Uniform minimum variance unbiased estimators for bivariate families

Summary We consider uniform minimum variance unbiased (UMVU) estimation of an unbiased estimable function of distribution parameters for bivariate truncation (non-regular) parameter families. In particular, we derive the UMVU estimator of the probability thatY is less thanX.     

A note on Model Reference Adaptive System (MRAS) estimate with infinite variance

This paper discusses the estimation of a parameter in an autoregressive model with infinite variance. A recursive estimation procedure based on minimizing the prediction errors is provided. It is also shown that the model reference adaptive system estimate for an AR (1) model given in Aase (1983) is a special case.     

A note on estimation of variance components in a multi-stage sampling design based on interpenetrating sub-samples

Summary In this note it is shown that unbiased estimators of the components of the sampling variance of an estimator in the case of a stratified multi-stage sampling design could easily be obtained by selecting the samples at the different stages in the form of two or more independent interpenetrating sub-samples.     

Portfolio selection based on semivariance and distance correlation under minimum variance framework

In the minimum variance model, the covariance matrix plays an important role because it measures the risk and relationship of asset returns simultaneously under the normality assumption. However, in practice, the distribution of asset returns is nonnormal and has an obvious fat‐tail nature. In addition, the risk is one‐sided. In this paper, the main objective is to propose a better tool to replace the covariance matrix. The covariance matrix can be decomposed into two parts: a diagonal variance matrix and a square matrix with its elements being the Pearson correlation coefficient. A substitution of the covariance matrix is presented by replacing the variance and Pearson correlation coefficient in the decomposition of the covariance matrix with a semivariance and distance correlation coefficient, respectively. The proposed portfolio optimization strategy is applied to empirical data, and the numerical studies show the strategy performs well.     

A note on the equivalence of specification tests in the two-factor multivariate variance components model

This note offers a generalization of Hausman and Taylor's equivalence of specification tests in the single-equation variance (error) components model to the two-factor multivariate variance components case. The relationship between the specification tests and the hypothesis test in the model proposed by Mundlak is also discussed.     

Locally minimum variance unbiased estimator in a discontinuous density function

The exact forms of the locally minimum variance unbiased estimators and their variances are given in the case of a discontinuous density function.     

Futures minimum variance hedge ratio determination: An ex-ante analysis

Traditionally, futures Minimum Variance Hedge Ratios (MVHRs) are determined ex post. In this paper, we derive 3 increasingly realistic ex ante MVHRs, based on the carry cost and the Vasicek model. The hedging performance of the most realistic ex ante MVHR determination method is compared to, and found to be superior to, that of the traditional MVHR for the S&P 500 index, gold, and the EUR/USD exchange rate.     

A test for the weights of the global minimum variance portfolio in an elliptical model

In this paper we consider the weights of the global minimum variance portfolio (GMVP). The returns are assumed to follow a matrix elliptically contoured distribution, i.e., the returns are assumed to be neither independent nor normally distributed. A test for the general linear hypothesis is given. The distribution of the test statistic is derived under the null and the alternative hypothesis. It turns out that its distribution is invariant with respect to the type of the matrix elliptical distribution, i.e., the stochastic properties of the GMVP do not depend either on the mean vector or on the distributional assumptions imposed on asset returns. In an empirical study we analyze an international diversified portfolio.     

On uniformly minimum variance unbiased estimation when no complete sufficient statistics exist

Summary A simple generalization of the Lehmann-Scheffé theorem is given. It is used to find cases when UMVUE's exist but complete sufficient statistics do not. Another method to find such cases is also presented.     

Optimality of balanced designs for minimum norm quadratic unbiased estimation of variance components

This paper develops an approximate theory for the optimality of balanced designs under minimum norm quadratic unbiased estimation of variance components in one-way classified data.     

The finite-sample effects of VAR dimensions on OLS bias,OLS variance,and minimum MSE estimators

Vector autoregressions (VARs) are important tools in time series analysis. However, relatively little is known about the finite-sample behaviour of parameter estimators. We address this issue, by investigating ordinary least squares (OLS) estimators given a data generating process that is a purely nonstationary first-order VAR. Specifically, we use Monte Carlo simulation and numerical optimisation to derive response surfaces for OLS bias and variance, in terms of VAR dimensions, given correct specification and several types of over-parameterisation of the model: we include a constant, and a constant and trend, and introduce excess lags. We then examine the correction factors that are required for the least squares estimator to attain the minimum mean squared error (MSE). Our results improve and extend one of the main finite-sample multivariate analytical bias results of Abadir, Hadri and Tzavalis [Abadir, K.M., Hadri, K., Tzavalis, E., 1999. The influence of VAR dimensions on estimator biases. Econometrica 67, 163–181], generalise the univariate variance and MSE findings of Abadir [Abadir, K.M., 1995. Unbiased estimation as a solution to testing for random walks. Economics Letters 47, 263–268] to the multivariate setting, and complement various asymptotic studies.     

A note on redistribution

A consequence of income redistribution may well be to make everyone (including lower-income groups to which redistribution takes place) worse off after a period of years. Possibly income redistribution might gain consent because of risk aversion. The paper also draws attention to the tendency for people to be more concerned about poverty close at hand rather than far away.     

A note on linked bargaining

A recent result by Jackson and Sonnenschein (2007) describes a general framework for overcoming incentive constraints by linking together independent copies of a Bayesian decision problem. A special case of that work shows that if copies of a standard two-player Bayesian bargaining problem are independently linked (players receive valuations and trade simultaneously on a number of identical copies), then the utility cost associated with incentive constraints tends to 0 as the number of linked problems tends to infinity. We improve upon that result, increasing the rate of convergence from polynomial to exponential and eliminating unwanted trades in the limit, by introducing a mechanism that uses a slightly richer and more refined strategy space. Although very much in the same spirit, our declarations are constrained by a distribution which is skewed away from the expected distribution of player types. When a sufficiently large number of bargaining problems are linked, “truth” is an equilibrium. Moreover, this equilibrium is incentive compatible with the utility cost of incentive constraints almost surely equal to 0.     

A note on some Wishart expectations

Summary In a recent paper Sharma and Krishnamoorthy (1984) used a complicated decisiontheoretic argument to derive an identity involving expectations taken with respect to the Wishart distributionW _m (n, I). A more general result, proved using an elementary moment generating function argument, and some applications, are given in this paper.This work was supported by the National Science Foundation.     

A note on non-linear limited-information maximum-likelihood

A simplification of Amemiya's non-linear limited information estimator is presented which shows more clearly the differences between it and the estimators he considered.     

A note on preference for flexibility

A result of Kreps (1979) on preference for flexibility is extended from two to three periods (formally from preferences over sets to preferences over sets of sets). An intuitively easier route to Kreps' original result is also presented, making the proof essentially ready for use in a decision theory class. Received: 23 April 2001 / Accepted: 1 September 2001 First version October 1997.     

A note on fourth-order risk aversion

Keenan et al. (J Risk Uncertain 24:264–277, 2002) introduced a measure of downside risk aversion (third-order risk aversion), and in Theorem 1, they showed four equivalent definitions of increased downside risk aversion. This result is thought as a higher-order extension of Theorem 3 in Diamond et al. (J Econ Theory 8:337–360, 1974). We consider fourth-order risk aversion and show four equivalent definitions of increased fourth-order risk aversion. Our result is thought as a higher-order extension of Theorem 1 in Keenan et al. (2002).