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    Statistical Hypothesis Testing : Theory and Methods

    ISBN-10: 9812814361
    ISBN-13: 9789812814364
    Author(s): Ning-Zhong Shi, Jian Tao
    Description: "This book presents up-to-date theory and methods of statistical hypothesis testing based on measure theory. The so-called statistical space is a measurable space adding a family of probability measures. Most topics in the book will be developed  More...
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    List Price: $111.00
    Publisher: World Scientific Publishing Company, Incorporated
    Binding: Hardcover
    Size: 6.25" wide x 9.25" long x 1.00" tall
    Weight: 1.298
    Language: English

    "This book presents up-to-date theory and methods of statistical hypothesis testing based on measure theory. The so-called statistical space is a measurable space adding a family of probability measures. Most topics in the book will be developed based on this term. The book includes some typical data sets, such as the relation between race and the death penalty verdict, the behavior of food intake of two kinds of Zucker rats, and the per capita income and expenditure in China during the 1978-2002 period. Emphasis is given to the process of finding appropriate statistical techniques and methods of evaluating these techniques."--BOOK JACKET.

    Statistical Spaces
    Basic Properties of Statistical Spaces
    Measure in Statistical Spaces
    Equivalence and Divisibility of Family of Probability Distributions
    Conditional Probability and Sufficient Statistics
    Statistics and Random Variables
    Conditional Probability
    Sufficient Statistics
    Exponential Family and Completeness
    Exponential Family
    Sufficiency and Completeness
    Ancillary Statistics
    Estimation Methods Based on Statistical Space
    Moment Estimation and Median Estimation
    Maximum Likelihood Estimators
    Quality of Estimators
    Comparison of Estimators
    Nonparametric MLE for Population cdf
    Methods of Statistical Tests
    Introduction: Background of Problem
    Likelihood Ratio Tests
    The Likelihood Ratio Methods
    LRT's Limiting Distribution
    Tests of Goodness-of-fit
    Limiting Distribution
    Test of Independence in Two-Way Contingency Table
    Test of Independence in Three-Way Contingency Table
    Goodness-of-Fit Test of Distribution Function
    Sign Tests and Rank Tests
    Sign Tests
    Wilcoxon Signed Rank Tests
    Wilcoxon Rank Tests
    U-I Tests
    Empirical Likelihood-Ratio Tests
    The Comparison of Test Statistics
    Probability of Two Types of Error in Hypothesis Test
    Neyman-Pearson Fundamental Lemma
    Unbiased Test
    Comparing Power Functions
    Test Procedures
    Power Functions and Their Comparison
    Comparing Robustness
    Efficiency of Tests
    Asymptotic Relative Efficiency
    Interval Estimation Based on Test
    Interval Estimation and Acceptance Region
    Uniformly Most Accurate Confidence Interval
    Uniformly Most Accurate Unbiased Confidence Interval
    Uniformly Most Accuracy and Interval Length
    Parametric Tests for Simple Models
    One-Factor Model: Analysis of Variance
    One-Factor Model: Multiple Comparisons
    Multiple Comparisons
    Generalized Multiple Comparisons
    The False Discovery Rate Procedure
    One-Factor Model: Trend Tests
    Linearity Tests
    Likelihood Ratio Test
    Linear Rank Tests
    Multi-Factor Model: Analysis of Variance
    Model Without Interaction Effects
    Model with Interaction Effects
    Multi-Factor Model: Log-linear Models
    Two-Dimensional Contingency Table
    Three-Dimensional Contingency Table
    Ancillary Parameter Model
    Parametric Tests for Regression Models
    Linear Models
    Establishment of Model
    Estimating and Testing the Parameters
    Regression Models
    Regression Model and Linear Model
    Errors-in-Variables Model
    Logistic Regression Models
    One-Variable Case
    Multivariable Case
    Time Series: Trend Term Models
    Time Series: Autoregressive Models
    Random Walk and Brownian Motion
    Autoregressive Model
    Granger Causality Tests
    Granger Causality
    Integration of Order d
    Real Data Analysis

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