Intermediate Statistics and Econometrics: A Comparative Approach

1056 Pages·1995·9.95 MB·English

by  Dale J. Poirier

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title: Intermediate Statistics and Econometrics : A Comparative
Approach
author: Poirier, Dale J.
publisher: MIT Press
isbn10 | asin:
print isbn13: 9780262161497
ebook isbn13: 9780585134864
language: English
subject Economics--Statistical methods, Econometrics,
Mathematical statistics.
publication date: 1995
lcc: HB137.P645 1995eb
ddc: 330/.01/5195
subject: Economics--Statistical methods, Econometrics,
Mathematical statistics.
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Intermediate Statistics and Econometrics
A Comparative Approach
Dale J. Poirier
The MIT Press
Cambridge, Massachusetts
London, England

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© 1995 Massachusetts Institute of Technology
All rights reserved. No part of this book may be reproduced in any form by any electronic or
mechanical means (including photocopying, recording, or information storage and retrieval)
without permission in writing from the publisher.
This book was set in Times Roman by Asco Trade Typesetting Ltd., Hong Kong and was
printed and bound in the United States of America.
Library of Congress Cataloging-in-Publication Data
Poirier, Dale J.
Intermediate statistics and econometrics: a comparative approach
/Dale J. Poirier.
p. cm.
Includes bibliographical references and index.
ISBN 0-262-16149-4
1. EconomicsStatistical methods. 2. Econometrics.
3. Mathematical statistics. I. Title.
HB137.P645 1995
330'.01'5195dc20 94-28184
CIP

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Page v
To my parents,
for showing me the meaning of commitment.

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Page vii
Contents
Words of Wisdom xi
Preface xiii
1
Introduction
1
1.1 The Origin of Econometrics
1
1.2 Realism Versus Instrumentalism
4
1.3 The Shuttle Disaster
2
Basic Concepts
9
2.1 Probability
29
2.2 Random Variables
36
2.3 Univariate Mathematical Expectation
43
2.4 Joint and Conditional Distributions
52
2.5 Stochastic Independence
55
2.6 Multivariate Mathematical Expectation
64
2.7 Population Regression and Partial Correlation
76
2.8 Inequalities
3
Special Distributions
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81
3.1 Introduction
81
3.2 Discrete Univariate Distributions
93
3.3 Continuous Univariate Distributions
117
3.4 Multivariate Distributions I
136
3.5 Multivariate Distributions II
4
Distributions of Functions of Random Variables
143
4.1 Introduction
143
4.2 Cumulative Distribution Function Technique
147
4.3 Moment Generating Function Technique
149
4.4 Change-of-Variable Technique
155
4.5 Quadratic-Form Technique
5
Sampling Theory
165
5.1 Basic Concepts
168
5.2 Statistics and Sample Moments
176
5.3 Sampling Distributions
151
5.4 Order Statistics
185
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5.5 Stochastic Convergence
199
5.6 Laws of Large Numbers
201
5.7 Central Limit Theorems
210
5.8 Subjectivist View of Sampling

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6
Estimation
219
6.1 Likelihood and Sufficiency
226
6.2 Likelihood and Stopping Rule Principles
233
6.3 Sampling Properties of Point Estimators in Finite Samples
250
6.4 Sampling Properties of Point Estimators in Large Samples
259
6.5 An Overview of Frequentist Point Estimation
271
6.6 Classical Point Estimation Methods
288
6.7 Bayesian Point Estimation
318
6.8 Choice of Prior and Bayesian Sensitivity Analysis
334
6.9 Interval Estimation
343
6.10 Reflections on Conditioning
7
Hypothesis Testing
351
7.1 Introduction
354
7.2 Sampling Theory Approach
367
7.3 Asymptotic Tests
376
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7.4 Bayesian Posterior Odds
396
7.5 P-values
400
7.6 Postscript
8
Prediction
405
8.1 Introduction
411
8.2 The Simplest Case: Known Parameters
418
8.3 Structural Modelling
425
8.4 Predictive Likelihood
429
8.5 Classical Point and Interval Prediction
432
8.6 Bayesian Point and Interval Prediction
439
8.7 Combination of Forecasts
9
The Linear Regression Model
445
9.1 A Tale of Two Regressions
460
9.2 Classical Estimation in Multiple Linear Normal Regression
482
9.3 Estimation Subject to Exact Restrictions on Regression Coefficients
490
9.4 Distribution Theory for Classical Estimation
494
9.5 Confidence Intervals
498
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