In partially linear model selection, we develop a profiled forward regression (PFR) algorithm for ultrahigh dimensional variable screening. The PFR algorithm effectively combines the ideas of nonparametric profiling and forward regression. This allows us to obtain a uniform bound for the...

When the functional data are not homogeneous, e.g., there exist multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this paper, we propose a new estimation procedure for the Mixture of Gaussian Processes, to incorporate both functional and...

We study the efficient estimation of nonparametric regressions with conditional heteroskedasticity in a time series setting. We introduce a weighted local polynomial regression smoother that takes account of the dynamic heteroskedasticity. The effect of weighting on nonparametric regressions is...

This paper studies the estimation of dynamic covariance matrices with multiple conditioning variables, where the matrix size can be ultra large (divergent at an exponential rate of the sample size). We introduce an easy-to-implement semiparametric method to estimate each entry of the covariance...

We consider two semiparametric models for the weight function in a biased sample model. The object of our interest parametrizes the weight function, and it is either Euclidean or non Euclidean. One of the models discussed in this paper is motivated by the estimation the mixing distribution of...

We propose a new semiparametric observation-driven volatility model where the form of the error density directly influences the volatility dynamics. This feature distinguishes our model from standard semiparametric GARCH models. The link between the estimated error density and the volatility...