Ridge regression estimators in the linear regression models with non-spherical errors

The present paper considers a family of ordinary ridge regression estimators in the linear regression model when the disturbances covariance matrix depends upon a few unknown parameters. An asymptotic expansion for the distribution of the ridge regression estimator is developed and under the quadratic loss function its asymptotic risk is compared with that of the feasible GLS estimator.     

How non-normality affects the quadratic discriminant function

The quadratic discriminant function is commonly used for the two group classification problem when the covariance matrices in the two populations are substantially unequal. This procedure is optimal when both populations are multivariate normal with known means and covariance matrices. This study examined the robustness of the QDF to non-normality. Sampling experiments were conducted to estimate expected actual error rates for the QDF when sampling from a variety of non-normal distributions. Results indicated that the QDF was robust to non-normality except when the distributions were highly skewed, in which case relatively large deviations from optimal were observed. In all cases studied the average probabilities of misclassification were relatively stable while the individual population error rates exhibited considerable variability.     

Quadratic Assignment Problems and M/G/C/C/ State Dependent Network Flows

One of the most notorious network design problems is the Quadratic Assignment Problem (QAP). We develop an heuristic algorithm for QAPs along with an M/G/C/C state dependent queueing model for capturing congestion in the traffic system interconnecting the nodes in the network. Computational results are also presented.     

Smoothed Histograms for Frequency Data on Irregular Intervals

Frequency tables are often constructed on intervals of irregular width. When plotted as bar charts, the underlying true density information may be quite distorted. The majority of introductory statistics texts recommend tabulating data into intervals of equal width, but seldom caution the consequences of failing to do so. An occasional introductory text correctly emphasizes that area rather than frequency should be plotted. Nevertheless, the correctly scaled density figure is often visually less informative than one might expect, with wide bins at constant height. In many cases, the right most bin interval has no well-defined end point, making its depiction some what arbitrary. In this note, we introduce a regular histogram approximation that matches the frequencies and also minimizes a roughness criterion for visual and exploratory appeal. The resulting estimate can reveal the density structure much more clearly. We also formulate an alternative criterion that explicitly takes account of the uncertainty in the bin frequencies.     

多元Ismail—May算子的一致逼近

主要给出了多元Ismail—May算子在一致逼近意义下的正、逆定理及特征刻划。     

关于不定方程x^3-1=Dy^2

证明了如下结果：如果题设方程有非平凡整数解，D只有唯一的6k＋1形素因子p，则D要么没有其他素因子，要么任何其他素因子q都满足（3p／q）=1或（p／q）=1。     

SADDLEPOINT METHODS FOR BOOTSTRAP CONFIDENCE BANDS IN NONPARAMETRIC REGRESSION

Bootstrap techniques have been used to construct confidence bands in nonparametric regression problems (Härdle & Bowman, 1988). Yet the required simulation is generally computationally intensive and therefore makes it difficult to conduct further investigations. In this paper, two saddlepoint methods are considered as alternatives to the naive simulation procedure. Some improvements to Härdle & Bowman's bootstrap method are suggested. The improvements are numerically verified using these efficient and accurate analytic methods.     

LDPC编码的最优化HARQ方案研究

使用高斯近似和最优化理论的方法,对基于LDPC码度分布的混合自动重发请求(HARQ)方案的性能进行了研究。研究表明,根据LDPC编码的度分布和初始信道条件,能够确定一个编码码字中各个度数的比特所对应的最优的重发比例,如果按照该比例进行重发,重发功率的效率能够最大化。计算结果显示基于LDPC码度分布的混合自动重发请求方案具有最优的重发比例,是一种最优化方案。     

用逐次逼近法求解北半球斜上抛体问题

运用逐次逼近理论,给出了在北半球斜上抛体的三次近似解.     

实二次型的分解公式

本文把二元实二次型的分解公式推广到n元实二次型,得到比较简便的结果.