This paper discusses resampling procedures in the estimation of optimal portfolios when the returns are VAR(p) processes and VGARCH(p,q) processes. Then a consistency between the estimation error of the estimator of the mean-variance optimal portfolio parameter and that of the resampled one is shown. Based on this we construct an estimator of the lower tail of the estimation error. Moreover, we introduce the Estimation Error Efficient Portfolio which considers the estimation error as the portfolio risk. Numerical results show that our approach is applicable to actual portfolio management.
We investigate the empirical likelihood estimation for a parameter of linear processes whose innovations have i.i.d. symmetric α-stable distributions. To construct the estimating function for the empirical likelihood method, we make use of the empirical and theoretical characteristic functions. The asymptotic normality of the maximum empirical likelihood estimator is derived. The behavior of the asymptotic variance with respect to infinitesimal perturbations of the dependence effect is studied and we find that it is dependence robust when α > 1. Numerical studies are also given.
A desirable feature of the empirical likelihood (EL) method is its Bartlett correctability. Previous studies have only demonstrated that the Bartlett correctability of EL for independent cases. This paper considers the Bartlett correctability of EL in time series models. The validity of the formal Edgeworth expansion for the EL ratio statistic in the short-memory case is established and through meticulous calculations, a closed form expansion for the statistic is deduced. The order of the coverage error of the EL confidence region for time series is obtained based on such an Edgeworth expansion of the EL ratio statistic. It is further demonstrated that the coverage error can be reduced by an order of magnitude after using a Bartlett correction. Finally, a simulation study is presented to illustrate the Bartlett correctability of EL in the short-memory case.
Parametric estimation of cause-specific hazard functions in a competing risks model is considered. An approximate likelihood procedure for estimating parameters of cause-specific hazard functions based on competing risks data subject to right censoring is proposed. In an assumed parametric model that may have been misspecified, an estimator of a parameter is said to be consistent if it converges in probability to the pseudo-true value of the parameter as the sample size becomes large. Under censorship, the ordinary maximum likelihood method does not necessarily give consistent estimators. The proposed approximate likelihood procedure is consistent even if the parametric model is misspecified. An asymptotic distribution of the approximate maximum likelihood estimator is obtained, and the efficiency of the estimator is discussed. Datasets from a simulation experiment, an electrical appliance test, and a pneumatic tire test are used to illustrate the procedure.
The statistical inference concerning the difference between two independent binominal proportions has often been discussed in medical and statistical literature. This discussion is far more often based on the frequency theory of statistical inference than on the Bayesian theory. In this article, we propose the expression of the posterior probability density function (pdf) for the difference between two independent binominal proportions. In addition, we calculate the exact Highest Posterior Density (HPD) credible interval by using this expression. We also compare both the exact HPD credible interval and the approximate credible interval. We find that the former always has a narrower interval length than the latter.
In this article, several important problems of threshold estimation in a Bayesian framework for nonlinear time series models are discussed. The paper starts with the issue of calculating the maximum likelihood and the Bayesian estimators for threshold autoregressive models. It turns out that the asymptotic efficiency of the Bayesian estimators in this type of singular estimation problems is superior than the maximum likelihood estimators. To illustrate the properties of these estimators and to explain the proposed method, the paper begins with the study of a linear threshold autoregressive model with i.i.d. Gaussian noise. The paper then extends the idea to other nonlinear and non-Gaussian models and illustrates the paradigm of limiting likelihood ratio, which is applicable to a much wider class of nonlinear models. The article also investigates the robustness issue and the possibility of restricting the observation window by narrow bands, which allows one to obtain asymptotically efficient estimators. Finally, the paper indicates how these results can be generalized from a TAR(1) model to a higher-order TAR(p) model with multiple thresholds. The paper concludes with a discussion of other related problems and illustrates the methodology by numerical simulations.