This paper proposes a new hedging scheme of European derivatives under uncertain volatility environments, in which a weighted variance swap called the polynomial variance swap is added to the Black-Scholes delta hedging for managing exposure to volatility risk. In general, under these...

In this article, we consider the problem of testing the equality of mean vectors of dimension ρ of several groups with a common unknown non-singular covariance matrix Σ, based on <em>N</em> independent observation vectors where <em>N</em> may be less than the dimension ρ. This problem, known in the literature...

The empirical best linear unbiased predictor (EBLUP) in the linear mixed model (LMM) is useful for the small area estimation in the sense of increasing the precision of estimation of small area means. However, one potential difficulty of EBLUP is that when aggregated, the overall estimate for a...

In the small area estimation, the empirical best linear unbiased predictor (EBLUP) or the empirical Bayes estimator (EB) in the linear mixed model is recognized useful because it gives a stable and reliable estimate for a mean of a small area. In practical situations where EBLUP is applied to...

The linear mixed models (LMM) and the empirical best linear unbiased predictor (EBLUP) induced from LMM have been well studied and extensively used for a long time in many applications. Of these, EBLUP in small area estimation has been recognized as a useful tool in various practical statistics....

The Akaike information criterion, AIC, and Mallows' Cp statistic have been proposed for selecting a smaller number of regressor variables in the multivariate regression models with fully unknown covariance matrix. All these criteria are, however, based on the implicit assumption that the sample...

The empirical best linear unbiased predictor (EBLUP) or the empirical Bayes estimator (EB) in the linear mixed model is recognized useful for the small area estimation, because it can increase the estimation precision by using the information from the related areas. Two of the measures of...

This paper treats the problem of simultaneously estimating the precision matrices in multivariate normal distributions. A condition for improvement on the unbiased estimators of the precision matrices is derived under a quadratic loss function. The improvement condition is similar to the...

This paper is concerned with the problem of estimating a matrix of means in multivariate normal distributions with an unknown covariance matrix under the quadratic loss function. It is first shown that the modified Efron-Morris estimator is characterized as certain empirical Bayes estimator....

In this paper, we consider the problem of estimating the covaraince matrix and the generalized variance when the observations follow a nonsingular multivariate normal distribution with unknown mean. A new method is presented to obtain a truncated estimator that utilizes the information available...