234 Weil Hall
1949 Stadium Road
Gainesville, FL 32611
Rohit Patra, Ph.D.
Department of Statistics, University of Florida
Abstract: Inference in Two Problems Where the Loss Function is not Convex
Problem 1: Wireless sensor networks (WSNs) serve as key technological infrastructure for monitoring diverse systems across space and time. Examples of their widespread applications include: precision agriculture, surveillance, animal behavior, drone tracking, and emergent disaster response and recovery. A WSN consists of hundreds or thousands of identical sensors at fixed locations where each individual sensor observes the surrounding at fixed time intervals. In this work we estimate the location of a (signal emitting) target under the assumption that magnitude of signal detected at the sensor is a strictly decreasing function of the distance between the sensor and the signal emitting target. We propose an automated root-n-consistent estimator of the location the target under under only the monotonicity assumption. Our estimator is tuning parameter free. We show that our estimator has a Gaussian limit distribution and construct asymptotic confidence region for the location target. This is a joint work with George Michailidis and Moulinath Banerjee.
Problem 2: We consider estimation and inference in a single index regression model with an unknown convex link function. We propose a Lipschitz constrained least squares estimator (LLSE) for both the parametric and the nonparametric components given independent and identically distributed observations. We prove the consistency and find the rates of convergence of the LLSE when the errors are assumed to have only q≥2 moments and are allowed to depend on the covariates. In fact, we prove a general theorem which can be used to find the rates of convergence of LSEs in a variety of nonparametric/semiparametric regression problems under the same assumptions on the errors. Moreover when q≥5, we establish n^1/2-rate of convergence and asymptotic normality of the estimator of the parametric component. Moreover the LLSE is proved to be semiparametrically efficient if the errors happen to be homoscedastic. This is a joint work with Arun Kuchibhotla and Bodhisattva Sen.
Department of Industrial and Systems Engineering at the University of Florida