Showing papers by "Pranab Kumar Sen published in 2010"

A linear exponent AR(1) family of correlation structures

Abstract: In repeated measures settings, modeling the correlation pattern of the data can be immensely important for proper analyses. Accurate inference requires proper choice of the correlation model. Optimal efficiency of the estimation procedure demands a parsimonious parameterization of the correlation structure, with sufficient sensitivity to detect the range of correlation patterns that may occur. Many repeated measures settings have within-subject correlation decreasing exponentially in time or space. Among the variety of correlation patterns available for this context, the continuous-time first-order autoregressive correlation structure, denoted AR(1), sees the most utilization. Despite its wide use, the AR(1) structure often poorly gauges within-subject correlations that decay at a slower or faster rate than required by the AR(1) model. To address this deficiency we propose a two-parameter generalization of the continuous-time AR(1) model, termed the linear exponent autoregressive (LEAR) correlation structure, which accommodates much slower and much faster decay patterns. Special cases of the LEAR family include the AR(1), compound symmetry, and first-order moving average correlation structures. Excellent analytic, numerical, and statistical properties help make the LEAR structure a valuable addition to the suite of parsimonious correlation models for repeated measures data. Both medical imaging data concerning neonate neurological development and longitudinal data concerning diet and hypertension [DASH (Dietary Approaches to Stop Hypertension) study] exemplify the utility of the LEAR correlation structure.

Statistical inference in nonlinear regression under heteroscedasticity

Abstract: Nonlinear regression models are commonly used in toxicology and pharmacology. When fitting nonlinear models for such data, one needs to pay attention to error variance structure in the model and the presence of possible outliers or influential observations. In this paper, an M-estimation based procedure is considered in heteroscedastic nonlinear regression models where the standard deviation is modeled by a nonlinear function. The methodology is illustrated using toxicological data.

M-procedures in the general multivariate nonlinear regression model

Abstract: In the multivariate nonlinear regression model, parameter estimators and test statistics based on least squares and maximum likelihood methods are usually nonrobust. For this type of models, we introduce M-estimators and M-tests, which are robust to departures from normality. In addition, we study the asymptotic properties and consider a computational algorithm for these estimators.

The Theil–Sen estimator in a measurement error perspective

Abstract: In a simple measurement error regression model, the classical least squares estimator of the slope parameter consistently estimates a discounted slope, though sans normality, some other properties may not hold It is shown that for a broader class of error distributions, the Theil-Sen estimator, albeit nonlinear, is a median-unbiased, consistent and robust estimator of the same discounted parameter For a general class of nonlinear (including R−,M− and L− estimators), study of asymptotic properties is greatly facilitated by using some uniform asymptotic linearity results, which are, in turn, based on conti- guity of probability measures This contiguity is established in a measurement error model under broader distributional assumptions Some asymptotic prop- erties of the Theil-Sen estimator are studied under slightly different regularity conditions in a direct way bypassing the contiguity approach

Life and Work of Bhaskar Kumar Ghosh

Abstract: Bhaskar Ghosh, affectionately used to be addressed as Kumar by his colleagues and friends, died at an age of 72, of a heart problem on August 3, 2008. He is survived by his three daughters, Monica, Anita, and Rebecca; his wife Hedwig Graf passed away a year earlier. I have the privilege of knowing Bhaskar from our college days back in the early 1950s, collaborating with him in some statistical research, and more so in editorial activities. I take this opportunity to write a short biography of Bhaskar and appraise some aspects of his contributions to statistics with special emphasis on sequential methods. In particular, this journal, Sequential Analysis, was founded largely through the untiring efforts of Bhaskar, and I am proud to be a founding editor jointly with him. We (at least I) will miss him for quite sometime.

A KPSS better than KPSS Rank tests for short memory stationarity

Abstract: We propose a rank-test of the null hypothesis of short memory stationarity possibly after linear detrending. For the level-stationarity hypothesis, the test statistic we propose is a modied version of the popular KPSS statistic, in which ranks substitute the original observations. We prove that the rank KPSS statistic shares the same limiting distribution as the standard KPSS statistic under the null and diverges under I(1) alternatives. For the trend-stationarity hypothesis, we apply the same rank KPSS statistic to the residual of a Theil-Sen regression on a linear trend. We derive the asymptotic distribution of the Theil-Sen estimator under short memory errors and prove that the Theil-Sen detrended rank KPSS statistic shares the same weak limit as the least-squares detrended KPSS. We study the asymptotic relative eciency