Advances and Challenges in Parametric and Semi-parametric Analysis for Correlated Data
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Brajendra C. Sutradhar is an Honorary Research Professor at Memorial University, St. John's, and an Adjunct Research Professor at Carleton University in Ottawa, Canada. He is also a University Research Professor. This University Research Professor title was awarded to him by Memorial University in 2004 for his outstanding research in Statistical Science. Memorial University confers this prestigious title to at most two professors in any one year. Professor Sutradhar has published 126 papers in statistics journal in the area of familial and longitudinal data analysis with bio-statistical and econometric applications, multivariate estimation theory, time series analysis in both continuous and discrete setups, and complex sampling estimation theory for longitudinal survey data. He has served for 3 years as a member of the advisory committee on statistical methods in Statistics Canada. He has served as an associate editor for six years for Canadian Journal ofStatistics and for four years for the Journal of Environmental and Ecological Statistics . He is an elected member of the International Statistical Institute and a fellow of the American Statistical Association. Professor Sutradhar was awarded 2007 distinguished service award of Statistics Society of Canada for his many years of services to the society including his special services for society's annual meetings.
Professor Sutradhar is author of the books: (1) Dynamic Mixed Models for Familial Longitudinal Data, 2011 ; and (2) Longitudinal Categorical Data Analysis , 2014, published by Springer, New York. Also, he edited the special issue of the Canadian Journal of Statistics (2010, Vol. 38, June Issue, John Wiley) and the Lecture Notes in Statistics (2013, Vol. 211, Springer), with selected papers from two symposiums: International Symposium in Statistics, 2009 (ISS-2009) and ISS-2012, respectively.
Content
- Intro
- Preface
- Acknowledgments
- Contents
- List of Contributors
- Part I Elliptical t Distribution Theory
- Advances and Challenges in Inferences for Elliptically Contoured t Distributions
- 1 Introduction
- Case 1. Inference for Normal Models Using t Distribution
- Case 2. Independent t Models
- Case 3. Uncorrelated but Dependent t Models
- 2 Exact Versus Asymptotic Sampling Distribution Theory
- 2.1 Distribution Theory for Independent t Sample
- 2.1.1 Asymptotic Properties
- 2.1.2 Exact Sampling Distribution Theory Challenge
- 2.2 Distribution Theory for Uncorrelated but Dependent t Sample
- 2.2.1 Marginal Distribution
- 2.2.2 Distribution of Linear Combination of Elliptical t Variables
- 2.2.3 Distribution of the Sample Covariance Matrix Under Elliptical Distribution and Its Special Form Under Elliptical t Distribution
- 3 Parameter Estimation Difficulty Using Uncorrelated t Sample
- 3.1 Likelihood Estimator of Mean µ and Covariance Matrix S Under Elliptical Model (38)
- 3.1.1 MLE is Consistent for µ Under ECD t Model
- 3.1.2 MLE is Inconsistent for S Under ECD t Model
- 3.2 MLE Does Not Exist
- 3.2.1 Moment Estimator of ?, Say M Is Not Consistent for ?
- 4 Estimation of Parameters for Clustered (Familial or Longitudinal) Regression Models with t Data
- 4.1 Elliptical t Model for Uncorrelated Clustered (Familial) Responses
- 4.1.1 Consistent Estimator of S
- 4.1.2 Consistent Estimator of the Kurtosis Parameter ?
- 4.1.3 Consistent Estimator of the Kurtosis Parameter ß
- 4.2 Elliptical t Model for Correlated Clustered (Familial) Responses
- 4.2.1 Estimation of the Regression Effects ß
- 4.2.2 Estimation of the Kurtosis Parameter ?
- 4.2.3 Estimation of the Variance Component Parameter s2?
- 4.3 Longitudinal Elliptical t Model with Correlated Repeated Observations
- 4.3.1 GLS Estimation for ß
- 4.3.2 Moment Estimation for Kurtosis Parameter ?
- 4.3.3 Moment Estimation for Lag Autocorrelation
- 4.3.4 Moment Estimation for S=(suv) : p p
- 5 Testing for Linear Regression in Uncorrelated t Models
- 5.1 Classical F-Statistic Is Null Robust
- 5.2 Classical F-Statistic Is Not Non-null Robust
- 5.2.1 Power Computation
- 6 Concluding Remarks
- References
- Longitudinal Mixed Models with t Random Effects for Repeated Count and Binary Data
- 1 Introduction
- 1.1 Conditional and Unconditional (Normality Based) Correlation Structures for Repeated Count Data
- 1.2 Conditional and Unconditional (Normality Based) Correlation Structures for Repeated Binary Data
- 1.3 Plan of the Paper Under the Proposed t Random Effects with Unknown Degrees of Freedom ?
- 2 Poisson Mixed Model with t? Random Effects
- 2.1 Basic Properties of the Poisson Mixed Model: Unconditional Mean and Variance
- 2.2 Correlation Properties of the Poisson Mixed Model: Unconditional Covariances
- 3 GQL Estimation for the Parameters of the Poisson Mixed Model
- 3.1 GQL Estimation for the Regression Effects ß
- 3.1.1 Asymptotic Properties of the GQL Estimator of ß
- 3.2 GQL Estimation for the Scale and Shape Parameters
- 3.2.1 Computation of Oi(CI) O*i(ß,??,?)
- 3.2.2 Asymptotic Properties of the GQL Estimator GQL=[?,GQL,GQL]': 2 1
- 3.3 Moment Estimation of Correlation Index Parameter ?
- 4 Binary Dynamic Mixed Logit Model with t? Random Effects
- 4.1 Basic Properties of the Binary Mixed Model: Unconditional Mean and Variance
- 4.2 Computation of Unconditional Covariances for BDML Model with t? Random Effects
- 5 GQL Estimation for the Parameters of the BDML Model with t? Random Effects
- 5.1 Computation Higher Order Moments to Construct Oi in (84)
- 5.2 Asymptotic Normality and Consistency of GQL
- 6 Discussion
- References
- Part II Spatial and/or Time Series Volatility Models with Applications
- Zero-Inflated Spatial Models: Application and Interpretation
- 1 Introduction
- 2 Zero-Inflation Models
- 3 Case Study: Pine Weevil Infestations
- 4 Model Specification
- 5 Model Implementation
- 6 Results
- 7 Discussion
- References
- Inferences in Stochastic Volatility Models: A New Simpler Way
- 1 Introduction
- 2 GMM Versus QML Estimation for Volatility Models
- 2.1 Existing GMM Estimation and Complexity
- 2.2 QML Estimation
- 3 Proposed Estimation
- 3.1 Unbiased Moment Equations
- 3.1.1 Algorithm
- 3.2 Remarks on Large Sample Moment Estimation
- 3.3 A GQL (Generalized Quasi-Likelihood) Approximation
- 3.4 A Modified QML Approach
- 4 Estimation Performance: A Simulations BasedEmpirical Study
- 4.1 Simulation Design
- 4.2 Relative Performance of the MM and QML Approaches
- 4.3 Further Simulations for the MM Versus Approximate GQL (AGQL) Approach
- 5 Asymptotic Properties of the MM Estimators
- 5.1 Asymptotic Variance of the Estimator of ?1
- 5.2 Asymptotic Variance of the Estimator of s2?
- 6 Understanding Volatility Through Kurtosis of the Data
- 7 Volatility in US-Dollar and Swiss-Franc Exchange Rate: A Numerical Illustration
- 8 Concluding Remarks
- References
- Part III Longitudinal Multinomial Models in Parametric and Semi-parametric Setups
- A Generalization of the Familial Longitudinal Binary Model to the Multinomial Setup
- 1 Introduction
- 2 Proposed Familial Longitudinal Multinomial Model
- 2.1 Basic Properties of the Model
- 3 Likelihood Estimation for the MDML Model Parameters
- 3.1 Construction of the Likelihood Function
- 3.2 Likelihood Estimating Equations
- 3.2.1 Likelihood Estimating Equation for ß
- 3.2.2 Likelihood Estimating Equation for ?M
- 3.2.3 Likelihood Estimating Equation for st
- 4 A Remark on Likelihood Versus GQL Estimationfor the Binary Case
- 4.1 Computation of Asymptotic Variance of the Likelihood Estimators
- 4.2 Computation of Asymptotic Variance of the GQL Estimators
- 4.3 An Empirical Asymptotic Efficiency ComparisonBetween GQL and ML Estimates
- 5 An Illustration: Fitting MDL Model to the TMISL Data
- Appendix
- Algebras for the Likelihood Estimating Equation (32) for ß
- Algebras for the Likelihood Estimating Equation (39) for ??M
- Algebras for the Likelihood Estimating Equation (47) for st
- References
- Dynamic Models for Longitudinal Ordinal Non-stationary Categorical Data
- 1 Introduction
- 2 MDL Model for Repeated Nominal Categorical Data
- 3 Cumulative MDL Model for Ordinal Categorical Data
- 3.1 Marginal Cumulative Model at Time t=1
- 3.2 Lag 1 Transitional Cumulative Model at Time t=2,.,T
- 3.3 Likelihood Construction and Estimation of Parameters Under Cumulative MDL Model
- 3.3.1 Likelihood Estimating Equation for ß
- 3.3.2 Likelihood Estimating Equation for ?
- 3.4 Estimation of the Basic Properties of the Model
- 3.5 Asymptotic Properties of the Regression Estimates
- 4 BDL Model for Repeated Ordinal Responses
- 4.1 Basic Properties of the BDL Model
- 4.1.1 Marginal Means and Variances
- 4.2 Likelihood Estimation of the Parameters
- 5 Concluding Remarks
- References
- Semi-parametric Models for Longitudinal Count, Binary and Multinomial Data
- 1 Introduction
- 2 Semi-parametric Linear Longitudinal Models and Inferences
- 2.1 SQL Estimation of the Non-parametric Function ?(zij)
- 2.2 SGQL Estimation of ß
- 2.3 Moment Estimation of ?
- 3 Semi-parametric Longitudinal Models for Count Data and Inferences
- 3.1 SQL Estimation of the Non-parametric Function ?(zij)
- 3.2 SGQL Estimation of ß
- 3.3 Moment Estimation of Correlation Index Parameter ?
- 4 Semi-parametric Multinomial Dynamic Logit Models and Inferences
- 4.1 Semi-parametric Weighted Likelihood Estimation of the Non-parametric Functions ?(c)(z) for c=1,.,C-1
- 4.2 Likelihood Estimation for the Regression Effects ß
- 4.3 Likelihood Estimation for the Dynamic Dependence Parameters ?
- 5 Concluding Remarks
- References
- Part IV An Extension of the GQL Estimation Approach for Longitudinal Data Analysis
- Penalized Generalized Quasi-Likelihood Based Variable Selection for Longitudinal Data
- 1 Introduction
- 2 Generalized Quasi-Likelihood
- 3 Penalized Generalized Quasi-Likelihood (PGQL)
- 3.1 Numerical Algorithm
- 4 Performance Analysis
- 4.1 Stationary Count Data
- 4.2 Over-Dispersed Stationary Count Data
- 5 Health Care Utilization Data Study
- 6 Concluding Remarks
- References
- Index
