arXiv subjects

Nabendu Pal

Publications and source records attributed to Nabendu Pal.

5 recordsLinked to original sources

arXiv2026

Analysis of Nonnegative Observations using Gamma Model with 2 Factors (ANOGaM-2): Theory, Method and Applications with Real-life Data (including R code)

Two-factor ANOVA is widely used in experimental studies but relies on additivity, normality, independence, and homoscedasticity. These assumptions are often violated for nonnegative, positively skewed observations. Although Box--Cox-type transformations are commonly used, they may reduce interpretability and require a subjective choice of transformation. We propose an alternative framework in which nonnegative observations affected by two factors are modeled by gamma distributions with unknown shape and scale parameters that may depend on factor levels. We develop likelihood ratio tests (LRTs) for main and interaction effects. The asymptotic LRT (ALRT) uses the asymptotic chi-square distribution, which may be inaccurate for small to moderate samples. We therefore propose a parametric bootstrap LRT (PBLRT) that determines critical values by simulation. Extensive simulations show that the PBLRT maintains the nominal significance level well. Real-data examples demonstrate its applicability and show that its inferences can differ from those of traditional ANOVA.

stat.ME↗

arXiv2026

A Revisit to Point Estimation Through the Empirical Bayes Method: The Case of Binomial Distribution with Beta Prior and Extension to Poisson Distribution

Between the classical (frequentist) approach, which is based solely on the data, and a fully Bayesian set-up where one assumes a prior distribution for the model parameters, lies the Empirical Bayes (EB) approach which appears to be a good compromise between the aforementioned two approaches. Even though many researchers have suggested various variants of the EB method, the standard practice is to derive the Bayes estimator under a family of suitable priors indexed by its own parameter(s), called the hyperparameter(s), and then replace the unknown hyperparameter(s) by their estimate(s) obtained from the marginal distribution of the data. But the fundamental question that is being raised here is: does the EB method really work to produce an improved estimator - the so-called Empirical Bayes Estimator (EBE)? In this work we are going to revisit the widely cited simple problem of estimating a Binomial parameter using the regular two-parameter Beta family of priors under the quadratic loss function, and prove that the Type-II maximum likelihood (ML-II) step does not work. If we further restrict our attention to one-parameter symmetric Beta family of priors then still the resultant EBE does not show any remarkable performance compared to the MLE details of which have been provided with extensive computations. The Binomial study has been extended to the Poisson model as well.

stat.ME↗

arXiv2026

Bivariate Frank Copula: Some More Results on Point Estimation of the Association Parameter from a Bayesian Perspective and Revisiting the Goodness of Fit Tests with an Application to Model Groundwater Data from Dong Thap, Vietnam

This work has two major parts. First, we extend the recent study of Pham et al. (2025) on point estimation of the association parameter of a bivariate Frank copula. We investigate two Bayes estimators under the generalized flat prior and the Jeffreys prior, and compare them with the maximum likelihood estimator (MLE). Simulation results show that, for small sample sizes (n <= 25), the Bayes estimator under the Jeffreys prior uniformly outperforms both the generalized flat prior estimator and the MLE in terms of mean squared error (MSE). For moderate and large sample sizes, all estimators have very similar performances in terms of bias and MSE. We also discuss computational issues in the R package implementation that may significantly affect the computation of the MLE for very small samples. In the second part, we apply the Frank copula to analyze the association between groundwater arsenic concentration and other hydrochemical variables using a recent dataset from Vietnam. We revisit the goodness-of-fit tests proposed by Genest et al. (2006), investigate several non-intuitive behaviors of the test statistics, and provide extensive simulated critical value tables. Our results complement and refine the computational findings reported in the earlier literature.

stat.ME↗

arXiv2025

Some Results on Point Estimation of the Association Parameter of a Bivariate Frank Copula

This work deals with estimation of the association parameter of a bivariate Frank Copula in a comprehensive way. Even though Frank Copula is a member of Archimedean class of copulas, and has been widely used in finance, relatively little attention has been paid to its association parameter from a statistical inferential point of view. Most of the existing works which have used Frank Copula have focused on estimating the parameter computationally, and then proceeded with its application in the applied fields, mostly in finance. Here, in this investigation, we have looked at the point estimation of the association parameter in a comprehensive manner, and studied three estimators in terms of bias, mean squared error (MSE), relative bias and relative MSE. It has been noted that in the neighborhood of zero, the method of moment estimators (MMEs) do perform well compared to the maximum likelihood estimator (MLE), even though the latter has the best overall performance. Further, in terms of bias, MMEs and MLE have opposite behavior. However, some of our results do not match with those reported by Genest (1987) \cite{Genest1987}. Nevertheless, this study complements Genest's (1987)\cite{Genest1987} expository work, and provides some interesting insights into the behaviors of three point estimators including the MLE whose asymptotic behavior holds pretty well, as we have found, for $n\ge 75$.

stat.ME↗

arXiv2025

A revisit to maximum likelihood estimation of Weibull model parameters

In this work, we revisit the estimation of the model parameters of a Weibull distribution based on iid observations, using the maximum likelihood estimation (MLE) method which does not yield closed expressions of the estimators. Among other results, it has been shown analytically that the MLEs obtained by solving the highly non-linear equations do exist (i.e., finite), and are unique. We then proceed to study the sampling distributions of the MLEs through both theoretical as well as computational means. It has been shown that the sampling distributions of the two model parameters' MLEs can be approximated fairly well by suitable Weibull distributions too. Results of our comprehensive simulation study corroborate some recent results on the first-order bias and first-order mean squared error (MSE) expressions of the MLEs.

stat.CO↗