arXiv subjects

Nabaneet Das

Publications and source records attributed to Nabaneet Das.

6 recordsLinked to original sources

arXiv2026

Estimation of the complexity of a network under a Gaussian graphical model

The proportion of edges in a Gaussian graphical model (GGM) characterizes the complexity of its conditional dependence structure. Since edge presence corresponds to a nonzero entry of the precision matrix, estimation of this proportion can be formulated as a large-scale multiple testing problem. We propose an estimator that combines p-values from simultaneous edge-wise tests, conducted under false discovery rate control, with Storey's estimator of the proportion of true null hypotheses. We establish weak dependence conditions on the precision matrix under which the empirical cumulative distribution function of the p-values converges to its population counterpart. These conditions cover high-dimensional regimes, including those arising in genetic association studies. Under such dependence, we characterize the asymptotic bias of the Schweder--Spj{\o}tvoll estimator, showing that it is upward biased and thus slightly underestimates the true edge proportion. Simulation studies across a variety of models confirm accurate recovery of graph complexity.

stat.ME↗

arXiv2024

Estimation of Proportion of Null Hypotheses Under Dependence

Estimation of the proportion of null hypotheses in a multiple testing problem can greatly enhance the performance of the existing algorithms. Although various estimators for the proportion of null hypotheses have been proposed, most are designed for independent samples, and their effectiveness in dependent scenarios is not well explored. This article investigates the asymptotic behavior of the BH estimator and evaluates its performance across different types of dependence. Additionally, we assess Storey's estimator and another estimator proposed by Patra and Sen (2016) to understand their effectiveness in these settings.

math.ST↗

arXiv2023

Correction Factor of FWER for Normal Distribution in Nearly Independent Setup

In this paper, we have attempted to study the behaviour of the family wise error rate (FWER) for Bonferroni's procedure in a nearly independent setup for normal distribution. In search for a suitable correlation penalty, it has been noted that the root mean square (RMS) of correlations is not appropriate under this setup as opposed to the study of \cite{efron2007correlation}. We have provided a suitable correction factor for deviation from independence and approximated the FWER under this nearly independent setup.

math.ST↗

arXiv2023

Optimal test statistic under normality assumption

The idea of an optimal test statistic in the context of simultaneous hypothesis testing was given by Sun and Tony Cai (2009) which is the conditional probability of a hypothesis being null given the data. Since we do not have a simplified expression of the statistic, it is impossible to implement the optimal test in more general dependency setup. This note simplifies the expression of optimal test statistic of Sun and Tony Cai (2009) under the multivariate normal model. We have considered the model of Xie et. al.(2011), where the test statistics are generated from a multivariate normal distribution conditional to the unobserved states of the hypotheses and the states are i.i.d. Bernoulli random variables. While the equivalence of LFDR and optimal test statistic was established under very stringent conditions of Xie et. al.(2016), the expression obtained in this paper is valid for any covariance matrix and for any fixed 0<p<1. The optimal procedure is implemented with the help of this expression and the performances have been compared with Benjamini Hochberg method and marginal procedure.

math.ST↗

arXiv2020

Observation on F.W.E.R. and F.D.R. for correlated normal

In this paper, we have attempted to study the behaviour of the family wise error rate (FWER) for Bonferroni's procedure and false discovery rate (FDR) of the Benjamini-Hodgeberg procedure for simultaneous testing problem with equicorrelated normal observations. By simulation study, we have shown that F.W.E.R. is a concave function for small no. of hypotheses and asymptotically becomes a convex function of the correlation. The plots of F.W.E.R. and F.D.R. confirms that if non-negative correlation is present, then these procedures control the type-I error rate at a much smaller rate than the desired level of significance. This confirms the conservative nature of these popular methods when correlation is present and provides a scope for improvement in power by appropriate adjustment for correlation.

stat.ME↗

arXiv2019

Bound on FWER for correlated normal distribution

In this paper,our main focus is to obtain an asymptotic bound on the family wise error rate (FWER) for Bonferroni-type procedure in the simultaneous hypotheses testing problem when the observations corresponding to individual hypothesis are correlated. In particular, we have considered the sequence of null hypotheses H_{0i} : X_i follows N(0,1) , (i=1,2,....,n) and equicorrelated structure of the sequence (X_1,....,X_n). Distribution free bound on FWER under equicorrelated setup can be found in Tong(2014). But the upper bound provided in Tong(2014) is not a bounded quantity as the no. of hypotheses(n) gets larger and larger and as a result,FWER is highly overestimated for the choice of a particular distribution (e.g.- normal). In the equicorrelated normal setup, we have shown that FWER asymptotically is a convex function (as a function of correlation (rho)) and hence an upper bound on the FWER of Bonferroni-(alpha) procedure is alpha(1-\rho).This implies,Bonferroni's method actually controls the FWER at a much smaller level than the desired level of significance under the positively correlated case and necessitates a correlation correction.

math.ST↗