Amazon no longer offers textbook rentals. We do!

Testing Statistical Hypotheses

by: Lehmann, E. L.; Romano, Joseph P.

Testing Statistical Hypotheses

by: Lehmann, E. L.; Romano, Joseph P.

ISBN 13:
9780387988641
ISBN 10:
0387988645
Edition: 3rd
Format: Hardcover
Copyright: 03/30/2005
Publisher: Springer Nature

Rent

Sorry, this item is currently unavailable on Knetbooks.com

Click the link below to purchase this eBook from our trusted partner, eCampus.com.

View eBook

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Extend or Purchase Your Rental at Any Time

Need to keep your rental past your due date? At any time before your due date you can extend or purchase your rental through your account.

Summary

This classic textbook, now available from Springer, summarizes developments in the field of hypotheses testing. Optimality considerations continue to provide the organizing principle. However, they are now tempered by a much stronger emphasis on the robustness properties of the resulting procedures. This book is an essential reference for any graduate student in statistics.

Preface

vii

I Small-Sample Theory

(416)

The General Decision Problem

(25)

Statistical Inference and Statistical Decisions

(1)

Specification of a Decision Problem

(4)

Randomization; Choice of Experiment

(1)

Optimum Procedures

(2)

Invariance and Unbiasedness

(3)

Bayes and Minimax Procedures

(2)

Maximum Likelihood

(1)

Complete Classes

(1)

Sufficient Statistics

(3)

Problems

(6)

Notes

(1)

The Probability Background

(28)

Probability and Measure

(3)

Integration

(3)

Statistics and Subfields

(2)

Conditional Expectation and Probability

(5)

Conditional Probability Distributions

(3)

Characterization of Sufficiency

(2)

Exponential Families

(4)

Problems

(5)

Notes

(1)

Uniformly Most Powerful Tests

(54)

Stating The Problem

(3)

The Neyman--Pearson Fundamental Lemma

(4)

p-values

(2)

Distributions with Monotone Likelihood Ratio

(7)

Confidence Bounds

(5)

A Generalization of the Fundamental Lemma

(4)

Two-Sided Hypotheses

(2)

Least Favorable Distributions

(3)

Applications to Normal Distributions

(6)

Univariate Normal Models

(3)

Multivariate Normal Models

(3)

Problems

(15)

Notes

107

(3)

Unbiasedness: Theory and First Applications

110

(40)

Unbiasedness For Hypothesis Testing

110

(1)

One-Parameter Exponential Families

111

(4)

Similarity and Completeness

115

(4)

UMP Unbiased Tests for Multiparameter Exponential Families

119

(5)

Comparing Two Poisson or Binomial Populations

124

(3)

Testing for Independence in a 2 x 2 Table

127

(3)

Alternative Models for 2 x 2 Tables

130

(2)

Some Three-Factor Contingency Tables

132

(3)

The Sign Test

135

(4)

Problems

139

(10)

Notes

149

(1)

Unbiasedness: Applications to Normal Distributions

150

(62)

Statistics Independent of a Sufficient Statistic

150

(3)

Testing the Parameters of a Normal Distribution

153

(4)

Comparing the Means and Variances of Two Normal Distributions

157

(4)

Confidence Intervals and Families of Tests

161

(3)

Unbiased Confidence Sets

164

(4)

Regression

168

(3)

Bayesian Confidence Sets

171

(5)

Permutation Tests

176

(1)

Most Powerful Permutation Tests

177

(4)

Randomization As A Basis For Inference

181

(3)

Permutation Tests and Randomization

184

(3)

Randomization Model and Confidence Intervals

187

(3)

Testing for Independence in a Bivariate Normal Distribution

190

(2)

Problems

192

(18)

Notes

210

(2)

Invariance

212

(65)

Symmetry and Invariance

212

(2)

Maximal Invariants

214

(4)

Most Powerful Invariant Tests

218

(5)

Sample Inspection by Variables

223

(2)

Almost Invariance

225

(4)

Unbiasedness and Invariance

229

(3)

Admissibility

232

(7)

Rank Tests

239

(3)

The Two-Sample Problem

242

(4)

The Hypothesis of Symmetry

246

(2)

Equivariant Confidence Sets

248

(3)

Average Smallest Equivariant Confidence Sets

251

(4)

Confidence Bands for a Distribution Function

255

(2)

Problems

257

(19)

Notes

276

(1)

Linear Hypotheses

277

(42)

A Canonical Form

277

(4)

Linear Hypotheses and Least Squares

281

(4)

Tests of Homogeneity

285

(2)

Two-Way Layout: One Observation per Cell

287

(3)

Two-Way Layout: m Observations Per Cell

290

(3)

Regression

293

(4)

Random-Effects Model: One-way Classification

297

(3)

Nested Classifications

300

(4)

Multivariate Extensions

304

(2)

Problems

306

(11)

Notes

317

(2)

The Minimax Principle

319

(29)

Tests with Guaranteed Power

319

(3)

Examples

322

(4)

Comparing Two Approximate Hypotheses

326

(3)

Maximin Tests and Invariance

329

(2)

The Hunt-Stein Theorem

331

(6)

Most Stringent Tests

337

(1)

Problems

338

(9)

Notes

347

(1)

Multiple Testing and Simultaneous Inference

348

(44)

Introduction and the FWER

348

(6)

Maximin Procedures

354

(9)

The Hypothesis of Homogeneity

363

(12)

Scheffe's S-Method: A Special Case

375

(5)

Scheffe's S-Method for General Linear Models

380

(5)

Problems

385

(6)

Notes

391

(1)

Conditional Inference

392

(25)

Mixtures of Experiments

392

(3)

Ancillary Statistics

395

(5)

Optimal Conditional Tests

400

(4)

Relevant Subsets

404

(5)

Problems

409

(5)

Notes

414

(3)

II Large-Sample Theory

417

(275)

Basic Large Sample Theory

419

(63)

Introduction

419

(5)

Basic Convergence Concepts

424

(20)

Weak Convergence and Central Limit Theorems

424

(7)

Convergence in Probability and Applications

431

(9)

Almost Sure Convergence

440

(4)

Robustness of Some Classical Tests

444

(15)

Effect of Distribution

444

(4)

Effect of Dependence

448

(3)

Robustness in Linear Models

451

(8)

Nonparametric Mean

459

(10)

Edgeworth Expansions

459

(3)

The t-test

462

(4)

A Result of Bahadur and Savage

466

(2)

Alternative Tests

468

(1)

Problems

469

(11)

Notes

480

(2)

Quadratic Mean Differentiable Families

482

(45)

Introduction

482

(1)

Quadratic Mean Differentiability (q.m.d.)

482

(10)

Contiguity

492

(11)

Likelihood Methods in Parametric Models

503

(14)

Efficient Likelihood Estimation

504

(4)

Wald Tests and Confidence Regions

508

(3)

Rao Score Tests

511

(2)

Likelihood Ratio Tests

513

(4)

Problems

517

(8)

Notes

525

(2)

Large Sample Optimality

527

(56)

Testing Sequences, Metrics, and Inequalities

527

(7)

Asymptotic Relative Efficiency

534

(6)

AUMP Tests in Univariate Models

540

(9)

Asymptotically Normal Experiments

549

(4)

Applications to Parametric Models

553

(14)

One-sided Hypotheses

553

(6)

Equivalence Hypotheses

559

(5)

Multi-sided Hypotheses

564

(3)

Applications to Nonparametric Models

567

(7)

Nonparametric Mean

567

(3)

Nonparametric Testing of Functionals

570

(4)

Problems

574

(8)

Notes

582

(1)

Testing Goodness of Fit

583

(48)

Introduction

583

(1)

The Kolmogorov-Smirnov Test

584

(6)

Simple Null Hypothesis

584

(5)

Extensions of the Kolmogorov-Smirnov Test

589

(1)

Pearson's Chi-squared Statistic

590

(9)

Simple Null Hypothesis

590

(4)

Chi-squared Test of Uniformity

594

(3)

Composite Null Hypothesis

597

(2)

Neyman's Smooth Tests

599

(8)

Fixed k Asymptotics

601

(2)

Neyman's Smooth Tests With Large k

603

(4)

Weighted Quadratic Test Statistics

607

(9)

Global Behavior of Power Functions

616

(6)

Problems

622

(7)

Notes

629

(2)

General Large Sample Methods

631

(61)

Introduction

631

(1)

Permutation and Randomization Tests

632

(11)

The Basic Construction

632

(4)

Asymptotic Results

636

(7)

Basic Large Sample Approximations

643

(5)

Pivotal Method

644

(2)

Asymptotic Pivotal Method

646

(1)

Asymptotic Approximation

647

(1)

Bootstrap Sampling Distributions

648

(13)

Introduction and Consistency

648

(5)

The Nonparametric Mean

653

(2)

Further Examples

655

(3)

Stepdown Multiple Testing

658

(3)

Higher Order Asymptotic Comparisons

661

(7)

Hypothesis Testing

668

(5)

Subsampling

673

(9)

The Basic Theorem in the I.I.D. Case

674

(3)

Comparison with the Bootstrap

677

(3)

Hypothesis Testing

680

(2)

Problems

682

(8)

Notes

690

(2)

A Auxiliary Results

692

(10)

A.1 Equivalence Relations; Groups

692

(1)

A.2 Convergence of Functions; Metric Spaces

693

(3)

A.3 Banach and Hilbert Spaces

696

(2)

A.4 Dominated Families of Distributions

698

(2)

A.5 The Weak Compactness Theorem

700

(2)

References

702

(55)

Author Index

757

(10)

Subject Index

767

Amazon no longer offers textbook rentals. We do!

Testing Statistical Hypotheses

Testing Statistical Hypotheses

9780387988641

0387988645

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Testing Statistical Hypotheses

Testing Statistical Hypotheses

9780387988641

0387988645

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

Related Products