Developments in Statistics

Developments in Statistics

1st Edition - August 28, 1978

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  • Editor: Paruchuri R. Krishnaiah
  • eBook ISBN: 9781483264868

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Description

Development in Statistics, Volume 1 is a collection of papers that deals with theory and application of parameter estimation in stochastic differential systems, the comparative aspects of the study of ordinary time series, and real multivariate distributions. Some papers discuss covariance analysis of nonstationary time series, nonparametric repeated significance tests, as well as discrete optimal factorial designs for statisticians and investigators of experiments. One paper cites an application of parameter estimation in stochastic differential systems in approximates of stability and control derivatives from flight test data. Another paper cites cases where procedures of ordinary time series (or point processes) have direct analogs in the study of point processes (or ordinary time series). One paper explains the applications of multivariate distributions in simultaneous tests on the equality of eigenvalues toward the covariance matrix, canonical correlation matrix, and a matrix associated with the multivariate analysis of variance. Another paper reviews two types of repeated significance tests, namely, the genuinely distribution-free tests based on a broad class of nonparametric statistics; and the asymptotically distribution-free tests based on a broad class of parametric statistics but having asymptotically nonparametric behavior. Both types can provide a unified solution to a broad class of problems. The collection can be valuable for mathematicians, students, and professors of calculus, statistics, or advanced mathematics.

Table of Contents


  • List of Contributors

    Preface

    Contents of Volume 2

    Parameter Estimation in Stochastic Differential Systems: Theory and Application

    1. Introduction

    2. White Noise: Basic Notions

    3. Radon-Nikodym Derivatives of Weak Distributions

    4. Dynamic Systems

    5. Application

    References

    Comparative Aspects of the Study of Ordinary Time Series and of Point Processes

    1. Introduction

    2. Foundations

    3. Inference

    References

    Some Recent Developments on Real Multivariate Distributions

    1. Introduction

    2. Preliminaries and Evaluation of Some Integrals

    3. Joint Distributions of the Eigenvalues of Certain Random Matrices

    4. Distributions of the Individual Roots of a Class of Random Matrices

    5. Distributions of the Ratios of the Roots

    6. Distributions of Elementary Symmetric Functions

    7. Distributions of the Likelihood Ratio Statistics

    8. Applications in Inference on Covariance Structures and Simultaneous Test Procedures

    9. Applications in Simultaneous Tests for the Equality of the Eigenvalues

    References

    Covariance Analysis of Nonstationary Time Series

    1. Introduction and Outline

    2. A General Class of Nonstationary Time Series

    3. Nonstationary Series Generated by Difference Equations

    4. Series Generated by Differential Equations: Flows

    5. Asymptotic Distributions of Estimators

    6. Equivalence of Gaussian Time Series

    7. Likelihood Ratios and Tests

    References

    Nonparametric Repeated Significance Tests

    1. Introduction

    2. Type A Repeated Significance Tests

    3. Type B Repeated Significance Tests

    4. Some Specific Repeated Significance Tests

    5. Asymptotic Distribution Theory under Null Hypotheses

    6. Asymptotic Distribution Theory under Local Alternatives

    7. Efficiency of Repeated Significance Tests

    8. Some General Remarks

    References

    A Review of Some Recent Work on Discrete Optimal Factorial Designs for Statisticians and Experimenters

    1. Introduction

    2. Preliminaries for Users of Designs

    3. 2m Factorial Designs

    4. The Counting Operator and the Information Matrix

    5. Orthogonal Designs and Orthogonal Arrays

    6. Balanced Designs and Balanced Arrays

    7. Existence Conditions for Balanced Arrays

    8. The Characteristic Roots of the Information Matrix for Balanced Designs

    9. Optimal Balanced 2m Factorial Designs of Resolution V, m = 4, 5, 6

    10. Optimal Balanced Designs of Resolution V of the 27 Series, N ≤ 42

    11. Optimal Balanced 27 Factorial Designs with 43 ≤ N ≤ 68

    12. The Case m = 8

    13. Tables of Optimal Designs and How to Use Them

    14. Comparison of Optimality Criteria

    15. Search Designs

    References

    Author Index

    Subject Index

Product details

  • No. of pages: 352
  • Language: English
  • Copyright: © Academic Press 1978
  • Published: August 28, 1978
  • Imprint: Academic Press
  • eBook ISBN: 9781483264868

About the Editor

Paruchuri R. Krishnaiah

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