Model checking for general linear error-in-covariables model with validation data

In this paper, model checking problem is considered for general linear model when covariables are measured with error and an independent validation data set is available. Without assuming any error model structure between the true variable and the surrogate variable, the author first apply nonparametric method to model the relationship between the true variable and the surrogate variable with the help of the validation sample. Then the author construct a score-type test statistic through model adjustment. The large sample behaviors of the score-type test statistic are investigated. It is shown that the test is consistent and can detect the alternative hypothesis close to the null hypothesis at the rate n ^−r with 0 ≤ r ≤ 1/2. Simulation results indicate that the proposed method works well.     

一类股市波动性预测模型的多变点检验

讨论了一类股市波动性预测模型的多变点检验问题.基于累积和(CUSUM)统计量,提出一种新的波动性预测模型多变点的拟似然比检验,在原假设下给出统计量的极限分布及渐近临界值的解析表达式.多变点的递归检验是本文的一个主要方面,即在检验时允许原假设含有变点,备择假设比原假设多一个变点,并在递归检验的过程中同时得到变点时刻与变点个数的一致估计,因此为处理含多变点的金融数据时确定变点个数提供了一种建模策略.数值模拟与实例分析说明了方法的有效性.     

Consistency of Chi-Squared Test with Varying Number of Classes

The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.     

OPTIMAL AND ROBUST DETECTION OF MULTIVARIATE OUTLIERS FOR ELLIPTICALLY CONTOURED DISTRIBUTION

The outlier problem for a multivariate elliptically contoured distribu-tion's random sample with mean slippage is defined and the likelihood ratio test ofthe null hypothesis,in which there are no outliers,versus the alternative hypothesis,in which some outliers are present,is derived.We show that the testing problemis invariant under a group of affine transformations and obtain the maximal in-variance which is equivalent to the likelihood ratio testing statistic.Furthermore,the non-null and null density distribution functions of the likelihood ratio testingstatistic are derived.We find that the null density distribution function of thetesting statistic is robust and the density distribution function is a monotonicallikelihood ratio function of the maximal invariance.Therefore,the likelihood ratiotest is a uniformly most powerful invariant test among the group of affine transfor-mations.In the last section,we give an example of detecting multivariate outliersin elliptically contoured distribution.     

Testing serial correlation in semiparametric varying coefficient partially linear errors-in-variables model

The authors propose a V _{N, p} test statistic for testing finite-order serial correlation in a semiparametric varying coefficient partially linear errors-in-variables model. The test statistic is shown to have asymptotic normal distribution under the null hypothesis of no serial correlation. Some Monte Carlo experiments are conducted to examine the finite sample performance of the proposed V _{N, p} test statistic. Simulation results confirm that the proposed test performs satisfactorily in estimated size and power. This research is supported by the National Natural Science Foundation of China under Grant Nos. 10871217 and 40574003; the Science and Technology Project of Chongqing Education Committee under Grant No. KJ080609; the Doctor's Start-up Research Fund under Grant No. 08-52204; and the Youth Science Research Fund of Chongqing Technology and Business University under Grant No. 0852008.     

Test for Heteroscedasticity in Partially Linear Regression Models

Testing heteroscedasticity determines whether the regression model can predict the dependent variable consistently across all values of the explanatory variables. Since the proposed tests could not detect heteroscedasticity in all cases, more precisely in heavy-tailed distributions, the authors established new comprehensive test statistic based on Levene's test. The authors built the asymptotic normality of the test statistic under the null hypothesis of homoscedasticity based on the recent theory of analysis of variance for the infinite factors level. The proposed test uses the residuals from a regression model fit of the mean function with Levene's test to assess homogeneity of variance. Simulation studies show that our test yields better than other methods in almost all cases even if the variance is a nonlinear function. Finally, the proposed method is implemented through a real data-set.     

基于小波的非参数回归模型均值变点的Bootstrap监测

本文首次考虑非参数回归模型均值函数结构变点的在线监测问题. 首先对回归函数的局部线性估计值进行小波变换， 基于得到的小波系数构造监测统计量， 并在原假设和备择假设下推导出监测统计量的渐近分布； 为提高监测效果， 进一步构造了Bootstrap在线监测方法， 定义了停时； 模拟结果和实例分析显示该方法可以很好地监测到变点， 并具有较短的检测延迟.     

Sample-size determination for two independent binomial experiments

Sample size determination is commonly encountered in modern medical studies for two independent binomial experiments. A new approach for calculating sample size is developed by combining Bayesian and frequentist idea when a hypothesis test between two binomial proportions is conducted. Sample size is calculated according to Bayesian posterior decision function and power of the most powerful test under 0-1 loss function. Sample sizes are investigated for two cases that two proportions are equal to some fixed value or a random value. A simulation study and a real example are used to illustrate the proposed methodologies.     

Inference on coefficient function for varying-coefficient partially linear model

One important model in handling the multivariate data is the varying-coemcient partially linear regression model.In this paper,the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not.It is showed that the normalized proposed test follows asymptoticallyχ~2-distribution and the Wilks phenomenon under the null hypothesis,and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing.Some simulation studies illustrate that the test works well.     

THE ESTIMATE AND TEST IN THE SYMMETRICAUXILIARY INFORMATION

1.IntroductionLetX,XI,X2,''lXui.i.d.~FO.TheempiricaldistributionFn=Z::,6x./niswellknowntobethenonparametricmaximumlikelihoodestimateofFObasedonXI,X2,'')Xu.Here6:denotesapointmassatx.ThelikelihoodfunctionthatFimaximizesisL(G)=fi:=,G{xi},whereG{xi}istheprobabilityoftheset{xi}underG,xiistheobservedvalueofXiandGisanyprobabilitymeasureonCP.WedefinetheempiricallikelihoodfunctionnL(G)=fiG{xi},whereG<相似文献   

A nonparametric test against an umbrella alternative for stratified data

Trend test in dose-response has been a central problem in medicine. This paper treats the problem of comparing umbrella pattern treatment effects. Under an ordered m × r × k table, this article considers testing the hypothesis that all multinomial populations are conditional independence against the alternative that they are in an umbrella trend. For this hypothesis test problem, this article introduces a model-free test method by using likelihood ratio test statistic and gives the asymptotic distribution of the test statistic. Simulation study is conducted to compare the empirical power performed via the proposed method and others. Finally, two real data are studied to illustrate the validity of the proposed method.     

Distance-Based Regression Analysis for Measuring Associations

Distance-based regression model, as a nonparametric multivariate method, has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies, genomic analyses, and many other research areas. Based on it, a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim. To the best of our knowledge, the statistical properties of the pseudo-F statistic has not yet been well established in the literature. To fill this gap, the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables. Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large, the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root. The asymptotic null distribution of the new test statistic and power of both tests are also investigated. Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test. Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.

     

A new procedure for testing normality based on the L 2 Wasserstein distance

This paper proposes a new goodness-of-fit test for normality based on the L ₂ Wasserstein distance. The authors first construct a probability through the Bootstrap resampling. Although the probability is not distributed uniformly on the interval (0, 1) under the null hypothesis, it is shown that its distribution is free from the unknown parameters, which indicates that such a probability can be taken as the test statistic. It emerges from the simulation study of power that the new test is able to better discriminate between the normal distribution and those distributions with short tails. For such alternatives, it has a substantially better power than existing tests including the Anderson-Darling test and Shapiro-Wilk test, which are two of the best tests for normality. In addition, the sensitivity analysis of tests is also investigated in the presence of moderate perturbation, which shows that the new test is a rather robust test.     

双参数指数分布参数变点的统计推断

讨论双参数指数分布尺度参数发生变化、两个参数可能同时发生变化时，变点的统计推断问题。关于尺度参数变点问题，继续Wang和Bhatti(1998)的讨论，给出检验的渐近分布，同时也研究变点的估计问题。对于位置参数和尺度参数可能同时发生变化时，给出参数变点检验统计量，并利用随机模拟的方法给出检验的临界值。     

Monitoring Mean and Variance Change-Points in Long-Memory Time Series

This paper proposes two ratio-type statistics to sequentially detect mean and variance change-points in the long-memory time series. The limiting distributions of monitoring statistics under the no change-point null hypothesis, alternative hypothesis as well as change-point misspecified hypothesis are proved. In particular, a sieve bootstrap approximation method is proposed to determine the critical values. Simulations indicate that the new monitoring procedures have better finite sample performance than the available off-line tests when the change-point nears to the beginning time of monitoring, and can discriminate between mean and variance change-point. Finally, the authors illustrate their procedures via two real data sets: A set of annual volume of discharge data of the Nile river, and a set of monthly temperature data of northern hemisphere. The authors find a new variance change-point in the latter data.

     

Rank-Based Test for Partial Functional Linear Regression Models

This paper investigates the hypothesis test of the parametric component in partial functional linear regression models. Based on a rank score function, the authors develop a rank test using functional principal component analysis, and establish the asymptotic properties of the resulting test under null and local alternative hypotheses. A simulation study shows that the proposed test procedure has good size and power with finite sample sizes. The authors also present an illustration through fitting the Berkeley Growth Data and testing the effect of gender on the height of kids.     

Test on Stochastic Block Model: Local Smoothing and Extreme Value Theory

In this paper, to obtain a consistent estimator of the number of communities, the authors present a new sequential testing procedure, based on the locally smoothed adjacency matrix and the extreme value theory. Under the null hypothesis, the test statistic converges to the type I extreme value distribution, and otherwise, it explodes fast and the divergence rate could even reach n in the strong signal case where n is the size of the network, guaranteeing high detection power. This method is simple to use and serves as an alternative approach to the novel one in Lei (2016) using random matrix theory. To detect the change of the community structure, the authors also propose a two-sample test for the stochastic block model with two observed adjacency matrices. Simulation studies justify the theory. The authors apply the proposed method to the political blog data set and find reasonable group structures.

     

Statistical Diagnosis for HIV Dynamics Based on Mean Shift Outlier Model

Ordinary differential equation(ODE) are widely used for quantifying HIV viral dynamics.It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. In this study, the authors use the Mean Shift Outlier Model(MSOM) to detect outliers in HIV model based on the two-step estimation of ODE. Approximate formula for shift parameter is derived. Furthermore, a score test statistic is constructed and its approximating distribution is established. The simulation results show that: 1) The boundary points have more impact on the parameter estimation relative to interior points. 2) The proposed procedure can detect the outliers effectively. The authors illustrate the proposed approach using an application example from an HIV clinical trial and find similar pattern to the simulation studies.     

Testing inequality constraints in a linear regression model with spherically symmetric disturbances

This paper develops a Wald statistic for testing the validity of multivariate inequality constraints in linear regression models with spherically symmetric disturbances, and derive the distributions of the test statistic under null and nonnull hypotheses. The power of the test is then discussed. Numerical evaluations are also carried out to examine the power performances of the test for the case in which errors follow a multivariate student-t （Mt） distribution.     

多径环境下的无源分布式孔径雷达成像方法

研究多径环境下分布式孔径无源雷达成像方法,首先针对分布式孔径探测,给出一种新的无源雷达回波模型,该模型适用于复杂的多径散射环境,而且不需要已知发射源信息。然后研究一种基于二元假设检验的成像方法,依据最大信噪比原则构造检验统计量,该统计量依赖于空间位置信息,通过对成像区域中的每个位置进行检测,可实现空间分辨,获得成像结果。接着详细分析该方法在多径散射环境中的性能,并在模拟多径环境中采用地面数字电视信号对成像方法进行仿真实验验证。理论分析和实验结果表明,采用空间可分辨的检验统计量形成图像可以正确重建目标,并且可利用多径效应进行成像。