Calculating the density and distribution function for the singly and doubly noncentral F

Simple, closed form saddlepoint approximations for the distribution and density of the singly and doubly noncentral F distributions are presented. Their overwhelming accuracy is demonstrated numerically using a variety of parameter values. The approximations are shown to be uniform in the right tail and the associated limitating relative error is derived. Difficulties associated with some algorithms used for exact computation of the singly noncentral F are noted.     

Fast and Accurate Inference for the Smoothing Parameter in Semiparametric Models

A fast and accurate method of confidence interval construction for the smoothing parameter in penalised spline and partially linear models is proposed. The method is akin to a parametric percentile bootstrap where Monte Carlo simulation is replaced by saddlepoint approximation, and can therefore be viewed as an approximate bootstrap. It is applicable in a quite general setting, requiring only that the underlying estimator be the root of an estimating equation that is a quadratic form in normal random variables. This is the case under a variety of optimality criteria such as those commonly denoted by maximum likelihood (ML), restricted ML (REML), generalized cross validation (GCV) and Akaike's information criteria (AIC). Simulation studies reveal that under the ML and REML criteria, the method delivers a near‐exact performance with computational speeds that are an order of magnitude faster than existing exact methods, and two orders of magnitude faster than a classical bootstrap. Perhaps most importantly, the proposed method also offers a computationally feasible alternative when no known exact or asymptotic methods exist, e.g. GCV and AIC. An application is illustrated by applying the methodology to well‐known fossil data. Giving a range of plausible smoothed values in this instance can help answer questions about the statistical significance of apparent features in the data.     

一种基于加权F-范数的半正定矩阵的逼近方法

正定性是许多金融预测模型的重要假设前提，然而从实际样本中得到的相关系数矩阵并不能保证其正定性。为此在介绍如何根据样本设定相关系数矩阵以及范数逼近原理的基础上，如何根据该原理找到与之最接近的相关系数矩阵，即最接近的单位对角半正定对称矩阵。通过实证，验证了其方法的有效性。     

On the inapproximability of the exemplar conserved interval distance problem of genomes

In this paper we present two main results about the inapproximability of the exemplar conserved interval distance problem of genomes. First, we prove that it is NP-complete to decide whether the exemplar conserved interval distance between any two genomes is zero or not. This result implies that the exemplar conserved interval distance problem does not admit any approximation in polynomial time, unless P=NP. In fact, this result holds, even when every gene appears in each of the given genomes at most three times. Second, we strengthen the first result under a weaker definition of approximation, called weak approximation. We show that the exemplar conserved interval distance problem does not admit any weak approximation within a super-linear factor of , where m is the maximal length of the given genomes. We also investigate polynomial time algorithms for solving the exemplar conserved interval distance problem when certain constrains are given. We prove that the zero exemplar conserved interval distance problem of two genomes is decidable in polynomial time when one genome is O(log n)-spanned. We also prove that one can solve the constant-sized exemplar conserved interval distance problem in polynomial time, provided that one genome is trivial.     

随机需求下基于“自营+外包”模式的配送中心选址-配送问题研究

针对顾客需求量不确定情况下末端配送中心选址及提前备货问题,提出了基于“自营+外包”配送模式的配送中心选址-配送问题。以自营配送中心的固定运行成本、提前备货成本和各种场景下的自营配送成本、外包配送成本以及缺货损失成本的期望值之和最小化为目标,建立了两阶段连续型随机规划模型。第一阶段确定自营配送中心的选址位置和各个配送中心的提前备货量;第二阶段确定各种场景下的自营配送货运量、外包配送货运量和客户点的缺货量等,使总成本期望值达到最小。基于Monte Carlo抽样理论设计了求解模型的样本均值近似方法;以及求解大规模问题L-shaped分解算法。通过模拟算例验证了两阶段随机规划模型的优越性和样本均值近似方法的有效性;并对自营配送中心固定运行成本、单位商品的自营配送成本和外包配送成本等进行灵敏度分析,得到了不同参数对应的最优配送策略,结果表明,正常情况下“自营+外包”配送模式是企业的最佳选择。本文同时将配送中心选址和提前备货量作为随机规划模型的第一阶段决策变量,可以帮助企业降低物流成本、提高顾客的满意度。     

Landau多项式算子与无界函数逼近

利用扩展乘数法构造了 Landau型多项式算子逼近全空间或有界集上无界函数的若干收敛定理 ,给出了具有一般性的结论 ,从而推广了已有文献的若干结果 .     

Approach to normality of mean and M-estimators of location

The approach to normality of an estimate is displayed graphically by the nonlinearity in the derivative of the log density, and this nonlinearity is related to the accuracy of the normal approximation for the tail area. Using techniques from small-sample asymptotics, an alternate proof of the central limit theorem is given and same indices of tail behavior are examined.     

Infinite Parameter Estimates in Logistic Regression, with Application to Approximate Conditional Inference

This paper discusses recovery of information regarding logistic regression parameters in cases when maximum likelihood estimates of some parameters are infinite. An algorithm for detecting such cases and characterizing the divergence of the parameter estimates is presented. A method for fitting the remaining parameters is also presented . All of these methods rely only on sufficient statistics rather than less aggregated quantities, as required for inference according to the method of Kolassa & Tanner (1994). These results are applied to approximate conditional inference via saddlepoint methods. Specifically, the double saddlepoint method of Skovgaard (1987) is adapted to the case when the solution to the saddlepoint equations exists as a point at infinity     

On Robust Analysis of a Normal Location Parameter

Pericchi and Smith considered a normal location parameter problem with double-exponential and Student t prior distributions. These two prior distributions both belong to the class of scale mixtures of normal distributions and are useful in providing a robust analysis of the normal location parameter problem. In this paper we extend the analysis to other scale mixtures of normal distributions, such as the exponential power and the symmetric stable distributions.     

COVARIANCE MODELS FOR LATTICE DATA

Given observations on an m × n lattice, approximate maximum likelihood estimates are derived for a family of models including direct covariance, spatial moving average, conditional autoregressive and simultaneous autoregressive models. The approach involves expressing the (approximate) covariance matrix of the observed variables in terms of a linear combination of neighbour relationship matrices, raised to a power. The structure is such that the eigenvectors of the covariance matrix are independent of the parameters of interest. This result leads to a simple Fisher scoring type algorithm for estimating the parameters. The ideas are illustrated by fitting models to some remotely sensed data.