arXiv subjects

Abhijit Mandal

Publications and source records attributed to Abhijit Mandal.

31 records · Page 2Linked to original sources

arXiv2019

An Optimal Test for the Additive Model with Discrete or Categorical Predictors

In multivariate nonparametric regression the additive models are very useful when a suitable parametric model is difficult to find. The backfitting algorithm is a powerful tool to estimate the additive components. However, due to complexity of the estimators, the asymptotic $p$-value of the associated test is difficult to calculate without a Monte Carlo simulation. Moreover, the conventional tests assume that the predictor variables are strictly continuous. In this paper, a new test is introduced for the additive components with discrete or categorical predictors, where the model may contain continuous covariates. This method is also applied to the semiparametric regression to test the goodness-of-fit of the model. These tests are asymptotically optimal in terms of the rate of convergence, as they can detect a specific class of contiguous alternatives at a rate of $n^{-1/2}$. An extensive simulation study is presented to support the theoretical results derived in this paper. Finally, the method is applied to a real data to model the diamond price based on its quality attributes and physical measurements.

stat.ME↗

arXiv2019

Stratified Random Sampling for Dependent Inputs

A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations of functions of the corresponding output variables. The advantage of the proposed method over the existing methods is that it preserves the exact form of the joint distribution on the input variables. The asymptotic distribution of the new estimator is derived. Asymptotically, the variance of the estimator using the proposed method is less than that obtained using the simple random sampling, with the degree of variance reduction depending on the degree of additivity in the function being integrated. This technique is applied to a practical example related to the performance of the river flood inundation model.

stat.ME↗

arXiv2018

The B-Exponential Divergence and its Generalizations with Applications to Parametric Estimation

In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed, where the defining convex function has an exponential nature. These estimators avoid the necessity of using an intermediate kernel density and many of them also have strong robustness properties. It is further demonstrated that the proposed approach can be extended to construct a class of generalized estimating equations, where the pool of the resultant estimators encompass a large variety of minimum divergence estimators and range from highly robust to fully efficient based on the choice of the tuning parameters. All of the resultant estimators are M-estimators, where the defining functions make explicit use of the form of the parametric model. The properties of these estimators are discussed in detail; the theoretical results are substantiated by simulation and real data examples. It is observed that in many cases, certain robust estimators from the above generalized class provide better compromises between robustness and efficiency compared to the existing standards.

stat.ME↗

arXiv2018

A Robust Wald-type Test for Testing the Equality of Two Means from Log-Normal Samples

The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis for comparing the means of two independent log-normal distributions is an issue of significant interest. In this paper we present a robust test for this problem. The unknown parameters of the model are estimated by minimum density power divergence estimators (Basu et al 1998, Biometrika, 85(3), 549-559). The robustness as well as the asymptotic properties of the proposed test statistics are rigorously established. The performance of the test is explored through simulations and real data analysis. The test is compared with some existing methods, and it is demonstrated that the proposed test outperforms the others in the presence of outliers.

stat.ME↗

arXiv2016

A Wald-type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator

In this paper a robust version of the classical Wald test statistics for linear hypothesis in the logistic regression model is introduced and its properties are explored. We study the problem under the assumption of random covariates although some ideas with non random covariates are also considered. The family of tests considered is based on the minimum density power divergence estimator instead of the maximum likelihood estimator and it is referred to as the Wald-type test statistic in the paper. We obtain the asymptotic distribution and also study the robustness properties of the Wald type test statistic. The robustness of the tests is investigated theoretically through the influence function analysis as well as suitable practical examples. It is theoretically established that the level as well as the power of the Wald-type tests are stable against contamination, while the classical Wald type test breaks down in this scenario. Some classical examples are presented which numerically substantiate the theory developed. Finally a simulation study is included to provide further confirmation of the validity of the theoretical results established in the paper.

math.ST↗

arXiv2016

Phase transition and critical phenomena of black holes: A general approach

We present a general framework to study the phase transition of a black hole. Assuming that there is a phase transition, it is shown that without invoking any specific black hole, the critical exponents and the scaling powers can be obtained. We find that the values are exactly same which were calculated by taking explicit forms of different black hole spacetimes. The reason for this universality is also explained. The implication of the analysis is -- one does not need to investigate this problem case by case, what the people are doing right now. We also observe that these, except two such quantities, are independent of the details of the spacetime dimensions.

gr-qc↗

arXiv2015

Testing Composite Hypothesis based on the Density Power Divergence

In any parametric inference problem, the robustness of the procedure is a real concern. A procedure which retains a high degree of efficiency under the model and simultaneously provides stable inference under data contamination is preferable in any practical situation over another procedure which achieves its efficiency at the cost of robustness or vice versa. The density power divergence family of Basu et al. (1998) provides a flexible class of divergences where the adjustment between efficiency and robustness is controlled by a single parameter $β$. In this paper we consider general tests of parametric hypotheses based on the density power divergence. We establish the asymptotic null distribution of the test statistic and explore its asymptotic power function. Numerical results illustrate the performance of the theory developed.

stat.ME↗

arXiv2015

Thermodynamic Products for Einstein-Gauss-Bonnet Black Hole with α-Corrected Entropy Term

In the present work, we consider a charged black hole in five dimensional Einstein-Gauss-Bonnet gravity where the α corrected entropy term is considered. We examine the horizon radii product, entropy product, Hawking temperature product and free energy product for both event horizon and Cauchy horizon. Our motive is to check whether the same quantity for event horizon and Cauchy horizon is free of mass, i.e., global or not. We further study the stability of such black hole by computing the specific heat and free energy for both the horizons. All these calculation might be helpful to understand the microscopic nature of such black holes.

physics.gen-ph↗

arXiv2015

Influence Analysis of Robust Wald-type Tests

We consider a robust version of the classical Wald test statistics for testing simple and composite null hypotheses for general parametric models. These test statistics are based on the minimum density power divergence estimators instead of the maximum likelihood estimators. An extensive study of their robustness properties is given though the influence functions as well as the chi-square inflation factors. It is theoretically established that the level and power of these robust tests are stable against outliers, whereas the classical Wald test breaks down. Some numerical examples confirm the validity of the theoretical results.

math.ST↗

arXiv2015

Quantum Corrected Schwarzschild Black Hole: Inner Horizon Thermodynamic Behaviors

The thermodynamic properties of Cauchy horizon is a matter of interest. Event horizon and Cauchy horizon together can enlighten us about the micro-states of a black hole. In addition, if we consider a black hole metric modified with quantum terms, which is not forcing the geodesics to focus at a singularity, the study of horizons becomes much more interesting. The spacelike behavior inside the Cauchy horizon has a deep impact on the related thermodynamics. We analyze different thermodynamic product to check whether a right left string theory mode's addition type representation for the concerned thermodynamic parameters is possible or not. Stability of Cauchy horizon is studied.

gr-qc↗

arXiv2015

Black Hole Thermodynamic Products in Einstein Gauss Bonnet Gravity

We study the thermodynamic properties of black hole horizons in Einstein Gauss Bonnet gravity. We derive the thermodynamic products of characteristic parameters to mark which are global. We further interpret the stability of the black holes by computing the specific heat for both horizons. Stable and unstable phases of horizons are pointed out. The phase transitions with respect to the charge in nature of specific heat are also observed. All these calculation might be helpful to understand the microscopic nature of such black holes.

gr-qc↗

arXiv2015

Generalized Wald-type Tests based on Minimum Density Power Divergence Estimators

In testing of hypothesis the robustness of the tests is an important concern. Generally, the maximum likelihood based tests are most efficient under standard regularity conditions, but they are highly non-robust even under small deviations from the assumed conditions. In this paper we have proposed generalized Wald-type tests based on minimum density power divergence estimators for parametric hypotheses. This method avoids the use of nonparametric density estimation and the bandwidth selection. The trade-off between efficiency and robustness is controlled by a tuning parameter $β$. The asymptotic distributions of the test statistics are chi-square with appropriate degrees of freedom. The performance of the proposed tests are explored through simulations and real data analysis.

stat.ME↗

arXiv2014

Robust Tests for the Equality of Two Normal Means based on the Density Power Divergence

Statistical techniques are used in all branches of science to determine the feasibility of quantitative hypotheses. One of the most basic applications of statistical techniques in comparative analysis is the test of equality of two population means, generally performed under the assumption of normality. In medical studies, for example, we often need to compare the effects of two different drugs, treatments or preconditions on the resulting outcome. The most commonly used test in this connection is the two sample $t$-test for the equality of means, performed under the assumption of equality of variances. It is a very useful tool, which is widely used by practitioners of all disciplines and has many optimality properties under the model. However, the test has one major drawback; it is highly sensitive to deviations from the ideal conditions, and may perform miserably under model misspecification and the presence of outliers. In this paper we present a robust test for the two sample hypothesis based on the density power divergence measure (Basu et al., 1998), and show that it can be a great alternative to the ordinary two sample $t$-test. The asymptotic properties of the proposed tests are rigorously established in the paper, and their performances are explored through simulations and real data analysis.

stat.ME↗