Bad Luck In Quadratic Improvement of The Linear Estimator In A Special Linear Model

The paper concludes our investigations in looking for the locally best linear-quadratic estimators of mean value parameters and of the covariance matrix elements in a special structure of the linear model (2 variables case) where the dispersions of the observed quantities depend on the mean value parameters. Unfortunately there exists no linear-quadratic improvement of the linear estimator of mean value parameters in this model.     

A class of estimators with estimated optimum values in sample surveys

Srivastava and Jhajj (1981) proposed a class of estimators for population mean of a character using auxiliary information and optimum values involving unknown parameters. From the practical point of view, their results have very little utility. In view of practical utility, we propose a class of estimators with estimated optimum values. Further, it is shown that the proposed class with estimated optimum values attains the same minimum mean square error of the class of estimators based on optimum values.     

用monte Carlo法求积分区域为 曲面体的高维积分

本文讨论了用Monte Carlo法求积分区域为曲面体的高维积分，分别根据积分区域G的体积为已知和未知两种情形，给出两种估计法及收敛性定理.另外也对求曲面体的重心进行了讨论.     

多元线性模型中条件最优预测的稳健性

研究了多元线性模型中条件最优线性无偏预测的稳健性问题,得到了条件线性可预测变量的这种预测关于协方差矩阵具有稳健性的充要条件.     

交会测量中具有自适应权因子的最优无偏方法

在利用多台测量站对空中运动物体进行交会测量过程中，测量站两两交会得到的测量结果并不会完全一致，有时甚至会有很大差别。讨论了具有自适应权的最优无偏方法：首先利用最小二乘法的原理，推导出了最小二乘解的表达式。在求解最优无偏解的过程中，通过求条件极值的方法导出了最优无偏解的权因子。由于权因子中的某些因素与目标像在CCD像面上的位置有关，提出了“自适应权”的思想，即权因子随目标像点位置的不同而自动调整。与传统的方法相比，具有自适应权的最优无偏方法，在一定程度上更充分地利用了不同情况下来自不同测量站的测量信息，从而提高了测量精度。经实际计算表明，在低空目标定位时，具有自适应权的最优无偏方法的平均偏差为传统方法平均偏差的40％左右。     

Mutually unbiased bases

After a brief review of the notion of a full set of mutually unbiased bases in an N-dimensional Hilbert space, we summarize the work of Wootters and Fields (W K Wootters and B C Fields, Ann. Phys. 191, 363 (1989)) which gives an explicit construction for such bases for the case N=p ^r , where p is a prime. Further, we show how, by exploiting certain freedom in the Wootters-Fields construction, the task of explicitly writing down such bases can be simplified for the case when p is an odd prime. In particular, we express the results entirely in terms of the character vectors of the cyclic group G of order p. We also analyse the connection between mutually unbiased bases and the representations of G.     

泊松统计的无偏估计

当泊松分布的平均值依赖于被估参数时, 从单次实验结果给出的关于参数的最大似然估计一般是统计学意义上有偏的. 借助矩的表达形式, 提出了一种关于被估参数的无偏估计方法.     

A Loss function approach to identifying environmental exceedances

A frequent problem in environmental science is the prediction of extrema and exceedances. It is well known that Bayesian and empirical-Bayesian predictors based on integrated squared error loss (ISEL) tend to overshrink predictions of extrema toward the mean. In this paper, we consider a geostatistical extension of the weighted rank squared error loss function (WRSEL) of Wright et al. (2003), which we call the integrated weighted quantile squared error loss (IWQSEL), as the basis for prediction of exceedances and their spatial location. The loss function is based on an ordering of the underlying spatial process using a spatially averaged cumulative distribution function. We illustrate this methodology with a Bayesian analysis of surface-nitrogen concentrations in the Chesapeake Bay and compare the new IWQSEL predictor with a standard ISEL predictor. We also give a comparison to predicted extrema obtained from a “plug-in” goestatistical analysis. AMS 2000 Subject Classification Primary—62M30; Secondary—62H11     

A note on testing two-dimensional normal mean

Summary For the problem of testing a composite hypothesis with one-sided alternatives of the mean vector of a two-dimensional normal distribution, a characterization of similar tests is presented and an unbiased test dominating the likelihood ratio test is proposed. A sufficient condition for admissibility is given, which implies the result given by Cohen et al. (1983,Studies in Econometrics, Time Series and Multivariate Statistics, Academic Press): the admissibility of the likelihood ratio test.