A Test for Linear vs. Convex Regression FUnction Using Shape-Restricted Regression

An unbiased test for the appropriateness for the simple linear regression model is presented. The null hypothesis is that the underlying regression function is indeed a line, and the alternative is that it is convex. The exact distribution for a likelihood ration test statistics is that of a mixture of beta random variables, with the mixing distribution calculated from relative volumes of polyhedral convex cones determined by the convex shape restriction.

TR Number: 
2002-19
Mary C. Meyer
Key Words: 
Convex regression, effective dimension, likelihood ration test

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Comparisons and Validation of Statistical Clustering Techniques for Microarray Gene Expression Data

Motivation:  With the advent of microarray chip technology, large data sets are emerging containing the simultaneous expression levels of thousands of genes at various time points during a biological process. Biologists are attempting to group genes based on the temporal pattern of their expression levels. While the use of hierarchical clustering (UPGMA) with correlation "distance" has been the most common in the microarray studies, there are many more choices of clustering algorithms in pattern recognition and statistics literature.

TR Number: 
2002-20
Susmita Datta and Somnath Datta
Key Words: 

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Multiplex Relative Risk and Estimation of the Number of Loci Underlying an Inherited Disease

Knowledge of the number of causative loci is necessary to estimate the power of mapping studies of complex diseases. IN this paper we re-examine theory developed by Risch (1990a) and its implications for estimating the number L of causative loci affection a complex inherited disease. We first show that methods based on Risch's analysis can produce estimates of L that are inconsistent with the observed population prevalence of the disease.

TR Number: 
2002-21
Paul Schliekelman and Montgomery Slatkin
Key Words: 

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Transient Dynamics in Multilocus Invasions by Transgenic Organisms

With recent advances in molecular genetics, it is likely that releases of genetically modified organisms will be used for a variety of purposes. In many cases, such systems would utilize organisms that have been modified on multiple genetic Ioci. Predicting the effect of such releases will require an understanding of the transient dynamics in the system. However, theoretical understanding of transient dynamics in multilocus systems is limited, particularly for early generations when gametic disequilibrium is still high.

TR Number: 
2002-22
Paul Schliekelman
Key Words: 

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First-Order Seasonal Autoregressions with Periodic Autocorrelations

A time series model combining a first-order periodic autoregressive structure with classical Box-Jenkins seasonality is introduced. Periodic stationarity conditions for the model are established and its autocovariance function is derived. The limit distribution of least squares estimates of the model parameters are obtained.

TR Number: 
2002-23
Ishwar V. Basawa, Robert Lund and Qin Shao
Key Words: 
Periodic time series, seasonality, autoregression, periodic autocovariances, asymptotics

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Multivariate Multilevel Nonlinear Mixed Effects Models for Timber Yield Projections

Nonlinear mixed-effects models have become important tools for growth and yield modeling in forestry. To date, applications have concentrated on modeling single growth variables such as tree height or bole volume. Here, we propose multivariate multilevel nonlinear mixed effects models for describing several plot-level timber quantity characteristics simultaneously. We describe how such models can be used to produce future predictions of timber volume (yield).

TR Number: 
2002-24
Daniel B. Hall and Michael Clutter
Key Words: 
Clustered Data, Growth, Prediction, Random Effects, Repeated Measures, Volume

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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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