Developments in 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