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AuthorWeerahandi, Samaradasa. author
TitleExact Statistical Methods for Data Analysis [electronic resource] / by Samaradasa Weerahandi
ImprintNew York, NY : Springer New York : Imprint: Springer, 1995
Connect tohttp://dx.doi.org/10.1007/978-1-4612-0825-9
Descript XIV, 329 p. online resource

SUMMARY

Now available in paperback


CONTENT

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


Statistics Probabilities Statistics Statistical Theory and Methods Probability Theory and Stochastic Processes



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