Exact Statistical Methods for Data Analysis

Exact Statistical Methods for Data Analysis by Samaradasa Weerahandi.

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Bibliographic Details
Main Author: Weerahandi, Samaradasa (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1995.
Edition:1st ed. 1995.
Series:Springer Series in Statistics,
Springer eBook Collection.
Subjects:
Statistics .
Probabilities.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1 Preliminary Notions
  • 1.1 Introduction
  • 1.2 Sufficiency
  • 1.3 Complete Sufficient Statistics
  • 1.4 Exponential Families of Distributions
  • 1.5 Invariance
  • 1.6 Maximum Likelihood Estimation
  • 1.7 Unbiased Estimation
  • 1.8 Least Squares Estimation
  • 1.9 Interval Estimation
  • Exercises
  • 2 Notions in significance testing of hypotheses
  • 2.1 Introduction
  • 2.2 Test Statistics and Test Variables
  • 2.3 Definition of p-Value
  • 2.4 Generalized Likelihood Ratio Method
  • 2.5 Invariance in Significance Testing
  • 2.6 Unbiasedness and Similarity
  • 2.7 Interval Estimation and Fixed-Level Testing
  • Exercises
  • 3 Review of Special Distributions
  • 3.1 Poisson and Binomial Distributions
  • 3.2 Point Estimation and Interval Estimation
  • 3.3 Significance Testing of Parameters
  • 3.4 Bayesian Inference
  • 3.5 The Normal Distribution
  • 3.6 Inferences About the Mean
  • 3.7 Inferences About the Variance
  • 3.8 Quantiles of a Normal Distribution
  • 3.9 Conjugate Prior and Posterior Distributions
  • 3.10 Bayesian Inference About the Mean and the Variance
  • Exercises
  • 4 Exact Nonparametric Methods
  • 4.1 Introduction
  • 4.2 The Sign Test
  • 4.3 The Signed Rank Test and the Permutation Test
  • 4.4 The Rank Sum Test and Allied Tests
  • 4.5 Comparing k Populations
  • 4.6 Contingency Tables
  • 4.7 Testing the Independence of Criteria of Classification
  • 4.8 Testing the Homogeneity of Populations
  • Exercises
  • 5 Generalized p-Values
  • 5.1 Introduction
  • 5.2 Generalized Test Variables
  • 5.3 Definition of Generalized p-Values
  • 5.4 Frequency Interpretations and Generalized Fixed-Level Tests
  • 5.5 Invariance
  • 5.6 Comparing the Means of Two Exponential Distributions
  • 5.7 Unbiasedness and Similarity
  • 5.7 Comparing the Means of an Exponential Distribution and a Normal Distribution
  • Exercises
  • 6 Generalized Confidence Intervals
  • 6.1 Introduction
  • 6.2 Generalized Definitions
  • 6.3 Frequency Interpretations and Repeated Sampling Properties
  • 6.4 Invariance in Interval Estimation
  • 6.5 Interval Estimation of the Difference Between Two Exponential Means
  • 6.6 Similarity in Interval Estimation
  • 6.7 Generalized Confidence Intervals Based on p-Values
  • 6.8 Resolving an Undesirable Feature of Confidence Intervals
  • 6.9 Bayesian and Conditional Confidence Intervals
  • Exercises
  • 7 Comparing Two Normal Populations
  • 7.1 Introduction
  • 7.2 Comparing the Means when the Variances are Equal
  • 7.3 Solving the Behrens-Fisher Problem
  • 7.4 Inferences About the Ratio of Two Variances
  • 7.5 Inferences About the Difference in Two Variances
  • 7.6 Bayesian Inference
  • 7.7 Inferences About the Reliability Parameter
  • 7.8 The Case of Known Stress Distribution
  • Exercises
  • 8 Analysis of Variance
  • 8.1 Introduction
  • 8.2 One-way Layout
  • 8.3 Testing the Equality of Means
  • 8.4 ANOVA with Unequal Error Variances
  • 8.5 Multiple Comparisons
  • 8.6 Testing the Equality of Variances
  • 8.7 Two-way ANOVA without Replications
  • 8.8 ANOVA in a Balanced Two-way Layout with Replications
  • 8.9 Two-way ANOVA under Heteroscedasticity
  • Exercises
  • 9 Mixed Models
  • 9.1 Introduction
  • 9.2 One-way Layout
  • 9.3 Testing Variance Components
  • 9.4 Confidence Intervals
  • 9.5 Two-way Layout
  • 9.6 Comparing Variance Components
  • Exercises
  • 10 Regression
  • 10.1 Introduction
  • 10.2 Simple Linear Regression Model
  • 10.3. Inferences about Parameters of the Simple Regression Model
  • 10.3 Multiple Linear Regression
  • 10.4 Distributions of Estimators and Significance Tests
  • 10.5 Comparing Two Regressions with Equal Variances
  • 10.6 Comparing Regressions without Common Parameters
  • 10.7 Comparison of Two General Models
  • Exercises
  • Appendix A
  • Elements of Bayesian Inference
  • A.1 Introduction
  • A.2 The Prior Distribution
  • A.3 The Posterior Distribution
  • A.4 Bayes Estimators
  • A.5 Bayesian Interval Estimation
  • A.6 Bayesian Hypothesis Testing
  • Appendix B Technical Arguments
  • References.

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