Consistency and Asymptotic Distribution of Regression Estimators from the Inverted Plot Q-Q

A simple graphic, the "inverted q-q plot," enables visualization of the monotonic function that transforms data to a desired target distribution. An important special case is use of the Box-Cox family to transform data to a normal distribution. This graphic can be used to develop novel estimates of parameters in a transformation. We describe here the asymptotic properties of these parameter estimates.

TR Number: 
2004-18
Glen A. Satten and Somnath Datta

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Convergence Properties of an Adaptive Kernel Density Estimator for Finite Mixture Models

Kernel smoothing methods are widely used in many areas of statistics with great success. In particular, minimum distance procedures heavily depend on kernel density estimators. It has been argued that when estimating mixture parameters in finite mixture models, adaptive kernel density estimators would be preferable over non-adaptive kernel density estimators. Cutler and Cordero-Brana (1996) introduced such an adaptive kernel density estimator for the minimum Hellinger distance estimation in finite mixture models.

TR Number: 
2004-19
R. J. Karunamuni, J. Wu and T. N. Sriram

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Combining Functional Information in Selecting Clustering Algorithms

Motivation: A cluster analysis is the most commonly performed procedure (often regarded as a first step) on a set of gene expression profiles. Numerous attempts have been made in the literature in order to validate the results of an existing or a novel clustering algorithm often within the context of microarray data analysis. A closely related problem is that of selecting a clustering algorithm that is optimal in some way from a rather impressive list of clustering algorithms that currently exist.

TR Number: 
2004-20
Susmita Datta and Somnath Datta

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Common Canonical variates for Independent Groups Using Information Theory

Suppose that data on (X, Y) are collected from C independent but closely related populations and one is interested in measuring the amount of relationship between sets of variables Y and X within each population. Goria and Flury (1996) argued that in these situations it is more meaningful to construct common canonical variates that are identical across populations, while the canonical correlations themselves may vary across populations. Their method of constructing common canonical variates is based on classical normal theory and is more suitable for measuring only linear relationships.

TR Number: 
2005-01
Xiangrong Yin and T.N. Sriram

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An Alternative Derivation of the Distributions of the Maximum Likelihood Estimators of the Parameters in an Inverse Gaussian Distribution

In this note we provide a simpler derivation of the sampling properties of the maximum likelihood estimators of the parameters in an inverse Gaussian distribution described below.

TR Number: 
2005-02
Gauri Sankar Datta

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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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