arXiv subjects

Soumendra Nath Lahiri

Publications and source records attributed to Soumendra Nath Lahiri.

3 recordsLinked to original sources

arXiv2020

Two-sample Testing on Latent Distance Graphs With Unknown Link Functions

We propose a valid and consistent test for the hypothesis that two latent distance random graphs on the same vertex set have the same generating latent positions, up to some unidentifiable similarity transformations. Our test statistic is based on first estimating the edge probabilities matrices by truncating the singular value decompositions of the averaged adjacency matrices in each population and then computing a Spearman rank correlation coefficient between these estimates. Experimental results on simulated data indicate that the test procedure has power even when there is only one sample from each population, provided that the number of vertices is not too small. Application on a dataset of neural connectome graphs showed that we can distinguish between scans from different age groups while application on a dataset of epileptogenic recordings showed that we can discriminate between seizure and non-seizure events.

stat.ME↗

arXiv2019

A Statistical Analysis of Noisy Crowdsourced Weather Data

Spatial prediction of weather-elements like temperature, precipitation, and barometric pressure are generally based on satellite imagery or data collected at ground-stations. None of these data provide information at a more granular or "hyper-local" resolution. On the other hand, crowdsourced weather data, which are captured by sensors installed on mobile devices and gathered by weather-related mobile apps like WeatherSignal and AccuWeather, can serve as potential data sources for analyzing environmental processes at a hyper-local resolution. However, due to the low quality of the sensors and the non-laboratory environment, the quality of the observations in crowdsourced data is compromised. This paper describes methods to improve hyper-local spatial prediction using this varying-quality noisy crowdsourced information. We introduce a reliability metric, namely Veracity Score (VS), to assess the quality of the crowdsourced observations using a coarser, but high-quality, reference data. A VS-based methodology to analyze noisy spatial data is proposed and evaluated through extensive simulations. The merits of the proposed approach are illustrated through case studies analyzing crowdsourced daily average ambient temperature readings for one day in the contiguous United States.

stat.AP↗

arXiv2017

Second Order Correctness of Perturbation Bootstrap M-Estimator of Multiple Linear Regression Parameter

Consider the multiple linear regression model $y_{i} = \boldsymbol{x}'_{i} \boldsymbolβ + ε_{i}$, where $ε_i$'s are independent and identically distributed random variables, $\mathbf{x}_i$'s are known design vectors and $\boldsymbolβ$ is the $p \times 1$ vector of parameters. An effective way of approximating the distribution of the M-estimator $\boldsymbol{\barβ}_n$, after proper centering and scaling, is the Perturbation Bootstrap Method. In this current work, second order results of this non-naive bootstrap method have been investigated. Second order correctness is important for reducing the approximation error uniformly to $o(n^{-1/2})$ to get better inferences. We show that the classical studentized version of the bootstrapped estimator fails to be second order correct. We introduce an innovative modification in the studentized version of the bootstrapped statistic and show that the modified bootstrapped pivot is second order correct (S.O.C.) for approximating the distribution of the studentized M-estimator. Additionally, we show that the Perturbation Bootstrap continues to be S.O.C. when the errors $ε_i$'s are independent, but may not be identically distributed. These findings establish perturbation Bootstrap approximation as a significant improvement over asymptotic normality in the regression M-estimation.

math.ST↗