Testing Statistical Hypotheses,9780387988641

Testing Statistical Hypotheses

by ;
Edition: 3rd
ISBN13: 9780387988641
ISBN10: 0387988645
Format: Hardcover
Pub. Date: 2005-03-30
Publisher(s): Springer Nature
  • Free Shipping Icon

    This Item Qualifies for Free Shipping!*

    *Excludes marketplace orders.

List Price: $104.99

Rent Textbook

Select for Price
Add to Cart
There was a problem. Please try again later.

Rent Digital

Rent Digital Options
Online:30 Days access
Downloadable:30 Days
$28.80
Online:60 Days access
Downloadable:60 Days
$38.40
Online:90 Days access
Downloadable:90 Days
$48.00
Online:120 Days access
Downloadable:120 Days
$57.60
Online:180 Days access
Downloadable:180 Days
$62.40
Online:1825 Days access
Downloadable:Lifetime Access
$95.99
$62.40
Add to Cart

New Textbook

We're Sorry
Sold Out

Used Textbook

We're Sorry
Sold Out

Buy from our Marketplace starting at $37.36

How Marketplace Works:

  • This item is offered by an independent seller and not shipped from our warehouse
  • Item details like edition and cover design may differ from our description; see seller's comments before ordering.
  • Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
  • Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
  • Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.

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.

Author Biography

E.L. Lehmann is Professor of Statistics Emeritus at the University of California, Berkeley. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and the recipient of honorary degrees from the University of Leiden, The Netherlands and the University of Chicago. He is the author of Elements of Large-Sample Theory and (with George Casella) he is also the author of Theory of Point Estimation, Second Edition.Joseph P. Romano is Professor of Statistics at Stanford University. He is a recipient of a Presidential Young Investigator Award and a Fellow of the Institute of Mathematical Statistics. He has coauthored two other books, Subsampling with Dimitris Politis and Michael Wolf, and Counterexamples in Probability and Statistics with Andrew Siegel.

Table of Contents

Preface vii
I Small-Sample Theory
1(416)
The General Decision Problem
3(25)
Statistical Inference and Statistical Decisions
3(1)
Specification of a Decision Problem
4(4)
Randomization; Choice of Experiment
8(1)
Optimum Procedures
9(2)
Invariance and Unbiasedness
11(3)
Bayes and Minimax Procedures
14(2)
Maximum Likelihood
16(1)
Complete Classes
17(1)
Sufficient Statistics
18(3)
Problems
21(6)
Notes
27(1)
The Probability Background
28(28)
Probability and Measure
28(3)
Integration
31(3)
Statistics and Subfields
34(2)
Conditional Expectation and Probability
36(5)
Conditional Probability Distributions
41(3)
Characterization of Sufficiency
44(2)
Exponential Families
46(4)
Problems
50(5)
Notes
55(1)
Uniformly Most Powerful Tests
56(54)
Stating The Problem
56(3)
The Neyman--Pearson Fundamental Lemma
59(4)
p-values
63(2)
Distributions with Monotone Likelihood Ratio
65(7)
Confidence Bounds
72(5)
A Generalization of the Fundamental Lemma
77(4)
Two-Sided Hypotheses
81(2)
Least Favorable Distributions
83(3)
Applications to Normal Distributions
86(6)
Univariate Normal Models
86(3)
Multivariate Normal Models
89(3)
Problems
92(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

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.