Asymptotic optimality of the nonnegative garrote estimator in threshold models

Abstract

In this paper, it is aimed to broad Xiong's scope of analysis to the threshold models and develop an adjusted Mallows criterion to select the garrote parameter vector. Compared with other penalized least-squares methods, the nonnegative garrote (NG) method has a natural penalty and tuning parameter. Furthermore, we show the asymptotic optimality of the NG estimator by referring to the idea of the asymptotic optimality of the model averaging estimator under some regular conditions. Our investigation of finite-sample performance demonstrates that the proposed method exhibits very favorable properties with respect to the ratio of the correct number of zero estimated components (RCNZ) and the root mean square error (RMSE) compared to the least absolute shrinkage and selection operator (LASSO), the smoothly clipped absolute deviation (SCAD) and the minimax concave penalty (MCP) penalized regression methods. The proposed method is applied to the analysis of body fat data, soil respiration data and the US unemployment rate data and performs well.