B0331
Title: Spatial modal regression
Authors: Tao Wang - University of Victoria (Canada) [presenting]
Abstract: Modal regression with spatial data $\{(Y_i, X_i); i \in Z^N\}$ observed over a rectangular domain is proposed to be estimated by assuming that the conditional mode of the response variable $Y_i$ given covariates $X_i$ follows a nonparametric regression structure, defined as $m:X \mapsto m(X)=Mode(Y_i \mid X_i)$. We study the newly developed spatial modal regression by utilizing the local linear approximation augmented with shrinking bandwidths. The asymptotic normal distributions of the proposed spatial modal estimators are established, and the explicit formulas for their asymptotic biases and variances are derived under mild regularity assumptions. We also show that the targeted spatial modal regression could be used as an alternative to a nonparametric spatial mean robust regression when the data are symmetrically distributed. The asymptotic distributions for such a spatial modal-based robust estimator are derived with the appropriate choices of bandwidths. We, in the end, generalize the propounded spatial modal regression model to an additive sum of the form in order to avoid the issue of the curse of dimensionality and develop a kernel-based backfitting algorithm for estimating, where we show that the proposed spatial modal estimator of each additive component is asymptotically normal and converges at the univariate nonparametric modal optimal rate.
