We propose a constrained least square estimator of the transformation function of a partially linear single-index transformation model, where the transformation function, single-index function and error distribution are all nonparametric. The estimators of the regression coefficients and the single-index function are provided by the similar idea to the minimum average variance estimation method. Basis function approximation is employed to estimate the transformation and single-index functions, and cross validation criteria are proposed to select suitable sets of basis functions. Asymptotical properties of the estimators in the sense of almost sure convergence are established. Simulations studies show that our proposed estimators work well. A real-world data analysis of total health care charges was used to illustrate the proposed procedure.
University of Washington