arXiv subjects

Aritra Chakravorty

Publications and source records attributed to Aritra Chakravorty.

3 recordsLinked to original sources

arXiv2023

Distributed estimation through parallel approximants

Designing scalable estimation algorithms is a core challenge in modern statistics. Here we introduce a framework to address this challenge based on parallel approximants, which yields estimators with provable properties that operate on the entirety of very large, distributed data sets. We first formalize the class of statistics which admit straightforward calculation in distributed environments through independent parallelization. We then show how to use such statistics to approximate arbitrary functional operators in appropriate spaces, yielding a general estimation framework that does not require data to reside entirely in memory. We characterize the $L^2$ approximation properties of our approach and provide fully implemented examples of sample quantile calculation and local polynomial regression in a distributed computing environment. A variety of avenues and extensions remain open for future work.

stat.ME↗

arXiv2022

Scalable $k$-d trees for distributed data

Data structures known as $k$-d trees have numerous applications in scientific computing, particularly in areas of modern statistics and data science such as range search in decision trees, clustering, nearest neighbors search, local regression, and so forth. In this article we present a scalable mechanism to construct $k$-d trees for distributed data, based on approximating medians for each recursive subdivision of the data. We provide theoretical guarantees of the quality of approximation using this approach, along with a simulation study quantifying the accuracy and scalability of our proposed approach in practice.

cs.DS↗

arXiv2013

Estimating Copula and Test of Independence based on a generalized framework of all rank-based Statistics in Bivariate Sample

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of formulating a multivariate distribution in such a way that various general types of dependence can be represented. In case of bivariate sample, the notion of estimating copula is closely related to that of testing independence in a bivariate sample, as when the components of the bivariate sample are independent the copula becomes simply product of two uniform distributions. So apart from non-parametric estimation of copulas we also considered it relevant to introduce some non-parametric tests to better understand the very essence of copula in the explanation of association between the components. In fact we will develop a general multivariate statistics that gives rise to a much larger class of non-parametric rank based statistics. This class of statistics can be used in estimation and testing for the association present in the bivariate sample. We choose some representative statistics from that class and compared their power in testing independence using simulation as an attempt to choose the best candidate in that class.

stat.ME↗