New estimation and inference procedures for a single-index conditional distribution model

This article employs a more flexible single-index regression model to characterize the conditional distribution. The pseudo least integrated squares approach is proposed to estimate the index coefficients. As shown in the numerical results, our estimator outperforms the existing ones in terms of the mean squared error. Moreover, we provide the generalized cross-validation criteria for bandwidth selection and utilize the frequency distributions of weighted bootstrap analogues for the estimation of asymptotic variance and the construction of confidence intervals. With a defined residual process, a test rule is built to check the correctness of an applied single-index conditional distribution model. To tackle the problem of sparse variables, a multi-stage adaptive Lasso algorithm is developed to enhance the ability of identifying significant variables. All of our procedures are found to be easily implemented, numerically stable, and highly adaptive to a variety of data structures. In addition, we assess the finite sample performances of the proposed estimation and inference procedures through extensive simulation experiments. Two empirical examples from the house-price study in Boston and the environmental study in New York are further used to illustrate applications of the methodology.