Value at Risk is a fundamental tool for managing market risks. It measures the worst loss to be expected of a portfolio over a given time horizon under normal market conditions at a given confidence level. Calculation of VaR frequently involves estimating the volatility of return processes and quantiles of standardized returns. In this paper, several semiparametric techniques are introduced to estimate the volatilities of the market prices of a portfolio. In addition, both parametric and nonparametric techniques are proposed to estimate the quantiles of standardized return processes. The newly proposed techniques also have the flexibility to adapt automatically to the changes in the dynamics of market prices over time. Their statistical efficiencies are studied both theoretically and empirically. The combination of newly proposed techniques for estimating volatility and standardized quantiles yields several new techniques for forecasting multiple period VaR. The performance of the newly proposed VaR estimators is evaluated and compared with some of existing methods. Our simulation results and empirical studies endorse the newly proposed time-dependent semiparametric approach for estimating VaR.

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With modern technology, massive data can easily be collected in a form of multiple sets of curves. New statistical challenge includes testing whether there is any statistically significant difference among these sets of curves. In this article we propose some new tests for comparing two groups of curves based on the adaptive Neyman test and the wavelet thresholding techniques introduced earlier by Fan. We demonstrate that these tests inherit the properties outlined by Fan and that they are simple and powerful for detecting differences between two sets of curves. We then further generalize the idea to compare multiple sets of curves, resulting in an adaptive high-dimensional analysis of variance, called HANOVA. These newly developed techniques are illustrated by using a dataset on pizza commercials where observations are curves and an analysis of cornea topography in ophthalmology where images of

Estimation of longitudinal data covariance structure poses significant challenges because the data usually are collected at irregular time points. A viable semiparametric model for covariance matrixes has been proposed that allows one to estimate the variance function nonparametrically and to estimate the correlation function parametrically by aggregating information from irregular and sparse data points within each subject. But the asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of parameters in the covariance model are largely unknown. We address this problem in the context of more general models for the conditional mean function, including parametric, nonparametric, or semiparametric. We also consider the possibility of rough mean regression function and introduce the difference-based method to reduce biases in the context of varying-coefficient partially linear mean regression

Discrepancy is a kind of important measure used in experimental design. Recently, a so-called discrete discrepancy has been applied to evaluate the uniformity of factorial designs. In this paper, we review some recent advances on application of the discrete discrepancy to several common experimental designs and summarize some important results.