Sévérien Nkurunziza

Shrinkage estimation in general linear models

We propose a James-Stein-type shrinkage estimator for the parameter vector in a general linear model when it is suspected that some of the parameters may be restricted to a subspace. The James-Stein estimator is shown to demonstrate asymptotically superior risk performance relative to the conventional least squares estimator under quadratic loss. An extensive simulation study based on a multiple linear regression model and a logistic regression model further demonstrates the improved performance of this James-Stein estimator in finite samples. The application of this new estimator is illustrated using Ontario newborn infants data spanning four fiscal years.

The risk of pretest and shrinkage estimators

In this paper, we establish the risk function of a class of estimator for the mean parameter matrix of a matrix variate normal distribution. In particular, the established result is useful in evaluating the performance of a class of shrinkage-pretest-type estimators.

Likelihood ratio test for a special predator-prey system

In this paper, we study an inference problem for a stochastic model where the deterministic Lotka–Volterra system of ordinary differential equations (ODE) is perturbed with random error. The deterministic system describes the ecological interaction between prey and predator, but depends on unknown parameters. More precisely, we consider testing problems concerning the interaction parameters of the ODE. By assuming that the random errors follow correlated Ornstein–Uhlenbeck processes, we propose a likelihood ratio test and study the asymptotic properties of this test. Finally, we perform some simulation studies that corroborate our theoretical results and we apply the suggested test to two real data sets (Canadian mink-muskrat and paramecium-didinium data sets).

The bias and risk functions of some Stein-rules in elliptically contoured distributions

In this paper, we derive the bias and risk functions of a class of shrinkage estimators of several mean parameter matrices of matrix-variate elliptically contoured distributions. More specifically, we generalize some recent findings in three ways. First, the class of distributions under consideration is more general than the Gaussian distribution case, which is often studied in literature. Second, the uncertain subspace candidate is more general than that considered in literature. Finally, we generalize some recent identities, which are useful in establishing the risk and the bias of matrix shrinkage estimators.

Shrinkage and LASSO strategies in high-dimensional heteroscedastic models

ABSTRACT In this paper, we consider the estimation problem of the parameter vector in the linear regression model with heteroscedastic errors. First, under heteroscedastic errors, we study the performance of shrinkage-type estimators and their performance as compared to theunrestricted and restricted least squares estimators. In order to accommodate the heteroscedastic structure, we generalize an identity which is useful in deriving the risk function. Thanks to the established identity, we prove that shrinkage estimators dominate the unrestricted estimator. Finally, we explore the performance of high-dimensional heteroscedastic regression estimator as compared to classical LASSO and shrinkage estimators.

On extension of some identities for the bias and risk functions in elliptically contoured distributions

In this paper, we are interested in an estimation problem concerning the mean parameter of a random matrix whose distribution is elliptically contoured. We derive two general formulas for the bias and risk functions of a class of multidimensional shrinkage-type estimators. As a by product, we generalize some recent identities established in Gaussian sample cases for which the shrinking random part is a single Kronecker-product. Here, the variance-covariance matrix of the shrinking random part is the sum of two Kronecker-products.

Performance of risk-adjusted cumulative sum charts when some assumptions are not met

ABSTRACT Monitoring health care performance outcomes such as post-operative mortality rates has recently become more common, spurring new statistical methodologies designed for this purpose. One such methodology is the Risk-adjusted Cumulative Sum chart (RA-CUSUM) for monitoring binary outcomes such as mortality after cardiac surgery. When building RA-CUSUMs, independence and model correctness are assumed. We carry out a simulation study to examine the effect of violating these two assumptions on the charts performance.

Improved Estimation Strategy in Multi-Factor Vasicek Model

We consider simultaneous estimation of the drift parameters of multivari-ate Ornstein-Uhlebeck process. In this paper, we develop an improved estimation methodology for the drift parameters when homogeneity of several such parameters may hold. However, it is possible that the information regarding the equality of these parameters may not be accurate. In this context, we consider Stein-rule (or shrinkage) estimators to improve upon the performance of the classical maximum likelihood estimator (MLE). The relative dominance picture of the proposed estimators are explored and assessed under an asymptotic distributional quadratic risk criterion. For practical arguments, a simulation study is conducted which illustrates the behavior of the suggested method for small and moderate length of time observation period. More importantly, both analytical and simulation results indicate that estimators based on shrinkage principle not only give an excellent estimation accuracy but outperform the likelihood estimation uniformly.

Improving the Estimation of Eigenvectors Under Quadratic Loss

Improved estimation of eigenvectors of a covariance matrix is considered under uncertain prior information (UP!) regarding the parameter vector. Like statistical models underlying the statistical inferences to be made, the prior information will be susceptible to uncertainty and the practitioners may be reluctant to impose the additional information regarding parameters in the estimation process. A very large gain in precision may be achieved by judiciously exploiting the information about the parameters which in practice will be available in any realistic problem. Several estimators based on preliminary test and the Stein-type shrinkage rules are constructed. The expressions for the bias and risk of the proposed estimators are derived and compared with the usual estimators. We demonstrate how the classical large sample theory of the conventional estimator can be extended to shrinkage and preliminary test estimators for the eigenvector of a covariance matrix. It is established that shrinkage estimators are asymptotically superior to the usual sample estimators. For illustration purposes, the method is applied to three data sets.

Bayesian inference in time‐varying additive hazards models with applications to disease mapping

Environmental health and disease mapping studies are often concerned with the evaluation of the combined effect of various socio-demographic and behavioral factors, and environmental exposures on time-to-events of interest, such as death of individuals, organisms or plants. In such studies, estimation of the hazard function is often of interest. In addition to known explanatory variables, the hazard function maybe subject to spatial/geographical variations, such that proximally located regions may experience similar hazards than regions that are distantly located. A popular approach for handling this type of spatially-correlated time-to-event data is the Coxs Proportional Hazards (PH) regression model with spatial frailties. However, the PH assumption poses a major practical challenge, as it entails that the effects of the various explanatory variables remain constant over time. This assumption is often unrealistic, for instance, in studies with long follow-ups where the effects of some exposures on the hazard may vary drastically over time. Our goal in this paper is to offer a flexible semiparametric additive hazards model (AH) with spatial frailties. Our proposed model allows both the frailties as well as the regression coefficients to be time-varying, thus relaxing the proportionality assumption. Our estimation framework is Bayesian, powered by carefully tailored posterior sampling strategies via Markov chain Monte Carlo techniques. We apply the model to a dataset on prostate cancer survival from the US state of Louisiana to illustrate its advantages.