Arun Kumar Kuchibhotla

Arun Kumar Kuchibhotla
  • PhD Student

Contact Information

  • office Address:

    450 Jon M. Huntsman Hall
    3730 Walnut Street
    Philadelphia, 19104

Overview

I completed B.Stat (Bachelors) and M.Stat (Masters) in statistics by 2015 starting from 2010 in Indian Statistical Institute, Kolkata.

Webpage: http://kuchibhotlaarunkumar.wordpress.com

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Research

I am currently working on wavelet non-parametric regression for random designs; the idea is to allow wavelets for single index model. I am interested in inference after selection of tuning parameters. This topic though closely related to post selection inference is different in the sense that I am not interested in model selection, it is more about selection of optimal criterion. I am also interested in self-normalized processes and high-dimensional central limit theorems.

  • Arun Kumar Kuchibhotla and Ayanendranath Basu (Draft), A Minimum Distance Weighted Likelihood Method of Estimation.

  • Arun Kumar Kuchibhotla, Lawrence D. Brown, Andreas Buja, Richard A. Berk, Linda Zhao, Edward I. George (Working), Valid Post-selection Inference in Assumption-lean Linear Regression.

    Abstract: This paper provides multiple approaches to perform valid post-selection inference in an assumption-lean regression analysis. To the best of our knowledge, this is the first work that provides valid post-selection inference for regression analysis in such a general settings that include independent, m-dependent random variables.

  • Arun Kumar Kuchibhotla, Rohit Kumar Patra, Bodhisattva Sen (Draft), Efficient Estimation in Convex Single Index Models.

    Abstract: We consider estimation and inference in a single index regression model with an unknown convex link function. We propose two estimators for the unknown link function: (1) a Lipschitz constrained least squares estimator and (2) a shape-constrained smoothing spline estimator. Moreover, both of these procedures lead to estimators for the unknown finite dimensional parameter. We develop methods to compute both the Lipschitz constrained least squares estimator (LLSE) and the penalized least squares estimator (PLSE) of the parametric and the nonparametric components given independent and identically distributed (i.i.d.) data. We prove the consistency and find the rates of convergence for both the LLSE and the PLSE. For both the LLSE and the PLSE, we establish root-n-rate of convergence and semiparametric efficiency of the parametric component under mild assumptions. Moreover, both the LLSE and the PLSE readily yield asymptotic confidence sets for the finite dimensional parameter. We develop the R package "simest" to compute the proposed estimators. Our proposed algorithm works even when n is modest and d is large (e.g., n=500, and d=100).

    Description: Authors listed in alphabetical order.

  • Arun Kumar Kuchibhotla, Somabha Mukherjee, Ayanendranath Basu (Draft), Statistical Inference based on Bridge Divergences.

    Description: M-estimators offer simple robust alternatives to the maximum likelihood estimator. Much of the robustness literature, however, has focused on the problems of location, location-scale and regression estimation rather than on estimation of general parameters. The density power divergence (DPD) and the logarithmic density power divergence (LDPD) measures provide two classes of competitive M-estimators (obtained from divergences) in general parametric models which contain the MLE as a special case. In each of these families, the robustness of the estimator is achieved through a density power down-weighting of outlying observations. Both the families have proved to be very useful tools in the area of robust inference. However, the relation and hierarchy between the minimum distance estimators of the two families are yet to be comprehensively studied or fully established. Given a particular set of real data, how does one choose an optimal member from the union of these two classes of divergences? In this paper, we present a generalized family of divergences incorporating the above two classes; this family provides a smooth bridge between the DPD and the LDPD measures. This family helps to clarify and settle several longstanding issues in the relation between the important families of DPD and LDPD, apart from being an important tool in different areas of statistical inference in its own right.

  • Arun Kumar Kuchibhotla and Ayanendranath Basu (2016), On The Asymptotics of Minimum Disparity Estimation, TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 22. 10.1007/s11749-016-0520-4

    Abstract: Inference procedures based on the minimization of divergences are popular statistical tools. Beran (1977) proved consistency and asymptotic normality of the minimum Hellinger distance (MHD) estimator. This method was later extended to the large class of disparities in discrete models by Lindsay (1994) who proved existence of a sequence of roots of the estimating equation which is consistent and asymptotically normal. However the current literature does not provide a general asymptotic result about the minimizer of a generic disparity. In this paper we prove, under very general conditions, an asymptotic representation of the minimum disparity estimator itself (and not just for a root of the estimating equation), thus generalizing the results of Beran (1977) and Lindsay (1994). This leads to a general framework for minimum disparity estimation encompassing both discrete and continuous models.

  • Andreas Buja, Richard A. Berk, Lawrence D. Brown, Edward I. George, Arun Kumar Kuchibhotla, Linda Zhao (2016), Models as Approximations, Part II: A General Theory of Model-Robust Regression, Statistical Science, (submitted).

  • Arun Kumar Kuchibhotla and Rohit Kumar Patra (Draft), Efficient Estimation in Single Index Models through Smoothing splines.

    Abstract: We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernel methods, we use smoothing splines to estimate the smooth link function. We develop a method to compute the penalized least squares estimators (PLSEs) of the parametric and the nonparametric components given independent and identically distributed (i.i.d.) data. We prove the consistency and find the rates of convergence of the estimators. We establish n^{-1/2}-rate of convergence and the asymptotic efficiency of the parametric component under mild assumptions. A finite sample simulation corroborates our asymptotic theory and illustrates the superiority of our procedure over kernel methods. We also analyze a car mileage data set and a ozone concentration data set. The identifiability and existence of the PLSEs are also investigated.

    Description: Authors listed in alphabetical order.

  • Arun Kumar Kuchibhotla and Ayanendranath Basu Robust Non-parametric Curve Estimation using Density Power Divergences.

    Description: This is a draft submitted to the Journal of Non-parametric Statistics. Not yet accepted.

  • Arun Kumar Kuchibhotla Testing in Additive and Projection Pursuit Models.

    Description: This was the paper submitted for ISI Jan Tinbergen Award 2015.

  • Arun Kumar Kuchibhotla and Ayanendranath Basu (2014), A general set up for minimum disparity estimation, Statistics and Probability Letters, 96, pp. 68-74.

Teaching

Past Courses

  • STAT111 - INTRODUCTORY STATISTICS

    Introduction to concepts in probability. Basic statistical inference procedures of estimation, confidence intervals and hypothesis testing directed towards applications in science and medicine. The use of the JMP statistical package.

Awards and Honors

  • ISI Jan TInbergen Award, 2015 Description

    The Jan Tinbergen Awards, named after the famous Dutch econometrician, are biannual awards to young statisticians from developing countries for best papers on any topic within the broad field of statistics. Up to three awards are made for each WSC (World Statistics Congress). The award was presented at ISI WSC 2015 held in Rio de Janeiro, Brazil. Some photos are included.

Activity

Latest Research

Arun Kumar Kuchibhotla and Ayanendranath Basu (Draft), A Minimum Distance Weighted Likelihood Method of Estimation.
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Awards and Honors

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