In this paper, the only assumptions on the distribution of data are those concerning first two moments. Our purpose is to estimate the parameter of interest in the presence of nuisance parameter under these weak assumptions on the distribution. We define a quasi-least favorable curve and...

The lasso and its variants have attracted much attention recently because of its ability of simultaneous estimation and variable selection. When some prior knowledge exists in applications, the performance of estimation and variable selection can be further improved by incorporating the prior...

To test heteroscedasticity in single index models, in this paper two test statistics are proposed via quadratic conditional moments. Without the use of dimension reduction structure, the first test has the usual convergence rate in nonparametric sense. Under the dimension reduction structure of...