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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First-order Observation-drive Integer-valued Autoregressive Processes

A first-order observation-driven integer-valued autoregressive model is introduced. Ergodicity of the process is established. Conditional least squares and maximum likelihood estimators of the model parameters are derived. The performances of these estimators are compared via simulation. The models are applied to a real data set.

TR Number: 
2006-01
Haitao Zheng and Ishwar V. Basawa

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Shape-Restricted Regression Splines

Regression splines are smooth, flexible, and parsimonious nonparametric function estimators, but the fits are sensitive to the choice of the number and placement of the knots. When a priori knowledge about the regression function includes monotonicity or convexity as well as smoothness, the shape-restricted versions of the regression splines may be used. These fits are more satisfactory as they satisfy shape requirements, with the additional benefit of insensitivity to the knot choices.

TR Number: 
2006-02
Mary C. Meyer

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Estimation of Process Parameters to Determine the Optimum Diagnosis Interval for Control of Defective Items

The on-line quality monitoring procedure for attributes proposed by Taguchi has been critically studied and extended by a few researchers. Determination of the optimum diagnosis interval requires estimation of some parameters related to the process failure mechanism. Improper estimates of these parameters may lead to incorrect choice of the diagnosis interval and consequently huge economic penalties. In this paper, we highlight both the theoretical and practical problems associated with the estimation of these parameters, and propose a structured approach to solve them.

TR Number: 
2006-03
Tirthankar Dasgupta and Abhyuday Mandal

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