Mode estimation for a bivariate distribution

Abstract

Given a sequence of independent and identically distributed random vectors $(X_1, Y_1),(X_2,Y_2),(X_3, Y_3),.....,(X_n,Y_n)$ with a unimodal bivariate distribution function F(x,y), a consistent estimator of the mode, $(theta_x,theta_y)$ is proposed by using spacings as defined by J.H. Venter (1967) (Ann. Math. Statist., 38, 1446-1455) for univariate distributions. The method is illustrated for a bivariate distribution.