Using the Markowitz mean-variance portfolio optimization theory, researchers have shown that the traditional estimated return greatly overestimates the theoretical optimal return, especially when the dimension to sample size ratio p/n is large. Bai, Liu, and Wong (2009) propose a...

This paper proposes the spectral corrected methodology to estimate the Global Minimum Variance Portfolio (GMVP) for the high dimensional data. In this paper, we analysis the limiting properties of the spectral corrected GMVP estimator as the dimension and the number of the sample set increase to...

Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile regression applied to the tails, is of interest in many...

Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile regression applied to the tails, is of interest in many...

In this paper, we propose a Markov Chain Quasi-Monte Carlo (MCQMC) approach for Bayesian estimation of a discrete-time version of the stochastic volatility (SV) model. The Bayesian approach represents a feasible way to estimate SV models. Under the conventional Bayesian estimation method for SV...

We consider median regression and, more generally, quantile regression in high-dimensional sparse models. In these models the overall number of regressors p is very large, possibly larger than the sample size n, but only s of these regressors have non-zero impact on the conditional quantile of...

This paper considers flexible conditional (regression) measures of market risk. Value-at-Risk modeling is cast in terms of the quantile regression function - the inverse of the conditional distribution function. A basic specification analysis relates its functional forms to the benchmark models...

Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile regression applied to the tails, is of interest in many...

This paper develops a theory of high and low (extremal) quantile regression: the linear models, estimation, and inference. In particular, the models coherently combine the convenient, flexible linearity with the extreme-value-theoretic restrictions on tails and the general heteroscedasticity...

In this work we study the large sample properties of the posterior-based inference in the curved exponential family under increasing dimension. The curved structure arises from the imposition of various restrictions, such as moment restrictions, on the model, and plays a fundamental role in...