Empirical likelihood for median regression model with designed censoring variables

We propose a new and simple estimating equation for the parameters in median regression models with designed censoring variables, and then apply the empirical log likelihood ratio statistic to construct confidence region for the parameters. The empirical log likelihood ratio statistic is shown to have a standard chi-square distribution, which makes this method easy to implement. At the same time, another empirical log likelihood ratio statistic is proposed based on an existing estimating equation and the limiting distribution of the empirical likelihood ratio statistic is shown to be a sum of weighted chi-square distributions. We compare the performance of the empirical likelihood confidence region based on the new estimating equation, with that based on the existing estimating equation and a normal approximation method by simulation studies.     

When is the pseudo-best estimator blue?

Summary Linear unbiased estimation of the mean of a random variable in Hilbert space is treated in the typical case where the mean belongs to a known subspace. The best linear estimate depends on the underlying covariance operatorB ₀ of the random variable. This operatorB ₀, however, is rarely completely known, so that an auxiliary operatorB is used to compute a “pseudo-best” estimate. It is shown that the best and the pseudo-best estimates coincide, if and only ifB ₀ B ⁻¹ leavesM invariant. Applications to linear regression are to be found in the references.     

水稻糙米粗蛋白近红外光谱定量分析模型的优化研究

筛选有代表性的191份糙米样品为试材,其中42份来自国家稻种资源库、149份来自水旱稻杂交产生的DH系,蛋白质含量变幅5.90％～14.50％,采用偏最小二乘法(PLS)建立模型,并构造模型的评价参数——目标函数[R/(1+RMSECV)], 同时借助校正集和验证集两个载荷向量得分二维空间投影图,对近红外定量模型进行评价和优化。结果表明: 在5 000～9 000 cm-1范围内,预处理方法为一阶导数,校正模型和外部检验的目标函数值分别为0.701和0.687;两载荷向量得分直观分布图显示样品的聚类结果与目标函数筛选结果一致,也进一步验证了目标函数是模型评价和优化的有效指标。     

Improved Model Selection Method for a Regression Function with Dependent Noise

This paper is devoted to nonparametric estimation, through the -risk, of a regression function based on observations with spherically symmetric errors, which are dependent random variables (except in the normal case). We apply a model selection approach using improved estimates. In a nonasymptotic setting, an upper bound for the risk is obtained (oracle inequality). Moreover asymptotic properties are given, such as upper and lower bounds for the risk, which provide optimal rate of convergence for penalized estimators.     

Kernel regression estimation for continuous spatial processes

We investigate here a kernel estimate of the spatial regression function r(x) = E(Y _u | X _u = x), x ∈ ℝ^d, of a stationary multidimensional spatial process { Z _u = (X _u, Y _u), u ∈ ℝ ^N }. The weak and strong consistency of the estimate is shown under sufficient conditions on the mixing coefficients and the bandwidth, when the process is observed over a rectangular domain of ℝ^N. Special attention is paid to achieve optimal and suroptimal strong rates of convergence. It is also shown that this suroptimal rate is preserved by using a suitable spatial sampling scheme.      

The Fast RODEO for Local Polynomial Regression

An open challenge in nonparametric regression is finding fast, computationally efficient approaches to estimating local bandwidths for large datasets, in particular in two or more dimensions. In the work presented here, we introduce a novel local bandwidth estimation procedure for local polynomial regression, which combines the greedy search of the regularization of the derivative expectation operator (RODEO) algorithm with linear binning. The result is a fast, computationally efficient algorithm, which we refer to as the fast RODEO. We motivate the development of our algorithm by using a novel scale-space approach to derive the RODEO. We conclude with a toy example and a real-world example using data from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite validation study, where we show the fast RODEO’s improvement in accuracy and computational speed over two other standard approaches.     

The structure of alternative tableaux

In this paper we study alternative tableaux introduced by Viennot [X. Viennot, Alternative tableaux, permutations and partially asymmetric exclusion process, talk in Cambridge, 2008]. These tableaux are in simple bijection with permutation tableaux, defined previously by Postnikov [A. Postnikov, Total positivity, Grassmannians, and networks, arXiv:math/0609764v1 [math.CO], 2006].We exhibit a simple recursive structure for alternative tableaux, from which we can easily deduce a number of enumerative results. We also give bijections between these tableaux and certain classes of labeled trees. Finally, we exhibit a bijection with permutations, and relate it to some other bijections that already appeared in the literature.     

Analysis of ordered categorical data to develop control charts for monitoring customer loyalty

In the highly competitive business environment of today, the cost to attract new customers is much higher than the cost required to maintain the existing ones. To keep the balance between the acquisition rate and defection rate through executing offensive and defensive marketing policies, it is required to have real time information using an efficient method to monitor customer loyalty. The relationship between customer loyalty and customer satisfaction should be kept in mind when one develops a method for loyalty monitoring. This paper presents several control charts classified in two groups based on the scale used to assess customer loyalty. In the first group of control charts, customer loyalty is considered as a binary random variable modeled by Bernoulli distribution whilst in the second group, an ordinal scale is considered to report loyalty level. Performance comparison of the proposed techniques using ARL criterion indicates that chi‐square and likelihood‐ratio control charts developed based on Pearson chi‐square statistic and ordinal logistic regression model respectively are able to rapidly detect the significant changes in loyalty behavior. To show how to apply the procedures and how to interpret their results, two illustrative synthetic cases are also explained. Copyright © 2009 John Wiley & Sons, Ltd.     

A simple construction of optimal estimation in multivariate marginal Cox regression

The multivariate extension of the Cox model proposed by Wei,Lin and Weissfeld in 1989 has been widely used for analyzing multivariate survival data.Under the model assumption,failure times from an individual are assumed to marginally follow their respective proportional hazards regression relation,leaving the joint distribution completely unspecified.This paper presents a simple approach to efficiency improvement through segmentation of stochastic integrals in the marginal estimating equations and incorporation of the limiting covariance structure.It is shown that when partition of the time interval is done at a suitable rate,the resulting estimator is consistent and asymptotically normal.Through the reproducing kernel Hilbert space arising from the covariance function of the limiting Gaussian process,it is also shown that the proposed estimator is asymptotically optimal within a reasonable class of estimators under marginal specification.Simulations are conducted to assess the finite-sample performance of the proposed method.     

Nonlinear wavelet estimation of regression function with random desigm

The nonlinear wavelet estimator of regression function with random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov spaceB ³ _p,q is proved under quite general assumpations. The adaptive nonlinear wavelet estimator with near-optimal convergence rate in a wide range of smoothness function classes is also constructed. The properties of the nonlinear wavelet estimator given for random design regression and only with bounded third order moment of the error can be compared with those of nonlinear wavelet estimator given in literature for equal-spaced fixed design regression with i.i.d. Gauss error. Project supported by Doctoral Programme Foundation, the National Natural Science Foundation of China (Grant No. 19871003) and Natural Science Fundation of Heilongjiang Province, China.