Nonparametric inference on jump regression surface

Estimators for jump location curve and jump size function of a two dimensional jump regression function (jump regression surface) are proposed. The estimators are obtained by fitting kernel weighted least squares regression based on the observations in the four quadrants of a neighborhood of a given point. The proposed procedure can be used in the case of jump in the regression surface and/or in its slope (jump in the partial derivatives). The limiting distributions and the asymptotic properties of the estimators are investigated. The procedure is illustrated through a simulation study.