Markov chain Monte Carlo (MCMC) methods have an important role in solving high dimensionality stochastic problems characterized by computational complexity. Given their critical importance, there is need for network and security risk management research to relate the MCMC quantitative...

In aftermath of the Financial Crisis, some risk management practitioners advocate wider adoption of Bayesian inference to replace Value-at-Risk (VaR) models for minimizing risk failures (Borison & Hamm, 2010). They claim reliance of Bayesian inference on subjective judgment, the key limitation...

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...

This paper develops optimal estimation of a potentially non-differentiable functional Γβ of a regular parameter β, when Γ satisfies certain conditions. Primary examples are min or max functionals that frequently appear in the analysis of partially identified models. This paper investigates...

We propose a novel varying coefficient model, called principal varying coefficient model (PVCM), by characterizing the varying coefficients through linear combinations of a few principal functions. Compared with the conventional varying coefficient model (VCM; Chen and Tsay, 1993; Hastie and...

We present some new asymptotic results for functionals of higher order differences of Brownian semi-stationary processes. In an earlier work we have derived a similar asymptotic theory for first order differences. However, the central limit theorems were valid only for certain values of the...

In order to discuss nonlinear, it is necessary to know linear regressive as a priori. Without simple regression as the starting point, it would be difficult to understand nonlinear regression. In words, in order to understand the curve and the behavior of a curve, it is necessary to known a...