First Order Random Coefficient Integer-valued Autoregressive Processes

A random coefficient INAR(1) model is introduced. Ergodicity of the process is established. Moments and autocovariance functions are obtained. Conditional least squares and quasi-likelihood estimators of the model parameters are derived and their asymptotic properties are established. The performance of these estimators are compared with the maximum likelihood estimator via simulation.

2005-3

TR Number: 
2005-03
H. Zheng, I. V. Basawa and S. Datta

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Dimension Reduction Via Marginal High Moments in Regression

Using central k-th moment subspace, Yin and Cook (2002) decomposed Sliced Inverse Regression (SIR) into focused marginal moment method, COV_k. Under central subspace, Ye and Weiss (2003) also studied general relations among SIR, sliced average variance estimate (SAVE), and Principal Hessian Direction (PHD) to form a new class of dimension reduction methods. In this note, by forming a new marginal method via inverse second moment called PHD_k for estimating directions in the central k-th moment subspace, we are able to decompose SAVE into some focused marginal moment methods.

TR Number: 
2005-04
Xiangrong Yin and R. Dennis Cook

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Generalized Least Squares Estimation for Explosive AR(1) Processes with Conditionally Heteroscedastic Errors

This article is concerned with explosive AR(1) processes generated by conditionally heteroscedastic errors. Conditional least squares as well as generalized least squares estimation for autoregressive parameter are discussed and relevant limiting distributions are expressed as products of certain random variables. These results can be viewed as generalizations of classical results obtained for the standard explosive AR(1) model with i.i.d. errors(cf. Fuller(1996, Ch.10)).

TR Number: 
2005-05
S.Y. Hwang, S. Kim, S.D. Lee, and I.V. Basawa

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A Novel Approach to Testing Equality of Survival Distributions When the Group Memberships are Censored

This paper introduces a novel nonparametric approach for testing the equality of two of more survival distributions when the group membership information are not available for the right censored individuals. Although such data structures arise in practice very often, this problem has received less than satisfactory treatment in the nonparametric testing literature. Currently there is no nonparametric test for this hypothesis in its full generality in the presence of right censored data.

TR Number: 
2005-06
Dipankar Bandyopadhyay and Somnath Datta

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Bias, Variance, Skewness and Kurtosis of Maximum Likelihood Estimators Using Maple*

The object of this paper is to describe the development of ideas of pertaining to sample size and maximum likelihood estimators of parameters associated with a probability function or density function. About forty years ago we considered a Taylor type series for a maximum likelihood estimator for qa, there being s parameters. First order bias and first order variance were included. Because of limitations in computer facilities, the skewness and kurtosis were avoided, and also because of the complicated structures involved.

TR Number: 
2005-07
K.O. Bowman and L. R. Shenton

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Inference for pth Order Random Coefficient Integer-Valued Autoregressive Processes

Random coefficient INAR(p) models are proposed for count data. Stationarity and ergodicity properties are established. Conditional least squares, modified quasi-likelihood and generalized method of moments are used to estimate the model parameters. Asymptotic properties of the estimates are derived. Simulation results on the comparison of the three estimates are reported. The model is applied to a real data set on epileptic seizure.

TR Number: 
2005-08
H. Zheng, I. V. Basawa and S. Datta

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Optimal and Efficient Crossover Designs When Subject Effects Are Random

Most studies on optimal crossover designs are based on models that assume subject effects to be fixed effects. In this paper we identify and study optimal and efficient designs for a model with random subject effects. With the number of periods not exceeding the number of treatments, we find that totally balanced designs are universally optimal for treatment effects in a large subclass of competing designs.

TR Number: 
2005-09
A.S. Hedayat, John Stufken and Min Yang

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Complete Enumeration of Two-Level Orthogonal Arrays of Strength d With d + 2 Constraints

Enumerating nonisomorphic orthogonal arrays is an important, yet very difficult problem. Although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases, general results are extremely rare. In this paper, we provide a complete solution to enumerating nonisomorphic two-level orthogonal arrays of strength d with d + 2 constraints for any d and any run size n = l2d. Our results not only give the number of nonisomorphic orthogonal arrays for given d and n, but also provide a systematic way of explicitly constructing these arrays.

TR Number: 
2005-10
John Stufken and Boxin Tang

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Optimal Crossover Designs for Two Treatments in the Presence of Mixed and Self Carryover Effects

The main purpose of this paper is to identify optimal crossover designs for two treatments under a model that includes mixed and self carryover effects. In addition, results are reported for optimal two-treatment crossover designs under several closely related models, and the performance of various designs for three and four periods is studied under the different models.

TR Number: 
2005-11
J. Kunert and John Stufken

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New Balanced Sampling Plans Excluding Adjacent Units

Hedayat, Rao, and Stufken (1988a and 1988b) first introduced balanced sampling designs for the exclusion of contiguous units. Sampling plans that excluded the selection of contiguous units within a given sample, while maintaining a constant second order inclusion probability for non-contiguous units, were investigated for finite populations of N units arranged in a circular, one-dimensional ordering. There remain many open questions about the existence of such plans and their extension to plans excluding adjacent units.

TR Number: 
2005-12
James H. Wright and John Stufken

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