A semiparametric Wald statistic for testing logistic regression models based on case-control data

We propose a semiparametric Wald statistic to test the validity of logistic regression models based on case-control data. The test statistic is constructed using a semiparametric ROC curve estimator and a nonparametric ROC curve estimator. The statistic has an asymptotic chisquared distribution and is an alternative to the Kolmogorov-Smirnov-type statistic proposed by Qin and Zhang in 1997, the chi-squared-type statistic proposed by Zhang in 1999 and the information matrix test statistic proposed by Zhang in 2001. The statistic is easy to compute in the sense that it requires none of the following methods: using a bootstrap method to find its critical values, partitioning the sample data or inverting a high-dimensional matrix. We present some results on simulation and on analysis of two real examples. Moreover, we discuss how to extend our statistic to a family of statistics and how to construct its Kolmogorov-Smirnov counterpart. This work was supported by the 11.5 Natural Scientific Plan (Grant No. 2006BAD09A04) and Nanjing University Start Fund (Grant No. 020822410110)     

A Hybrid Logistic Model for Case-Control Studies

For logistic regression in case-control studies, when risk factors associated with the outcome are exceedingly rare in the control group, the estimation of parameters in the model becomes difficult. In this paper, we propose a two-stage hybrid method to achieve this. In the first stage, we model the risk due to the rare factor, and in the second stage we model the residual risk due to the other factors using standard logistic model.     

A multi-objective-ACO-based data association method for bearings-only multi-target tracking

The study is concerned with data association of bearings-only multi-target tracking using two stationary observers in a 2-D scenario. In view of each target moving with a constant speed, two objective functions, i.e., distance and slope differences, are proposed and a multi-objective-ant-colony-optimization-based algorithm is then introduced to execute data association by minimizing the two objective functions. Numerical simulations are conducted to evaluate the effectiveness of the proposed algorithm in comparison with the data association results of the joint maximum likelihood (ML) method under different noise levels and track figurations.     

求解稀疏逻辑回归问题的嵌套BB算法的分裂增广拉格朗日算法

逻辑回归是经典的分类方法,广泛应用于数据挖掘、机器学习和计算机视觉.现研究带有程。模约束的逻辑回归问题.这类问题广泛用于分类问题中的特征提取,且一般是NP-难的.为了求解这类问题,提出了嵌套BB(Barzilai and Borwein)算法的分裂增广拉格朗日算法(SALM-BB).该算法在迭代中交替地求解一个无约束凸优化问题和一个带程。模约束的二次优化问题.然后借助BB算法求解无约束凸优化问题.通过简单的等价变形直接得到带程。模约束二次优化问题的精确解,并且给出了算法的收敛性定理.最后通过数值实验来测试SALM-BB算法对稀疏逻辑回归问题的计算精确性.数据来源包括真实的UCI数据和模拟数据.数值实验表明,相对于一阶算法SLEP,SALM-BB能够得到更低的平均逻辑损失和错分率.     

A class of bivariate distributions including the bivariate logistic

A univariate logistic distribution can be specified by considering a suitable form for the odds in favor of a failure against survival. This concept is extended to the bivariate case and a class of distributions, indexed by a parameter of association, having given marginals is proposed. Some properties of the proposed class of distributions are studied.     

Local linear regression for data with AR errors

In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.     

A nonparametric regression method for multiple longitudinal phenotypes using multivariate adaptive splines

In genetic studies of complex diseases, particularly mental illnesses, and behavior disorders, two distinct characteristics have emerged in some data sets. First, genetic data sets are collected with a large number of phenotypes that are potentially related to the complex disease under study. Second, each phenotype is collected from the same subject repeatedly over time. In this study, we present a nonparametric regression approach to study multivariate and time-repeated phenotypes together by using the technique of the multivariate adaptive regression splines for analysis of longitudinal data (MASAL), which makes it possible to identify genes, gene-gene and gene-environment, including time, interactions associated with the phenotypes of interest. Furthermore, we propose a permutation test to assess the associations between the phenotypes and selected markers. Through simulation, we demonstrate that our proposed approach has advantages over the existing methods that examine each longitudinal phenotype separately or analyze the summarized values of phenotypes by compressing them into one-time-point phenotypes. Application of the proposed method to the Framingham Heart Study illustrates that the use of multivariate longitudinal phenotypes enhanced the significance of the association test.     

Empirical likelihood method for quantiles with response data missing at random

Empirical likelihood is a nonparametric method for constructing confidence intervals and tests,notably in enabling the shape of a confidence region determined by the sample data.This paper presents a new version of the empirical likelihood method for quantiles under kernel regression imputation to adapt missing response data.It eliminates the need to solve nonlinear equations,and it is easy to apply.We also consider exponential empirical likelihood as an alternative method.Numerical results are presented to compare our method with others.     

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 discrete time model for software reliability with application to a flight control software

This work is motivated by a particular software reliability problem in a unit of flight control software developed by the Indian Space Research Organization (ISRO), in which the testing of the software is carried out in multiple batches, each consisting of several runs. As the errors are found during the runs within a batch, they are noted, but not debugged immediately; they are debugged only at the end of that particular batch of runs. In this work, we introduce a discrete time model suitable for this type of periodic debugging schedule and describe maximum likelihood estimation for the model parameters. This model is used to estimate the reliability of the software. We also develop a method to determine the additional number of error‐free test runs required for the estimated reliability to achieve a specific target with some high probability. We analyze the test data on the flight control software of ISRO. Copyright © 2011 John Wiley & Sons, Ltd.     

A regularized projection method for complementarity problems with non-Lipschitzian functions

We consider complementarity problems involving functions which are not Lipschitz continuous at the origin. Such problems arise from the numerical solution for differential equations with non-Lipschitzian continuity, e.g. reaction and diffusion problems. We propose a regularized projection method to find an approximate solution with an estimation of the error for the non-Lipschitzian complementarity problems. We prove that the projection method globally and linearly converges to a solution of a regularized problem with any regularization parameter. Moreover, we give error bounds for a computed solution of the non-Lipschitzian problem. Numerical examples are presented to demonstrate the efficiency of the method and error bounds.

     

生产函数中参数估计方法的改进

在原有生产函数参数估计方法的基础上,提出一种新的估计方法。计算实例表明:该估计方法具有最小的残差平方和,是一种比较理想的估计方法     

A comparison of statistical methods for prenatal screening for Down syndrome

Currently, prenatal screening for Down Syndrome (DS) uses the mother's age as well as three biochemical markers for risk prediction. Risk calculations for the biochemical markers use a quadratic discriminant function. In this paper we compare several classification procedures to quadratic discrimination methods for biochemical-based DS risk prediction, based on data from a prospective multicentre prenatal screening study. We investigate alternative methods including linear discriminant methods, logistic regression methods, neural network methods, and classification and regression-tree methods. Several experiments are performed, and in each experiment resampling methods are used to create training and testing data sets. The procedures on the test data set are summarized by the area under their receiver operating characteristic curves. In each experiment this process is repeated 500 times and then the classification procedures are compared. We find that several methods are superior to the currently used quadratic discriminant method for risk estimation for these data. The implications of these results for prenatal screening programs are discussed.     

A simple extension of boosting for asymmetric mislabeled data

This letter provides a simple extension of boosting methods for binary data where the probability of mislabeling depends on the label of an example. Loss functions are derived from the statistical perspective, which is based on likelihood analysis. Our proposed methods can be interpreted as a correction of the decision boundary of observed labels. This interpretation partially relates to cost-sensitive learning, a classification method for the case in which the ratio of two labels in a dataset is skewed. Numerical experiments show that the proposed methods work well for asymmetric mislabeled data even when the probabilities of mislabeling may not be precisely specified.     

A proximal bundle method with inexact data for convex nondifferentiable minimization

A proximal bundle method with inexact data is presented for minimizing an unconstrained nonsmooth convex function f$f$. At each iteration, only the approximate evaluations of f$f$ and its ε$\epsilon$-subgradients are required and its search directions are determined via solving quadratic programmings. Compared with the pre-existing results, the polyhedral approximation model that we offer is more precise and a new term is added into the estimation term of the descent from the model. It is shown that every cluster of the sequence of iterates generated by the proposed algorithm is an exact solution of the unconstrained minimization problem.     

A cross-validation method for data with ties in kernel density estimation

Limitation of the cross-validation method of bandwidth selection is well known when applied to data with ties. A method which resolves this problem and which is easy to understand and implement is proposed. We show that the proposed approach is viable in theory, by proving its asymptotic equivalence to the standard cross-validation method. The practical usefulness is shown in simulations and an application to a real data example.     

A divisive clustering method for functional data with special consideration of outliers

This paper presents DivClusFD, a new divisive hierarchical method for the non-supervised classification of functional data. Data of this type present the peculiarity that the differences among clusters may be caused by changes as well in level as in shape. Different clusters can be separated in different subregion and there may be no subregion in which all clusters are separated. In each step of division, the DivClusFD method explores the functions and their derivatives at several fixed points, seeking the subregion in which the highest number of clusters can be separated. The number of clusters is estimated via the gap statistic. The functions are assigned to the new clusters by combining the k-means algorithm with the use of functional boxplots to identify functions that have been incorrectly classified because of their atypical local behavior. The DivClusFD method provides the number of clusters, the classification of the observed functions into the clusters and guidelines that may be for interpreting the clusters. A simulation study using synthetic data and tests of the performance of the DivClusFD method on real data sets indicate that this method is able to classify functions accurately.     

Stability and error analysis for spectral Galerkin method for the Navier–Stokes equations with L2 initial data

In this article we consider the spectral Galerkin method with the implicit/explicit Euler scheme for the two‐dimensional Navier–Stokes equations with the L² initial data. Due to the poor smoothness of the solution on [0,1), we use the the spectral Galerkin method based on high‐dimensional spectral space H_M and small time step Δt² on this interval. While on [1,∞), we use the spectral Galerkin method based on low‐dimensional spectral space H_m(m = O(M^1/2)) and large time step Δt. For the spectral Galerkin method, we provide the standard H²‐stability and the L²‐error analysis. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007     

A posteriori error analysis for a boundary element method with nonconforming domain decomposition

We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions. The discretization under consideration is a nonconforming domain decomposition method based on the Nitsche technique. Assuming a saturation property, we establish quasireliability and efficiency of the error estimator in comparison with the error in a natural (nonconforming) norm. Numerical experiments with uniform and adaptively refined meshes confirm our theoretical results. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 947–963, 2014