This paper presents two analytical formulations for the distribution of the square of a sum of products involving independent Rician random variables. The expressions are derived through the application of the central limit theorem (CLT) and Laguerre series. To assess their accuracy, the derived expressions are compared with the empirical distribution acquired through a comprehensive simulation study. The comparison is made based on the Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises statistics, supplemented by information criteria such as AIC and BIC as indicators of goodness of fit. Finally, an application in wireless communications is presented to illustrate the importance of the proposed work. As a conclusion, it is shown that the expression obtained by Laguerre expansion method is more accurate and simpler than the one obtained by CLT. Journal of Statistical Research 2025, Vol. 59, No. 2, pp. 203-219

Abstract is not available. Journal of Statistical Research 2025, Vol. 59, No. 1, pp. 1-4.

This research introduces and investigates four approaches for constructing confidence intervals (CIs) associated with the parameter of the Rama distribution—a model often applied in lifetime data modeling. The methods under consideration comprise the likelihood-based, Wald-type, bootstrap-t, and bias-corrected and accelerated (BCa) bootstrap intervals. To assess their practical utility, both Monte Carlo simulations and real data applications were utilized, emphasizing key performance indicators such as empirical coverage probability (ECP) and average width (AW) under various experimental conditions. To improve computational efficiency, a closed-form expression for the Wald-type CI was formulated. Simulation findings indicated that, across most situations, the ECPs obtained from both the likelihood-based and Wald-type CIs remained closely aligned with the nominal 95% confidence level. However, when the sample size was small, both the bootstrap-t and BCa bootstrap CIs yielded ECPs that fell short of the nominal level. As the sample size increased, the ECPs associated with these methods progressively approached the targeted confidence level, though variations in parameter values continued to influence their performance. The practical utility of these CIs was further validated through their application to two real-world datasets: monthly tax revenue in Egypt and plasma concentrations of indomethacin. The results from these applications were consistent with the findings of the simulation study, confirming the robustness and applicability of the proposed methods. Journal of Statistical Research 2025, Vol. 59, No. 1, pp. 107-129

This paper explores the financial and operational factors that contribute to India’s Nonperforming Assets (NPA) problem and discusses practical solutions for mitigating the risk of future NPAs. Descriptive statistics, regression analysis, and time series analysis are used to identify the main drivers of NPAs of Indian banks, revealing that high levels of NPAs have resulted in lower profitability, increased provisioning requirements, and higher borrowing costs. The findings and recommendations of this study provide valuable insights for policymakers, regulators, and banking practitioners seeking to reduce the risk of NPAs in India. Journal of Statistical Research 2024, Vol. 58, No. 2, pp. 335-351

In periodontal disease surveillance in human populations, full-mouth clinical examinations to classify the disease status of individuals are the gold standard for estimating periodontitis prevalence. However, conducting full-mouth exams is resource intensive, time consuming, and costly, especially in studies involving thousands of participants. Partial-recording protocols have been utilized in oral health surveys worldwide to gather correlated binary outcomes of periodontal disease on selected teeth in lieu of full-mouth exams. Since the use of partial-recording protocols tends to underestimate disease prevalence, a statistical distributional approach considering the pattern of tooth-level disease in the mouth was proposed to substantially reduce bias for the estimation of periodontitis prevalence. This approach employed multivariate Bernoulli distributions for observation (tooth)-level disease indicators to define formulae for the prevalence of disease (periodontitis) at the cluster (person)-level for various full-mouth case definitions. In turn, prevalence estimators were based on plug- in estimates of parameters from a conditional linear family for binary data gathered under partial recording protocols. Work in this article extended existing prevalence estimators for simple case definitions based on single clinical measures of tooth-level periodontal disease to a definition of severe periodontitis using two measures as defined by the Centers for Disease Control and Prevention and the American Academy of Periodontology, and later adopted by the 2017 World Workshop in Periodontology. Simulations evaluated the finite-sample performance of the proposed estimators and their confidence intervals for three established partial-recording protocols. In general, the prevalence estimators performed well relative to bias and coverage when tooth-level probabilities of disease and within-mouth correlation structures were correctly specified and even when the pattern of tooth-pair correlations was misspecified. Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 3-31.

In many randomized multi-visit studies, some response variables have an ordinal scale for outcomes. The win odds (accounts for ties) and the win ratio (ignores ties) are useful for treatment comparisons for ordinal outcomes. This paper discusses the application of randomization-based covariance and stratification adjustment of the win odds (and win ratio) to enable their more convenient use. Adjustment for strata is through the weighted average of within stratum two-sample U statistics for numerators and denominators for the stratified win odds (or win ratio). As randomization-based, invocation of covariance adjustment is through constraints to zeros for baseline covariate differences in the joint vector with logarithms of stratified win odds (or win ratios) for the respective visits. Such adjustment has no formal assumptions about the distributions of response variables or co-variates or the relationships of covariates to response variables; but the resulting adjusted stratified win odds (or win ratios) have narrower confidence intervals than their unadjusted counterparts when covariates have at least moderately strong associations with response variables. There is illustration of such results for the stratified win odds (and win ratio) for a randomized multi-visit clinical trial with an ordinal outcome for a chronic respiratory disorder. Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 33-48

In medical studies, a disease’s progress is often monitored through indicators that signify the improved or worsened condition of the patient. These are known as longitudinal biomarkers, which are observed along with an event of importance. Together, they form the framework of joint modeling, which has a longitudinal process and an inherently associated time-to-event process. In clinical studies, the change in biomarkers is often monitored in the form of a change in the patient’s plasma level after a drug is administered to the patient. Again, in such studies, patients also withdraw from the trials prematurely or at a later phase, thus giving rise to dropouts. In most cases, this dropout is not random (Missing Not at Random). A joint model has been considered to incorporate this informative dropout in longitudinal response. To demonstrate this approach, a one-compartmental pharmacokinetic (PK) nonlinear mixed-effects model consisting of time-dependent parameters has been used in this work. The dropout mechanism has been introduced using a proportional hazard model. A Bayesian model framework is adopted to study the model’s performance through detailed simulation. A PK study on the drug Divalproex subject to an informative dropout model has been discussed. Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 97-110.

Several methods have been proposed in the literature for computing unbiased and efficient estimates of the parameters of generalized linear models when the covariates are measured with error. However, to our knowledge, no documented research on computational techniques for parameter estimation currently exist in the literature when the data is a longitudinal count data influenced by an unobservable latent variable and observable covariates that are measured with error. In this paper, we propose a nonstationary conditionally Poisson mixed model for such data and develop unbiased estimating equations with iterative methods for computing estimates of the effect of the covariates, variance of the latent variable, and the correlation index parameter. The performance of the iterative methods is examined through extensive simulation studies. The results show that the methods performed well when the magnitude of the measurement error is not so large as to dominate or mask the effect of the true covariates. Using observed longitudinal count data on the number of patents awarded to 168 firms in the United States from 1974 to 1979 along with associated covariate information on the type of firm, log of the book value of capital in 1972 and research and development (R & D) expenditures we have demonstrated how the methods proposed in this paper can be applied to a real data. In addition, we derive the influence function of the estimator of the covariate effect and discuss the asymptotic properties of the estimator. Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 151-180.

This paper proposes a longitudinal integer-valued auto-regressive model of order one with Negative-Binomial marginals. The proposed model is suitable for analyzing repeated count data that exhibits significant over-dispersion at each time point and that is exposed to sev- eral time-dependent covariates. The estimation of the model parameters is handled by two non-likelihood approaches: The Generalized Quasi-likelihood (GQL) and the adaptive Quadratic Inference function (AQIF). The consistency of the model estimators is assessed via Monte Carlo simulation experiments and application to the epileptic seizures is made. The results demonstrate that both approaches GQL and AQIF yield reliable estimates but GQL provides better standard errors. Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 243-257.


 
 
 Model-based clustering utilizes a finite mixture model to identify underlying patterns or clusters across samples. A finite mixture model is a convex combination of two or more distributions, where appropriate distributions are chosen depending on the type of the data. Recently, there has been a great interest in clustering human microbiome data. Microbiome data are compositional (yielding relative abundance) and are high-dimensional. Previously, a family of logistic normal multinomial factor analyzers (LNM-FA) for model-based clus- tering of high-dimensional microbiome data was proposed via a factor analyzer structure. This reduced the number of parameters and computation overhead compared to a traditional mixtures of logistic normal multinomial models. Here, we propose a penalized LNM-FA (PLNM-FA) model by utilizing lasso regularization to each entry of the loading matrix. This introduces further parsimony compared to LNM-FA and also estimates the number of latent factors simultaneously. Parameter estimation is done using a variational variant of the alternating expectation conditional maximization algorithm to maximize the penalized maximum likelihood. The performance of proposed algorithm is evaluated using simula- tion studies and real data.
 Journal of Statistical Research 2022, Vol. 56, No. 2, pp.185-216