On boosting kernel regression

In this paper we propose a simple multistep regression smoother which is constructed in an iterative manner, by learning the Nadaraya–Watson estimator with _L2$L_2$ boosting. We find, in both theoretical analysis and simulation experiments, that the bias converges exponentially fast, and the variance diverges exponentially slow. The first boosting step is analysed in more detail, giving asymptotic expressions as functions of the smoothing parameter, and relationships with previous work are explored. Practical performance is illustrated by both simulated and real data.     

Practical Automated Reasoning on Inequalities: Generic Programs for Inequality Proving and Discovering

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复杂桁架结构管端实际切割角优化算法

针对管一管复杂管桁架结构中管端焊接装配面实际切割角易发生突变而影响正常装配这一问题,分析了其形成 原因以及对数控管切割机的影响。在易于加工且不影响焊接装配的前提下,运用多项式插值的方法,对实际切割角突变 弧段进行了优化,使管端焊接装配面平滑,易于加工。最后结合实例算法与仿真,通过分析其弧长一实际切割角曲线以及 对比优化前后焊接装配面实际切割角三维模型效果,验证了该优化算法的可靠性。为数控管件切割方式的改进提出了 一种新思路。     

电信运营企业核心竞争力概念及模型分析

针对电信运营企业核心竞争力的特殊性问题,通过对电信运营企业性质、特点的分析,得出了电信运营企业核心竞争力的概念,包括融合、整合、以知识为核心三个方面,及电信运营企业核心竞争力价值的概念及其锥体模型,接下来又通过对其核心竞争力的锥体模型的构成要素的分析,进一步揭示了其构成要素的性质与相互的逻辑关系及与整体间的关系。     

Nonparametric Estimation of the Conditional Distribution at Regression Boundary Points

Abstract

Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for example, is easy to implement and performs quite well both at interior and boundary points. Estimating the conditional distribution function and/or the quantile function at a given regressor point is immediate via standard kernel methods but problems ensue if local linear methods are to be used. In particular, the distribution function estimator is not guaranteed to be monotone increasing, and the quantile curves can “cross.” In the article at hand, a simple method of correcting the local linear distribution estimator for monotonicity is proposed, and its good performance is demonstrated via simulations and real data examples. Supplementary materials for this article are available online.     

Jacobi and Laguerre polynomial approximations for the distributions of statistics useful in testing for outliers in exponential and gamma samples

Recently, Sanjel and Balakrishnan [A Laguerre Polynomial Approximation for a goodness-of-fit test for exponential distribution based on progressively censored data, J. Stat. Comput. Simul. 78 (2008), pp. 503–513] proposed the use of Laguerre orthogonal polynomials for a goodness-of-fit test for the exponential distribution based on progressively censored data. In this paper, we use Jacobi and Laguerre orthogonal polynomials in order to obtain density approximants for some test statistics useful in testing for outliers in gamma and exponential samples. We first obtain the exact moments of the statistics and then the density approximants, based on these moments, are expressed in terms of Jacobi and Laguerre polynomials. A comparative study is carried out of the critical values obtained by using the proposed methods to the corresponding results given by Barnett and Lewis [Outliers in Statistical Data, 3rd ed., John Wiley & Sons, New York, 1993]. This reveals that the proposed techniques provide very accurate approximations to the distributions. Finally, we present some numerical examples to illustrate the proposed approximations. Monte Carlo simulations suggest that the proposed approximate densities are very accurate.     

Probability inheritance algorithm and its implementation

An algorithm for functional evaluation of the likelihood of paternal and maternal recombination fractions for pedigree data is proposed. The idea behind the algorithm is that the probability of affected status and certain marker genotypes of ancestors is inherited by their descendants along with the inheritance of certain haplotypes. In this algorithm, the likelihood is evaluated by a single recursive call for each terminal sibling set along with the inheritance flow. The advantage of the algorithm is not only the simplicity of its implementation, but also its functional form of evaluation. The likelihood is obtained as a polynomial of the recombination fractions, making it easier to validate the likelihood more carefully, resulting in a more accurate localization of the disease locus. We report an experimental implementation of this algorithm in R, together with several practical applications.     

Variable selection in partially linear hazard regression for multivariate failure time data

The aim of this paper is to explore variable selection approaches in the partially linear proportional hazards model for multivariate failure time data. A new penalised pseudo-partial likelihood method is proposed to select important covariates. Under certain regularity conditions, we establish the rate of convergence and asymptotic normality of the resulting estimates. We further show that the proposed procedure can correctly select the true submodel, as if it was known in advance. Both simulated and real data examples are presented to illustrate the proposed methodology.     

Model‐Based Non‐parametric Variance Estimation for Systematic Sampling

Abstract. Systematic sampling is frequently used in surveys, because of its ease of implementation and its design efficiency. An important drawback of systematic sampling, however, is that no direct estimator of the design variance is available. We describe a new estimator of the model‐based expectation of the design variance, under a non‐parametric model for the population. The non‐parametric model is sufficiently flexible that it can be expected to hold at least approximately in many situations with continuous auxiliary variables observed at the population level. We prove the model consistency of the estimator for both the anticipated variance and the design variance under a non‐parametric model with a univariate covariate. The broad applicability of the approach is demonstrated on a dataset from a forestry survey.