Ralph A. Bradley

Ralph Bradley's contributions to the world of statistics fall under two headings: his statistical research (especially the Bradley-Terry Test used extensively in taste testing experiments) and his professional leadership role in statistical science, as evidenced by his development of statistical programs, by his Presidency (1981) of the American Statistical Association and by his editorial efforts. The conversation in Statistical Science (5) provides more details of his views and life.

TR Number: 
2002-25
Lynne Billard
Key Words: 
Ralph A. Bradley

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Non-Gaussian Bifurcating Models and Quasilikelihood Estimation

A general class of Markovian non-Gaussian bifurcating models for cell lineage data is presented. Examples include bifurcating autoregression, random coefficient autoregression, bivariate exponential, bivariate gamma, and bivariate Poisson models. Quasilikelihood estimation for the model parameters and large-sample properties of the estimates are discussed.

TR Number: 
2003-1
I.V. Basawa and J. Zhou
Key Words: 
Tree-Indexed Data, Bifurcating Autoregressive Models, Maximum Likelihood, Quasilikelihood Estimation, Markovian Models

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Inference in Shape-Restricted Regression with Time Series Data

Testing a constant mean (no trend) null hypothesis against an increasing alternative is frequently of interest to the time series analyst. Often a linear function is imposed as the alternative trend, sometimes by default as merely the simplest nonconstant function. This paper studies tests for trends with more general shape-restricted alternatives, which include nondecreasing and convex functions. Shape-restricted alternatives comprise a broad range of trends and may be appropriate when the alternative trend structure is not well understood.

TR Number: 
2003-2
Mary C. Meyer and Robert Lund
Key Words: 
Autocovariance, autoregression, convex regression, misspecified trend, monotone regression, trend estimation

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A Novel Empirical Bayes Adjustment to Increase the True Discovery Rate of Detecting Differentially Expressed Genes in Microarray Experiments

Motivation: Detection of differentially expressed genes is one of the major goals of microarray experiments. Pairwise comparison for each gene is not appropriate without controlling the overall (experimentwise) type 1 error rate. Dudoit et al. have advocated use of permutation-based step-down P-value adjustments to correct the observed significance levels for the individual (i.e., for each gene) two sample t-tests.

TR Number: 
2003-3
Susmita Datta, Glen A. Satten, Dale J. Benos, Jiazeng Xia, Marty Heslin, and Somnath Datta

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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

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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

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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: 

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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

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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

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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

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