In this paper, we study the local polynomial composite quantile regression (CQR) smoothing method for the nonlinear and nonparametric models under the Harris recurrent Markov chain framework. The local polynomial CQR regression method is a robust alternative to the widely-used local polynomial...

Ultrahigh dimensional data with both categorical responses and categorical covariates are frequently encountered in the analysis of big data, for which feature screening has become an indispensable statistical tool. We propose a Pearson chi-square based feature screening procedure for...

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...

It is not unusual for the response variable in a regression model to be subject to censoring or truncation. Tobit regression models are a specific example of such a situation, where for some observations the observed response is not the actual response, but rather the censoring value...

Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being...

For multivariate nonparametric regression models, existing variable selection methods with penalization require high-dimensional nonparametric approximations in objective functions. When the dimension is high, none of methods with penalization in the literature are readily available. Also,...

There has been considerable attention on estimation of conditional variance function in the literature. We propose here a nonparametric model for conditional covariance matrix. A kernel estimator is developed accordingly, its asymptotic bias and variance are derived, and its asymptotic normality...

In linear regression models with high dimensional data, the classical z-test (or t-test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and...

Investigation of the characteristics and estimation of quantities of hidden and hard-to-access population are of interest to scientists. Such populations are difficult to target because of their elusive nature or other prohibitive characteristics. So crafting designs of a representative sample...