一类图簇的伴随多项式的恒等式及其因式分解

本文通过研究图的伴随多项式的重要恒等式与因式分解,给出了证明色等价图的结构性质。     

On two-step estimation for varying coefficient models

In this note we discuss two-step kernel estimation of varying coefficient regression models that have a common smoothing variable. The method allows one to use different bandwidths for different coefficient functions. We consider local polynomial fitting and present explicit formulas for the asymptotic biases and variances of the estimators.     

Multidimensional scaling models with inequality and equality constraints

Recently, a lot of attention has been brought to constrained estimation theory in multidimensional scaling models. So far, only equality constraints have been thoroughly studied. In this paper, the optimization theory is extended to general multidi-mensional scaling models with both inequality and equality constraints. A Newton-Raphson based algorithm is developed to produce the constrained least squares estimate. To illustrate the theory, some classical color data are reanalyzed in the context of the linear Euclidean distance model.     

Statistical issues in studying the relative importance of body mass index,waist circumference,waist hip ratio and waist stature ratio to predict type 2 diabetes

Systematic and appropriate statistical analysis is needed to examine the relative performance of anthropometrical indices, viz. body mass index (BMI), waist circumference (WC), waist hip ratio (WHR) and waist stature ratio (WSR) for predicting type 2 diabetes. Using information on socio-demographic, anthropometric and biochemical variables from 2148 males, we examined collinearity and non-linearity among the predictors before studying the association between anthropometric indices and type 2 diabetes. The variable involving in collinearity was removed from further analysis, and the relative importance of BMI, WC and WHR was examined by logistic regression analysis. To avoid non-interpretable odds ratios (ORs), cut point theory is used. Optimal cut points are derived and tested for significance. Multivariable fractional polynomial (MFP) algorithm is applied to reconcile non-linearity. As expected, WSR and WC were collinear with WHR and BMI. Since WSR was jointly as well as independently collinear, it was dropped from further analysis. The OR for WHR could not be interpreted meaningfully. Cut point theory was adopted. Deciles emerged as the optimal cut point. MFP recognized non-linearity effects on the outcome. Multicollinearity among the anthropometric indices was examined. Optimal cut points were identified and used to study the relative ORs. On the basis of the results of analysis, MFP is recommended to accommodate non-linearity among the predictors. WHR is relatively more important and significant than WC and BMI.     

Enforcing shape constraints on a probability density estimate using an additive adjustment curve

A method is proposed for shape-constrained density estimation under a variety of constraints, including but not limited to unimodality, monotonicity, symmetry, and constraints on the number of inflection points of the density or its derivative. The method involves computing an adjustment curve that is used to bring a pre-existing pilot estimate into conformance with the specified shape restrictions. The pilot estimate may be obtained using any preferred estimator, and the optimal adjustment can be computed using fast, readily-available quadratic programming routines. This makes the proposed procedure generic and easy to implement.     

On matrix variate skew-normal distributions

Two new families of matrix variate distributions are introduced. They are based on matrix normal distribution and yet can be used to model data involving skewness. The properties of the two families are investigated. Among others, the marginals, conditionals, stochastic representation, linear and quadratic forms are studied.     

一类固定工件排序问题算法研究

针对一类＂可用机器数有限,存在机器与工件间匹配约束,以机器-工件分配成本最小为目标＂的固定工件排序问题,以固定工件的开始时刻、结束时刻为基准构建网络时序图,将＂机器-工件＂分配过程看成网络时序图中的网络流问题,并设计排序问题的模拟退火算法。通过算例发现：算法平均CPU时间为32.9秒,总成本最大误差为0.07%,时间复杂度为O（M（m3＋mn））,空间复杂度为O（m2n）。结果表明：算法为多项式算法,且可行。     

Further Properties of Frequentist Confidence Intervals in Regression that Utilize Uncertain Prior Information

Consider a linear regression model with n‐dimensional response vector, regression parameter and independent and identically distributed errors. Suppose that the parameter of interest is where a is a specified vector. Define the parameter where c and t are specified. Also suppose that we have uncertain prior information that . Part of our evaluation of a frequentist confidence interval for is the ratio (expected length of this confidence interval)/(expected length of standard confidence interval), which we call the scaled expected length of this interval. We say that a confidence interval for utilizes this uncertain prior information if: (i) the scaled expected length of this interval is substantially less than 1 when ; (ii) the maximum value of the scaled expected length is not too much larger than 1; and (iii) this confidence interval reverts to the standard confidence interval when the data happen to strongly contradict the prior information. Kabaila and Giri (2009) present a new method for finding such a confidence interval. Let denote the least squares estimator of . Also let and . Using computations and new theoretical results, we show that the performance of this confidence interval improves as increases and decreases.     

A Note on the Noncentral Beta Distribution Function

The noncentral beta and the related noncentral F distributions have received much attention during the last decade, as is evident from the works of Norton, Lenth, Frick, Lee, Posten, Chattamvelli, and Chattamvelli and Shanmugam. This article reviews the existing algorithms for computing the cumulative distribution function (cdf) of a noncentral beta random variable, and proposes a simple algorithm, based on a sharp error bound, for computing the cdf. A variation of the noncentral beta random variable when the noncentrality is associated only with the denominator χ² and its computational details are also discussed.     

Improved estimation of common location of two exponential populations with order restricted scale parameters using censored samples

ABSTRACT

Estimation of common location parameter of two exponential populations is considered when the scale parameters are ordered using type-II censored samples. A general inadmissibility result is proved which helps in deriving improved estimators. Further, a class of estimators dominating the MLE has been derived by an application of integrated expression of risk difference (IERD) approach of Kubokawa. A discussion regarding extending the results to a general k( ? 2) populations has been done. Finally, all the proposed estimators are compared through simulation.