Developments in Statistics

1st Edition, Volume 4 - April 28, 1983
Editor: Paruchuri R. Krishnaiah
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 6 4 2 2 - 6

Developments in Statistics, Volume 4 reviews developments in the theory and applications of statistics, covering topics such as time series, identifiability and model selection,… Read more

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Developments in Statistics, Volume 4 reviews developments in the theory and applications of statistics, covering topics such as time series, identifiability and model selection, and missing data. The application of structured exploratory data analysis to human genetics, specifically, the mode of inheritance, is also considered. Comprised of four chapters, this volume begins with an introduction to spectrum parameter estimation in time series analysis, restricting the discussion to the simplest univariate (that is, scalar) real-valued time series X(t). An accurate formulation of the general problem is presented. The accuracy of different consistent estimates obtained for large but fixed values of T (maximum likelihood estimates, Whittle's estimates, and simplified asymptotically efficient estimates) is also compared. The next chapter deals with identifiability and modeling in econometrics, focusing on the theoretical framework relating realization theory, identification, and parametrization. The realization theory is illustrated on various levels of generality by means of examples related to econometrics, along with some advanced applications of system theory. The book also examines inference on parameters of multivariate normal populations when some data are missing before concluding with an evaluation of structured exploratory data as applied to the study of the mode of inheritance. This monograph will be of interest to students and practitioners of statistics.

List of Contributors

Preface

Contents of Other Volumes

Chapter 1 Spectrum Parameter Estimation in Time Series Analysis

1. Introduction

2. Formulation of the Problem: Some Consistent Estimates of Parameters

3. The Efficiency of Consistent Estimates

4. Maximum Likelihood Estimates

5. Whittle's Estimates

6. Simplified Asymptotically Efficient Estimates

References

Chapter 2 Identifiability and Modeling in Econometrics

1. Background and Perspective

2. Realization

3. Parametrization

4. Stochastic Identification: An Example

5. Estimation of Simultaneous Equations

6. The ARMAX Model

7. Applications of Realization Theory

8. Conclusions

References

Chapter 3 Inference on Parameters of Multivariate Normal Populations When Some Data Is Missing

1. Introduction

2. First-Order Efficiency

3. Estimation of μ1

4. Estimation of ρ

5. Estimation of μ2

6. Estimation of δ = μ1÷ — μ2

7. Approximations to the Distributions of d(ρ) and μ2(ρ)

8. Estimation of σ2

9. Inference When Observations Are Missing on Both Variables

10. Asymptotic Distributions of Test Statistics When Some Data Is Missing

11. Tests for the Equality of Mean Vectors

12. Testing the Equality of Means under Intraclass Covariance Structure

13. Review of the Literature on Optimal Properties of Tests with Missing Data

References

Chapter 4 Structured Exploratory Data Analysis Applied to Mode of Inheritance

1. Introduction

A. Classical Methods for Assessing Mode of Inheritance

B. Philosophy of Structured Exploratory Data Analysis

2. Parent-Offspring Transmission Models

A. Major Gene Models (MGI)

B. Multifactorial Models

C. Sporadic Models

3. Statistics and Methodologies

A. Major Gene Index (MGI)

B. The OBP(β), ONM(β), ONF(β) Cumulant Functions

C. Midparent-Offspring Correlation Coefficient (MPCC)

D. Trimming Procedures

4. Theoretical Behavior of the SEDA Statistics Under the Various Models

A. Further Details on Modeling Specifications for Theoretical Calculations

B. Theoretical Behavior of the SEDA Statistics

C. Offspring-between-Parents Plots

5. Behavior of the SEDA Statistics for Various Simulated Transmission Schemes

A. Procedure for Simulating Genetic Transmission

B. Results of Simulations

6. Application of the SEDA Methodology to Data

A. Age Adjustment

B. COMT Enzyme Activity

C. Some IgE Family Data

7. Current Developments

A. Proposed Mechanisms for Gene-Environment Interaction

B. Methods for Exploring Gene-Environment Interaction

C. Refinements on the Analysis of Mode of Inheritance

Appendix A. Calculation of SEDA Statistics for the Major Gene Model

Appendix B. Calculation of SEDA Statistics for the Multifactorial Models

Appendix C. Calculation of SEDA Statistics for Sporadic Models

Appendix D. Equilibrium Covariance Structure and Concomitant Statistical Realizations under Multifactorial Model 1

Appendix E. Behaviors of SEDA Statistics with Respect to the Parameters of the Models

Appendix F. Convergence to Equilibrium for the General Multifactorial Model

References

Author Index

Subject Index