Showing papers by "Pranab Kumar Sen published in 1996"

Robust Statistical Procedures: Asymptotics and Interrelations

Abstract: ASYMPTOTICS AND INTERRELATIONS Preliminaries Robust Estimation of Location and Regression Asymptotic Representations for L-Estimators Asymptotic Representations for M-Estimators Asymptotic Representations for R-Estimators Asymptotic Interrelations of Estimators ROBUST STATISTICAL INFERENCE Robust Sequential and Recursive Point Estimation Robust Confidence Sets and Intervals Robust Statistical Tests Appendix References Indexes.

On smooth estimation of survival and density functions

Abstract: Incorporating the Hille theorem, smooth estimators of survival and density func- tions are considered , and their (asymptotic) properties are studied in an unified manner. A comparative picture of the so called kernel and nearest neighbor methods and the proposed one is presented with due emphasis on the (asymptotic) bias and mean square error criteria.

Regression rank scores estimation in ANOCOVA

Abstract: In semiparametric ANOCOVA (mixed-effects) models, the role of regression rank scores in robust estimation of fixed-effects parameters as well as covariate regression functionals is critically appraised, and the relevant asymptotic theory is presented.

Paired comparisons for multiple characteristics: An Anocova approach

Abstract: An analysis of covariance model is developed for paired comparisons to situations in which responses (on a preference order) to paired comparisons are obtained on some primary as well as concomitant traits. Along with the general rationality of the proposed test, its asymptotic properties are studied.

A Bivariate Exponential Model with Covariates in Competing Risk Data

Abstract: Sarkar's bivariate exponential distribution is incorporated in a competing risk model with two causes of failure. In view of the nonidentifiability of the parameters of this distribution under competing risk, reparameterization is advocated and covariates are related to the reparameterized parameters through logistic and loglinear models. The restricted alternative hypothe,is is considered for the comparison of the survival distributions of the two causes of failure, the test statistic based on Roy's unionintersection principle is used and compared with the score test statistic. An application is also considered,

The asymptotic covariance matrix for covariance estimators with standarization and raw-varimax rotation in factor analysis

Abstract: This work focuses on obtaining the analytical formulas for covariance matrix for covariance estimators of MLEs of standardized factor loadings with raw-varimax rotation in factor analysis. This is an extension of our previous work for unrotated case and we employed the same approach; as a first step, we expressed all the coordinatewise formulas that were previously derived by other researchers in terms of matrices. Then we obtained the necessary derivatives which map the differential of the sample covariance (or correlation) matrix (in vector form) into the differential of covariance estimators (in vector form). In obtaining the derivatives, we made extensive use of vec operator, Kronecker (direct) product, and the relevant properties.

4 Design and analysis of experiments: Nonparametric methods with applications to clinical trials

Abstract: Publisher Summary A sound statistical planning (design) of the experiment constitutes the first and foremost task in experimental studies. In a conventional setup, it is generally assumed that the response distribution is continuous, and further that it can be taken as normal whose mean (location parameter) depends linearly on the model based parameters, while the variance is a constant under varied experimental setups. The linearity of the model—that is, the additivity of the effects—homoscedasticity, and normality of the errors are the three basic regularity assumptions underlying the traditional parametric statistical analysis of experimental outcomes. In biological assays, biomedical and clinical experiments, the response variable is typically nonnegative and has a positively skewed distribution. Nonparametric and robust statistical procedures have their genesis in robustness and validity complex. Pedagogically, developments in nonparametrics started in the hypotheses testing sector, where under suitable hypotheses of invariance, the sample observations have a joint distribution which remains invariant under appropriate groups of transformations which map the sample space onto itself. This characterization of the null hypothesis generates exactly distribution-free (EDF) tests for some simple hypotheses testing problems.

Bivariate Survival Data Under Censoring: Simulation Procedure for Group Sequential Boundaries

Abstract: In clinical trials, ethical considerations dictate that the accumulating data be analyzed for potential early termination due to treatment differences or adverse effects. Group sequential procedures take into account the effect of such interim analyses in univariate cases. When the outcome is correlated bivariate, often the problem is simplified to a univariate situation with corresponding loss of information. We consider the bivariate exponential distribution of Sarkar to develop a parametric methodology for interim analysis of clinical trials. We first present the procedure for testing the hypothesis of no treatment difference assuming complete uncensored data. Secondly, we incorporate three types of censoring schemes into the procedure. Finally, we show how group sequential methods apply to the bivariate censored case. The method is illustrated by simulating two equal samples of size 500 from the bivariate exponential distribution of Sarkar. The samples for the experimental and the control groups were generated having mean failure times for each of the organs of 20 months and 16 months, respectively. Different correlations between the failure times of the organs were also considered. A program in C++ was written to obtain the estimators and standard errors using the Newton Raphson procedure and then we incorporated the group sequential procedures. Numerical results are presented.