Sugata Sen Roy

Estimation of regression parameters in the presence of outliers in the response

In this paper, we consider a regression model with non-spherical covariance structure and outliers in the response. The generalized least squares estimator obtained from the full data set is generally not used in the presence of outliers and an estimator based on only the non-outlying observations is preferred. Here we propose as an estimator a convex combination of the full set and the deleted set estimators and compare its performance with the other two.

Estimating the hazard functions of two alternately occurring recurrent events

Often two recurrent events of equal importance can occur alternately. The life-time patterns of the two events can then be of considerable interest. In this paper, we consider two such events, the inclusion and exclusion of players in a team sport, and study whether there is any inherent pattern in the time-lengths between these events. The life-time distributions are modelled and methods of estimating the model parameters suggested taking into account any relationship in the pattern of recurrence. The results are then applied to the inclusion and exclusion of players in the Indian national cricket team. As further illustration, a simulation study is made. Broad application areas are identified both in the introduction and conclusion.

Rate of convergence in the central limit theorem for parameter estimation in a causal, invertible ARMA(p, q) model

In this study we consider the estimators of the parameters of a stable ARMA(p, q) process. The autoregressive parameters are estimated by the instrumental variable technique while the moving average parameters are estimated using a derived autoregressive process. The estimators are shown to be asymptotically normal and their rate of convergence to normality is derived.

Rate of Convergence to Normality of Estimators in a Random Coefficient ARMA(p, q) Model

In this article, we consider a random coefficient ARMA(p, q) model with stable roots and show that the distribution of the estimators of the model parameters is asymptotically normal. The rate of convergence to normality is then derived.

A copula-based approach for estimating the survival functions of two alternating recurrent events

Abstract In this paper, we study the survival times of alternately occurring events. The dependence between the times to the two events is modelled through the Archimedean copula, while the dependence over the recurring cycles is modelled through a functional relationship of the distribution parameters. Taking account of appropriate censoring that may be present in the data, the model parameters are estimated using the maximum likelihood method. The standard errors of the estimators are then derived and confidence belts for the survival functions constructed. Methods for choosing the appropriate copula are also discussed. The results are illustrated through a clinical trial data on patients suffering from cystic fibrosis. A simulation study is also done to corroborate the results.

Measuring visible underemployment

In this paper we have looked into the problems of measuring visible underemployment. Some measures to gauge the intensity of visible underemployment have been suggested and their properties studied. Measures based on given time-norms for work are also suggested. The results are illustrated through examples.

Diagnostics of a Multiresponse Regression Model with Autocorrelated Errors

Ever since the early work of Cook (1977), extensive studies have been made on the diagnostics of multiple regression models with a single response using both the perturbation and the deletion techniques. Most of these studies were, however, applied to models with identically and independently distributed errors (refer Belsley, Kuh and Welsch (1980), Cook and Weisberg (1982) and Chatterjee and Hadi (1988) for a comprehensive discussion). The studies were later extended to models with correlated error structures. In the generalized least-squares context, Putterman (1988) studied the influence of the first transformed observation on the parameter estimates. Schall and Dunne (1988) distinguished three types of outliers for the general linear model with arbitrary known variance-covariance structure and developed a unified approach to test for the presence of these outliers and a method of adjusting the parameter estimates when such outliers are present. Martin (1992) considered a linear regression model with completely specified error covariance structure and generalized the usual measures based on leverages and residuals. Cerioli and Riani (2002) proposed a new robust technique for the analysis of spatial data through simultaneous autoregressive models. Sen Roy and Guria (2004) applied the deletion technique to a regression model with first-order autoregressive errors and obtained explicit expressions of the diagnostic measures. Zewotir and Galpin (2007) extended the standard diagnostic tools to a linear mixed model.

Missing Values in Linear Regression: Imputations Using An Error-Contaminated Linear Predictor

The problem of missing values problem is common in all branches of statistics and especially in regression analysis. Here we consider estimation of the regression parameters in the presence of missingness in the response. The usual method is to replace the missing value by its predicted value based on the available observations without any correction for the disturbance term. Instead we suggest a method which corrects the usual predictor with a guess of the disturbance term based on the available residuals. Comparison between the two methods shows that the latter leads to better results.

Why do we Attend Refresher Courses? - A Case Study of Preference Data Analysis

Abtsrcat Participants of a refresher course sponsored by the University Grants Commission (UGC) of India were asked to rank six possible reasons for attending the course. They were later also asked to rate the reasons on a five point preference scale. In this paper, our objective is to characterise and quantify the preference for these six reasons. Standard methods for the analysis of contingency tables are not appropriate for ranked preference data so we develop a variant of the y measure of association for ordinal data to examine excess preference in pairwise comparisons. The bootstrap is used to derive p-values and condence intervals for the proposed statistic. Finally, we fit a Bradley-Terry regression model to the rankings and estimate the preference for each reason in terms of ‘worth’ parameters. We repeat this analysis on the ratings data and estimate the worth parameters as functions of covariates. The model is further extended to include dependencies between the ratings. Salient results indicate that career advancement has the highest preference across all covariate classes while the preference for service to society is by far the lowest. However, the magnitude of the preferences is influenced by the number of years for which a participant has taught and whether or not he holds a doctoral degree. There are some differences in conclusions from the analysis of the ratings and rankings datasets.