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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Inference Using Shape-Restricted Regression Splines

Regression splines are smooth, flexible, and parsimonious nonparametric function estimators. They are known to be sensitive to knot number and placement, but if assumptions such as monotonicity or convexity may be imposed on the regression function, the shape-restricted regression splines are much more robust to knot choices. Monotone regression splines were introduced by Ramsay (1988). In this paper a more numerically efficient computational method is developed, and the method is extended to convex constraints.

TR Number: 
2006-05
Mary C. Meyer

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A simple derivation of the sampling distribution of the sample mean and the sample variance of a normal random sample

First we provide a simple derivation of the density of a chi-square random variable. Then we provide another simple proof of the statistical independence of the sample mean and the sample variance of a random sample from a normal distribution. The technique proving independence readily extends to the multivariate case.

TR Number: 
2007-02
Gauri Sankar Datta
Key Words: 
Chi-square distribution; Moment generating function; Wishart distribution.

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Software for Implementing the Sequential Elimination of Level Combinations Algorithm

Genetic algorithms (GAs) are a popular technology to search for an optimum in a large search space. Using new concepts of forbidden array and weighted mutation, Mandal, Wu and Johnson (2006) used elements of GAs to introduce a new global optimization technique called sequential elimination of level combinations (SELC), that efficiently finds optimums. A SAS macro, and Matlab and R functions are developed to implement the SELC algorithm.

TR Number: 
2007-03
Tan Ding, Abhyuday Mandal and Kjell Johnson

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Quantile Estimation for Discrete Data via Empirical Likelihood

Quantile estimation for discrete distributions has not been well studied, although discrete data are common in practice. Under the assumption that data are drawn from a discrete distribution, we examine the consistency of the maximum empirical likelihood estimator (MELE) of the pth population quantile µp, with the assistance of a jittering method and results for continuous distributions. The MELE and the sample quantile estimator are closely related, and they may or may not be consistent for µp, depending on whether or not the underlying distribution has a plateau at the level of p.

TR Number: 
2007-04
Jien Chen and Nicole Lazar
Key Words: 
Discrete distributions; Jittering; Bootstrap.

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