Statistical Decision Theory Nicholas T. Longford

Format:

Book

Author/Creator:

Longford, Nicholas T., 1955-

Series:

SpringerBriefs in statistics 2191-544X

SpringerBriefs in Statistics 2191-544X

Language:

English

Subjects (All):

Mathematical statistics.

Statistics.

Statistics, general.

statistics.

Local Subjects:

Statistics.

Statistics, general.

Physical Description:

1 online resource

Place of Publication:

Heidelberg Springer 2013

Language Note:

English

System Details:

PDF

text file

Summary:

This monograph presents a radical rethinking of how elementary inferences should be made in statistics, implementing a comprehensive alternative to hypothesis testing in which the control of the probabilities of the errors is replaced by selecting the course of action (one of the available options) associated with the smallest expected loss. Its strength is that the inferences are responsive to the elicited or declared consequences of the erroneous decisions, and so they can be closely tailored to the client's perspective, priorities, value judgments and other prior information, together with the uncertainty about them

Contents:

Preface

1. Introduction

2. Estimating the Mean

3. Estimating the Variance

4. The Bayesian Paradigm

5. Data from other Distributions

6. Classification

7. Small-area Estimation

8. Study Design

Index

Machine generated contents note: 1. Introduction

1.1. Role of Statistics

1.2. Preliminaries

1.3. Estimation

1.4. Assessing an Estimator

1.5. Confidence Intervals

1.6. Hypothesis Testing

1.7. Loss Function

1.8. Problems, Exercises and Suggested Reading References

2.1. Estimation with an Asymmetric Loss

2.2. Numerical Optimisation

2.3. Plausible Loss Functions

2.4. Other Classes of Loss Functions

2.4.1. LINEX Loss

2.5. Comparing Two Means

2.6. Problems, Exercises and Suggested Reading References

3.1. Unbiased and Efficient Estimation

3.2. Loss Functions for Variance Estimators

3.3. Variance Versus a Constant

3.3.1. Decision with Utilities

3.3.2. Multiplicative Loss

3.4. Estimating the Variance Ratio

3.5. Problems, Exercises and Suggested Reading References

4. Bayesian Paradigm

4.1. Bayes Theorem

4.2. Comparing Two Normal Random Samples

4.3. Decision with Estimated σ2

4.4. Problems, Exercises and Suggested Reading References

5. Data from Other Distributions

5.1. Binary Outcomes

5.2. Poisson Counts

5.3. Continuous Distributions: Transformations and Mixtures

5.4. Problems, Exercises and Suggested Reading References

6.1. Introduction

6.2. Normally Distributed Marker

6.3. Markers with Other Distributions

6.3.1. Markers with t Distribution

6.3.2. Beta Distributed Markers

6.3.3. Gamma Distributed Markers

6.4. Looking for Contaminants

6.5. Problems, Exercises and Suggested Reading References

7. Small-Area Estimation

7.1. Composition and Empirical Bayes Models

7.2. Estimation for a Policy

7.3. Application

7.3.1. Limited Budget

7.4. Conclusion

7.5. Appendix: Estimating

7.6. Problems, Exercises and Suggested Reading References

8.1. Sample Size Calculation for Hypothesis Testing

8.2. Sample Size for Decision Making

8.3. Problems, Exercises and Suggested Reading References

Notes:

Includes index

Includes bibliographical references and index

Other Format:

Printed edition:

ISBN:

9783642404337

3642404332

OCLC:

862577711

Publisher Number:

10.1007/978-3-642-40433-7

Access Restriction:

Restricted for use by site license