I have published over 100 research articles on several theoretical and applied topics in statistics such as Dirichlet Processes; Survival Analysis; Reliability Theory; Goodness of Fit Tests; Kalman Filter; Parametric and Nonparametric Bayesian Inference. In the following, I shall outline the nature and significance of these publications.

 Dirichlet Processes:

  The theory of Dirichlet processes, introduced by Ferguson (Annals of Statistics, 1973), is one of the building blocks of an area in statistics called nonparametric Bayesian inference. In this area, inference procedures such as estimation and hypothesis testing are developed by combining experts' opinions and the information in the data, while making minimal assumptions about the probability structures governing the generation of data.

Seven of my papers, including one joint with Ferguson, contain fundamental results dealing with mathematical properties such as new constructive definition and the weak convergence of Dirichlet processes. A series of five papers contains derivation of results on mixtures of Dirichlet processes essential to the development of inference procedures based on complete and incomplete data arising in real life situations such as progressive censoring, nomination sampling, record of failure and follow-ups, record breaking data random censoring and random trunctation. All other papers on the Dirichlet process address applications of the process to regression, probability of discovering a new species, analysis of drug dependence data and competing risks models. The papers on drug dependence data are the only ones in the literature linking Dirichlet processes and epidemiology.

  Reliability is an area in applied statistics. Research in this area is most useful to engineers. All of my work in this area is directly applicable to statistical analysis of data in industry. A series of 11 papers contains hypothesis testing procedures for various classes of "Life Distributions" using complete and censored data. Efficiency and power of these procedures render them superior to their competitors under typical conditions. In the other subseries of 13 papers Bayesian approach is proposed for data analysis in a variety of situations. These methods allow engineers to incorporate their knowledge of the process into data analysis and hence are quite appealing.

Parametric Bayesian Inference: 

In the field of statistical inference, methodologies are developed to draw conclusions about the unknown characterisitic of a very large set of objects based on the information in the sample collected. According to Bayesian philosophy, even though actual numerical value of the characteristic is unknown, experts can usually narrow down the number of possibilities. This approach, given the advancement of knowledge in today's modern world, is most sensible as it allows experts in various fields to play a meaningful role in the analysis of the data. My work in this area consists of a series of 14 papers, including papers on Kalman Filter, that address problems arising in economic studies. This is a pioneering work bridging the gap between economics and Bayesian inference. Another series of 8 papers deals with problems in several areas including reliability analysis and cancer research.

The most significant contribution of my work in this area includes the spacings (gaps between ordered data points) to develop goodness of fit tests as alternatives to popular Chi-square procedure. These tests make more complete use of the information in the data, and as a result are more efficient than their rivals.

A recent series of 4 papers describe goodness of fit tests for cause specific hazard rates in nonparametric setup.

In practice, quite often the data collection is subject to censoring wherein the experiment is terminated before a measurement of interest is obtained. In a series of articles, I have derived theory and methods for censored data for a wide range of problems from inference on quantile functions to competing risks. A major portion of work on this topic has appeared in a recent series of articles in JASA and JMA.