Stochastic Spanning

ABSTRACT

This study develops and implements methods for determining whether introducing new securities or relaxing investment constraints improves the investment opportunity set for all risk averse investors. We develop a test procedure for “stochastic spanning” for two nested portfolio sets based on subsampling and linear programming. The test is statistically consistent and asymptotically exact for a class of weakly dependent processes. A Monte Carlo simulation experiment shows good statistical size and power properties in finite samples of realistic dimensions. In an application to standard datasets of historical stock market returns, we accept market portfolio efficiency but reject two-fund separation, which suggests an important role for higher-order moment risk in portfolio theory and asset pricing. Supplementary materials for this article are available online.     

Estimating the distribution function of a transformed random vector

Frequently a random vector Y with known distribution function is readily observed. However, the random variable of interest is a transformation of Y say h(Y), and sample values of h are expensive to evaluate. The objective is to estimate the distribution function of using only a small sample on Y. Four estimators are proposed for use when Y is discrete. A Monte Carlo study of the estimators is presented This estimation problem frequently arises when Y is a parameter in a mathematical programming problem and h(Y) is the optimal objective function value. Two examples of this type are presented.     

Bias corrected estimates in multivariate student t regression models

The t distribution has proved to be a useful alternative to the normal distribution especially When robust estimation is desired. We consider the multivariate nonlinear Student-t regression model and show that the biased of the estimates of the regression coefficients can be computed from an auxiliary generalized linear regression. We give a formula for the biases of the estimates of the parameters in the scale matrix, which also can be computed by means of a generalized linear regression. We briefly discuss some important special cases and present simulation results which indicate that our bias-corrected estimates outperform the uncorrected ones in small samples.     

On a nonlinear Birnbaum–Saunders model based on a bivariate construction and its characteristics

Abstract

The Birnbaum-Saunders (BS) distribution is an asymmetric probability model that is receiving considerable attention. In this article, we propose a methodology based on a new class of BS models generated from the Student-t distribution. We obtain a recurrence relationship for a BS distribution based on a nonlinear skew–t distribution. Model parameters estimators are obtained by means of the maximum likelihood method, which are evaluated by Monte Carlo simulations. We illustrate the obtained results by analyzing two real data sets. These data analyses allow the adequacy of the proposed model to be shown and discussed by applying model selection tools.     

Detection of multiple change-points in multivariate data

The statistical analysis of change-point detection and estimation has received much attention recently. A time point such that observations follow a certain statistical distribution up to that point and a different distribution – commonly of the same functional form but different parameters after that point – is called a change-point. Multiple change-point problems arise when we have more than one change-point. This paper develops a method for multivariate normally distributed data to detect change-points and estimate within-segment parameters using maximum likelihood estimation.     

Some basic concepts of numerical treatment of Markov decision models

This survey reviews some results on numerical treatment of MARKOV Decision Models with respect to iV-stage-optimality, discounted optimality, and average optimality criteria. Especially, we deal with accelerated algorithms, approximation procedures and structured problems.

AMS 1980 subject classifications: 93C55, 90C40, 93D35     

Hybrid Bayesian inference on HIV viral dynamic models

Modelling of HIV dynamics in AIDS research has greatly improved our understanding of the pathogenesis of HIV-1 infection and guided for the treatment of AIDS patients and evaluation of antiretroviral therapies. Some of the model parameters may have practical meanings with prior knowledge available, but others might not have prior knowledge. Incorporating priors can improve the statistical inference. Although there have been extensive Bayesian and frequentist estimation methods for the viral dynamic models, little work has been done on making simultaneous inference about the Bayesian and frequentist parameters. In this article, we propose a hybrid Bayesian inference approach for viral dynamic nonlinear mixed-effects models using the Bayesian frequentist hybrid theory developed in Yuan [Bayesian frequentist hybrid inference, Ann. Statist. 37 (2009), pp. 2458–2501]. Compared with frequentist inference in a real example and two simulation examples, the hybrid Bayesian approach is able to improve the inference accuracy without compromising the computational load.