -- Chapter 1 Robustness of Some Classical Estimators and Tests -- 1.1 Introduction -- 1.2 Robustness of Sample Mean and Variance -- 1.3 Asymptotic Robustness of the t Test -- 1.4 Comparing Several Means -- 1.5 Robustness of t and F for small Samples -- 1.6 Distribution of F Under Non-Normality -- 1.7 Distribution of the one-way Classification Variance Ratio -- 1.8 Non-Normal Power Function -- 1.9 Effect of Non-Normality on the t Statistic -- 1.10 Testing Equality of two Variances -- Appendix 1A -- Appendix 1B -- Appendix 1C -- Chapter 2 Estimation of Location and Scale Parameters -- 2.1 Introduction -- 2.2 Maximum Likelihood -- 2.3 Modifield Likelihood -- 2.4 Estimating Location and Scale -- 2.5 Generalized Logistic -- 2.6 Extreme Value Distribution -- 2.7 Best Linear Unbiased Estimators -- 2.8 Numerical Examples -- 2.9 Asymptotic Distributions of the MML Estimators -- 2.10 Hypothesis Testing -- 2.11 Huber M-Estimators -- Appendix 2A : Asymptotic Equivalence -- Appendix 2B : Numerical Comparison -- Appendix 2C : Asymptotic Distributions -- Appendix 2D : The PSI-function -- Appendix 2E : Estimators Based on Censored Samples -- Chapter 3 Linear Regression with Normal and Non-normal Error Distributions -- 3.1 Introduction -- 3.2 Linear Regression -- 3.3 The Weibull Distribution -- 3.4 Modified Likelihood -- 3.5 Least Squares for the Weibull -- 3.6 Short-Tailed Symmetric Family -- 3.7 MML estimators for short-tailed family -- 3.8 Le estimators for Short-tailed family -- 3.9 Long-tailed symmetric family -- 3.10 General Linear model -- 3.11 Stochastic Linear Regression -- 3.12 MML estimators for the bivariate distribution -- 3.13 Hypothesis testing -- 3.14 Numerical examples -- Appendix 3A: Information matrix -- Appendix 3B: Value of E(Z) -- Chapter 4 Binary Regression with Logistic and Nonlogistic Density Functions
4.1 Introduction -- 4.2 Link Functions -- 4.3 Modified Likelihood estimators -- 4.4 Variances and Covariances -- 4.5 Hypothesis Testing -- 4.6 Logistic Density -- 4.7 Comparison of the ML and MML estimates -- 4.8 Non Logistic Density Functions -- 4.9 Quadratic Model -- 4.10 Multiple Covariates -- 4.11 Stochastic Covariates -- 4.12 Modified Likelihood -- 4.13 The MML estimators -- 4.14 Asymptotic Properties -- 4.15 Symmetric family -- Appendix 4A : Density and Cumulative Density functions -- Appendix 4B -- Appendix 4C -- Appendix 4D: Elements of the information matrix -- Chapter 5 Autoregressive Models in Normal and Non-Normal Situations -- 5.1 Introduction -- 5.2 A Simple Autoregressive Model -- 5.3 Gamma Distribution -- 5.4 Modified Likelihood -- 5.5 Asymptotic Covariance Matrix -- 5.6 Least Squares -- 5.7 Hypothesis Testing for Gamma -- 5.8 Short-tailed Symmetric Distributions -- 5.9 Asymptotic Covariance Matrix -- 5.10 Hypothesis testing for STS Distributions -- 5.11 Long-tailed Symmetric Distributions -- 5.12 Hypothesis testing for LTS Distubutions -- 5.13 Time Series Model -- 5.14 Asymptotic Properties -- 5.15 Unit root Problem -- 5.16 Unknown Location -- 5.17 Generalization to AR(q) Models -- Appendix : Expected value and Variance of Yt -- Chapter 6 Analysis of Variance in Experimental Design -- 6.1 Introduction -- 6.2 One-Way Classification -- 6.3 Generalized Logistic -- 6.4 Modified Likelihood -- 6.5 Testing Block Effects -- 6.6 The Weibull Family -- 6.7 Two-Way Classification and Interaction -- 6.8 Effects Under Non-Normality -- 6.9 Variance Ratio Statistics -- 6.10 Box-Cox Data -- 6.11 Linear Contrasts -- 6.12 Non-Normal Distributions -- 6.13 Non-Identical Error Distributions -- 6.14 Linear Contrast with Non-Identical Distributions -- 6.15 Normal Theory Test With Non-Identical Blocks
Chapter 7 Censored Samples from Normal and Non-Normal Distributions -- 7.1 Introduction -- 7.2 Estimation of Parameters -- 7.3 Censored Samples from Normal Distribution -- 7.4 Symmetric Censoring -- 7.5 Censored Samples in Experimental Design -- 7.6 Inliers in Normal Samples -- 7.7 Rayleigh Distribution -- 7. 8 Censored Samples From LTS Distributions -- 7.9 Variances and Covariances -- 7.10 Hypothesis Testing -- 7.11 Type I Censoring -- 7.12 Progressively Censored Samples -- 7.13 Truncated Normal Distribution -- 7.14 Experimental Design With Truncated Normal -- Appendix 7A Exponential Sample Spacings -- Appendix 7B -- Appendix 7C The Coefficients for Censored Normal Samples -- Chapter 8 Robustness of Estimators and Tests -- 8.1 Introduction -- 8.2 Robust Estimators of Location and Scale -- 8.3 Comparison for Skew Distributions -- 8.4 Comparison With Tukey and Tiku Estimators -- 8.5 Hypothesis Testing -- 8.6 Robustness for STS Distributions -- 8.7 Robustness of Regression Estimators -- 8.8 Robustness of Estimators in Binary Regression -- 8.9 Robustness of Autoregression Estimators -- 8.10 Robustness in Experimental Design -- Appendix 8A Simulated Means, Variances and Efficiencies -- Chapter 9 Goodness-of-fit and Detection of Outliers -- 9.1 Introduction -- 9.2 Q-Q Plots -- 9.3 Goodness of Fit Tests -- 9.4 Directional Test for Any Distribution -- 9.5 Omnibus Tests -- 9.6 Shapiro-Wilk Test -- 9.7 Filliben and Smith-Bain Statistic -- 9.8 Tiku Statistics Based on Spacings -- 9.9 Extension to Non-Exponential Distributions -- 9.10 The Omnibus U and U* Tests -- 9.11 Extreme Value Distribution -- 9.12 Multisample Situations -- 9.13 Sample Entropy Statistics -- 9.14 Censored Samples -- 9.15 Outlier Detection -- 9.16 Testing for Outliers -- 9.17 Tiku Approach to Outlier Detection -- 9.18 Power of the Outlier Tests -- 9.19 Testing the Sample for Outliers
Appendix 9A -- Appendix 9B -- Chapter 10 Estimation in Sample Survey -- 10.1 Introduction -- 10.2. Super-Population Model -- 10.3 Symmetric Family -- 10.4 Finite Population Model -- 10.5 Sample Size Determination -- 10.6 Stratified Sampling -- 10.7 Skew Distributions in Sample Survey -- 10.8 Estimating the Mean -- Appendix 10 A -- Chapter 11 Applications -- 11.1 Introduction -- 11.2 Estimators of Location and Scale Parameters -- 11.3 Determination of Shape Parameters -- 11.4 Estimation in Linear Regression Models -- 11.5. Multiple Linear Regression -- 11.6 Autoregression -- 11.7 Experimental Design -- Appendix 11A MMLE for the Beta Distribution -- Appendix 11B -- Appendix 11C -- Bibliography -- Index
In statistical theory and practice, a certain distribution is usually assumed and then optimal solutions sought. Since deviations from an assumed distribution are very common, one cannot feel comfortable with assuming a particular distribution and believing it to be exactly correct. That brings the robustness issue in focus. In this book, we have given statistical procedures which are robust to plausible deviations from an assumed mode. The method of modified maximum likelihood estimation is used in formulating these procedures. The modified maximum likelihood estimators are explicit functions of sample observations and are easy to compute. They are asymptotically fully efficient and are as efficient as the maximum likelihood estimators for small sample sizes. The maximum likelihood estimators have computational problems and are, therefore, elusive. A broad range of topics are covered in this book. Solutions are given which are easy to implement and are efficient. The solutions are also robust to data anomalies: outliers, inliers, mixtures and data contaminations. Numerous real life applications of the methodology are given
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Tiku, Moti L. Robust Estimation and Hypothesis Testing Daryaganj : New Age International Ltd,c2004 9788122415568
主題 Robust statistics.;Nonparametric statistics.;Estimation theory
Electronic books
Alt Author Akkaya, Aysen D
Record:   Prev Next