Stationarity and Moment Structure for Box-Cox Transformed Threshold Garch (1,1) Processes

This article introduces threshold GARCH (1,1) processes to which Box-Cox transformations are applied. This class of processes included nonlinear ARCH and GARCH models as special cases. The model accommodates asymmetries in conditional variances through a "threshold". The stationary solution is explicitly obtained and moment structures are investigated. Estimation for parameters is also discussed.

TR Number: 
2003-4
S.Y. Hwang and I.V. Basawa
Key Words: 
Box-Cox transformation, threshold GARCH, Stationary moments, Quasilikelihood estimation

To request a copy of this report send an email to Richard Worthington and a pdf copy will be sent to you if available.

Inference for Shot Noise

This paper studies estimation issues for shot noise processes from a process history taken on a discrete-tie lattice. Optimal estimating equation methods are constructed for the case when the impulse response function of the shot process is interval similar; moment-type methods are explored for compactly supported impulse responses. Asymptotic normality of the proposed estimates are established and the limiting covariance of the estimates is derived.

TR Number: 
2003-5
Yuanhui Xiao and Robert Lund
Key Words: 
Shot Noise, Inference, Estimating Equation, Conditional Expectation, Linear Prediction, Conditional Least Squares

To request a copy of this report send an email to Richard Worthington and a pdf copy will be sent to you if available.

Mixtures of generalized Linear Mixed-Effects Models for Cluster-Correlated Data

Finite mixtures of generalized linear mixed effect models are presented to handle situations where within-cluster correlation and heterogeneity (subpopulations) exist simultaneously. For this class of models, we consider maximum likelihood (ML) as our main approach to estimation. Due to the complexity of the marginal loglikelihood of this model, the EM algorithm is employed to facilitate computation. The major obstacle in this procedure is to integrate over the random effects' distribution to evaluation the expectation of the E-step.

TR Number: 
2003-6
Daniel B. Hall and Lihua Wang
Key Words: 

To request a copy of this report send an email to Richard Worthington and a pdf copy will be sent to you if available.

Marginal Models for Zero-Inflated Clustered Data

Over the last decade or so, there has been increasing interest in "zero-inflated" (ZI) regression models to account for "excess" zeros in data. Examples include ZI-Poisson, ZI-Binomial, ZI-Negative Binomial, and ZI-Tobit models. Recently, extensions of these models to the clustered data case have begun to appear. For example, Hall (2000, Biometrics) considered ZI-Poisson and ZI-Binomial models with cluster-specific random effects. In this paper, we consider an alternative approach based on marginal models and generalized estimating equation (GEE) methodology.

TR Number: 
2003-10
Daniel B. Hall and Zhengang Zhang
Key Words: 
Extended Generalized Estimating Equations, Finite Mixture, Generalized Linear Model, Longitudinal Data, Mixture of Experts, Repeated Measures

To request a copy of this report send an email to Richard Worthington and a pdf copy will be sent to you if available.

Optimal Confidence Interval for the Largest Normal Mean with Unknown Variance

In this paper, a single-sample procedure is proposed for obtaining an optimal confidence interval for the largest or smallest mean of several independent normal populations, where the common variance is unknown. It has been found that the optimal confidence interval in the sense of a reducing interval width. This optimal confidence interval is obtained by maximizing the coverage probability with the expected confidence width being fixed at a least favorable configuration of means. Tables of the critical values are given for the optimal confidence interval.

TR Number: 
2003-11
Hubert Chen and Shun-Yi Chen
Key Words: 
distribution, expected interval width, critical values, least favorable configuration

To request a copy of this report send an email to Richard Worthington and a pdf copy will be sent to you if available.

Maximum Likelihood Estimation for a First-Order Bifurcating Autoregressive Process with Exponential Errors

Exact and asymptotic distributions of the maximum likelihood estimator of the autoregressive parameter in a first-order bifurcating autoregressive process with exponential innovations are derived. The limit distributions for the stationary, critical and explosive cases are unified via a single pivot, using a random normalization. The pivot is shown to be asymptotically exponential for all values of the autoregressive parameter.

TR Number: 
2003-16
J. Zhou and I.V. Basawa
Key Words: 
Bifurcating autoregression, exponential innovations, maximum likelihood, exact distribution, limit distribution, non-standard asymptotics

To request a copy of this report send an email to Richard Worthington and a pdf copy will be sent to you if available.

Explosive Random Coefficient AR(1) Processes and Related Asymptotics for Least Squares Estimation

Large sample properties of the least squares and weighted least squares estimates of the autoregressive parameter of an explosive random coefficient AR(1) process are discussed. It is shown that, contrary to the standard AR(1) case, the least-squares estimator is inconsistent whereas the weighted least-squares estimator is consistent and asymptotically normal even when the error process is not necessarily Gaussian.

TR Number: 
2003-17
S.Y. Hwang and I.V. Basawa
Key Words: 
Conditional asymptotics, explosive random coefficient AR(1) processes, least-squares estimation, martingale convergence theorem

To request a copy of this report send an email to Richard Worthington and a pdf copy will be sent to you if available.

Direction Estimation in Single-Index Regressions

We propose a general dimension-reduction method that combines the ideas of likelihood, correlation, inverse regression and information theory. We do not require that the dependence be confined to particular conditional moments, nor do we place restrictions on the predictors or on the regression that are necessary for methods like ordinary least squares and sliced inverse regression. Although we focus on single-index regressions, the underlying idea is applicable more generally. Illustrative examples are presented.

TR Number: 
2003-19
Xiangrong Yin and Dennis Cook
Key Words: 
Central mean subspace, Central subspace, Dimension-reduction subspace, Regression graphics, Single index model

To request a copy of this report send an email to Richard Worthington and a pdf copy will be sent to you if available.

MAGNet Program

We are excited to announce the partnership of the University of Georgia Department of Statistics and State Farm through State Farm's Modeling and Analytics Graduate Network (MAGNet) program.  The new program is set to begin this fall and will offer select master's degree students the opportunity to gain real-world experience while completing their degree. More information about this exciting opportunity may be found at https://stat.uga.edu/MAGNet.

Mon, 06/23/2014
Alumni News: 

Alumnus Appointed Barnhart Family Distinguished Professor at M.D. Anderson Cancer Center

Congratulations to Dr. Sanjay Shete for being appointed the Barnhart Family Distinguished Professor at M.D. Anderson Cancer Center effective June 1, 2014.  Dr. Shete obtained his Ph.D. in Statistics under the guidance of Dr. T.N. Sriram in 1998.  According to Dr. Sriram, Dr. Shete has been "scaling new heights for some years now...Sanjay really makes us all proud."

Thu, 05/15/2014
Alumni News: 

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