Empirical likelihood based goodness-of-fit testing for generalized linear mixed models

In this paper, we propose a bias-corrected empirical likelihood （BCEL） ratio to construct a goodness- of-fit test for generalized linear mixed models. BCEL test maintains the advantage of empirical likelihood that is self scale invariant and then does not involve estimating limiting variance of the test statistic to avoid deteri- orating power of test. Furthermore, the bias correction makes the limit to be a process in which every variable is standard chi-squared. This simple structure of the process enables us to construct a Monte Carlo test proce- dure to approximate the null distribution. Thus, it overcomes a problem we encounter when classical empirical likelihood test is used, as it is asymptotically a functional of Gaussian process plus a normal shift function. The complicated covariance function makes it difficult to employ any approximation for the null distribution. The test is omnibus and power study shows that the test can detect local alternatives approaching the null at parametric rate. Simulations are carried out for illustration and for a comparison with existing method.     

Sign-based Test for Mean Vector in High-dimensional and Sparse Settings

In this article, we introduce a robust sparse test statistic which is based on the maximum type statistic. Both the limiting null distribution of the test statistic and the power of the test are analysed. It is shown that the test is particularly powerful against sparse alternatives. Numerical studies are carried out to examine the numerical performance of the test and to compare it with other tests available in the literature. The numerical results show that the test proposed significantly outperforms those tests in a range of settings, especially for sparse alternatives.     

Testing for changes in the mean or variance of long memory processes

In this paper, we study the asymptotic CUSUM tests for detecting changes in the mean or variance of a moving-average process with long memory. When there is no change over [O,T], the asymptotic distribution of the test statistic is derived, which allows us to find asymptotic critical values. When there is a change, the behavior of the test statistic is discussed. Conditions for the consistency of these tests are also discussed. Based on the asymptotic results, simulation studies of testing for changes in the mean show that the CUSUM test proposed performs well.     

OUTLIER TEST IN RANDOMIZED LINEAR MODEL

In this paper, we give an approach for detecting one or more outliers inrandomized linear model The likelihood ratio test statistic and its distributions under the null hypothesis and the alternative bypothesis are given. Furthermore, the rebustneas of the test statistic in a certain sere is proved. Finally, the optimality properties of the test are derived.     

Asymptotics of the goodness-of-fit test for a partial linear model with randomly censored data

In this paper, we discuss the problem of testing the hypothesis that the underlying regression is a partial linear model. A test statistic, which is based on the quadratic form of a cusum process of residuals, is proposed. The asymptotic distributions of the test statistic under null hypothesis and the local alternative hypothesis are given. The number simulation shows that the test is available.     

时间序列中参数变点的检测(英文)

The paper considers the problem of testing for a change point in the parameters of AR（p） models.It is shown that the asymptotically limiting distribution of the residual CUSUM of squares test（RCUSQ） is still the sup of a standard Brownian bridge under null hypothesis.We also show via simulations that our asymptotic results provide good approximations in finite samples.     

Testing Lack-of-fit for a Polynomial Errors-in-variables Model

When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial error-in-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables,we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the significance level well.The choice of weight functions involved in the test statistic and the related power study are also investigated.The application to two examples is illustrated. The approach can be readily extended to handle more general models.     

A Unit Root Test for an AR(1) Process with AR Errors by Using Random Weighted Bootstrap

A great deal of economic problems are related to detecting the stability of time series data,where the main interest is in the unit root test.In this paper,we consider the unit root testing problem with errors being long-memory processes with the LARCH structure.A new test statistic is developed by using the random weighted bootstrap method.It turns out that the proposed statistic has a chisquared distribution asymptotically regardless of the process being stationary or nonst at ionary,and with ...     

Inference of change-point in single index models

Single index models are widely used in medicine, econometrics and some other fields. In this paper, we consider the inference of a change point problem in single index models. Based on density-weighted average derivative estimation (ADE) method, we propose a statistic to test whether a change point exists or not. The null distribution of the test statistic is obtained using a permutation technique. The permuted statistic is rigorously shown to have the same distribution in the limiting sense under both null and alternative hypotheses. After the null hypothesis of no change point is rejected, an ADE-based estimate of the change point is proposed under assumption that the change point is unique. A simulation study confirms the theoretical results.     

Some Properties of A Lack-of-Fit Test for a Linear Errors in Variables Model

The relationship between the linear errors-in-variables model and the corresponding ordinary linear model in statistical inference is studied. It is shown that normality of the distribution of covariate is a necessary and sufficient condition for the equivalence. Therefore, testing for lack-of-fit in linear errors-in-variables model can be converted into testing for it in the corresponding ordinary linear model under normality assumption. A test of score type is constructed and the limiting chi-squared distribution is derived under the null hypothesis.Furthermore, we discuss the power of the test and the choice of the weight function involved in the test statistic.     

Subsampling tests for variance changes in the presence of autoregressive parameter shifts

In this paper, we consider the problem of testing for variance changes in the linear autoregressive processes including AR(p) processes when there are autoregressive parameter shifts. In performing a test, we employ the conventional residual CUSUM of squares test (RCUSQ) statistic. The RCUSQ test is based on the subsampling method introduced by Jach and Kokoszka (2004) [16] to eliminate the influence caused by autoregressive parameter shifts. It is shown that under regularity conditions, the test statistic behaves asymptotically the function of a standard Brownian bridge. We establish the asymptotic validity of this method and assess its performance both theoretically and numerically.     

Statistical inference for multivariate longitudinal data with irregular auto-correlated error process

Multivariate longitudinal data arise frequently in a variety of applications, where multiple outcomes are measured repeatedly from the same subject. In this paper, we first propose a two-stage weighted least square estimation procedure for the regression coefficients when the random error follows an irregular autoregressive(AR) process, and establish asymptotic normality properties for the resulting estimators. We then apply the smoothly clipped absolute deviation(SCAD) variable selection approach to determine the order of the AR error process. We further propose a test statistic to check whether multiple responses are correlated at the same observation time, and derive the asymptotic distribution of the proposed test statistic. Several simulated examples and real data analysis are presented to illustrate the finite-sample performance of the proposed method.     

The Order of the Error Term for Moments of the Log Likelihood Ratio Unit Root Test in an Autoregressive Process

This paper investigates the asymptotics of the log likelihood ratio test for a unit root in an autoregressive (AR) process of general order. The main result is that the expectation and variance (in fact, all moments) of the test statistic may, to the order of T-1, where T is the number of observations, be approximated by the expectation and variance of the corresponding test in an AR(1) process. This result has obvious implications for the asymptotics of unit root tests for panels. An explicit formula for the approximation error of a test in an AR(2) process is also given.     

Bootstrap tests for structural change with infinite variance observations

The quest of structural change with infinite variance observations appears to be relatively common. Conventional residual CUSUM of squares test (RCUSQ) are unreliable in the presence of such behavior, having nonpivotal asymptotic null distributions. In this paper we propose a residual-based bootstrap approach to RCUSQ testing that is valid against a range of infinite variance processes. Our proposed method does not require the practitioners to specify knowledge for tailed index. Consistency and the rate of convergence for the estimated change point are also obtained. We also show via simulations that our asymptotic results provide good approximations in finite samples. In addition, we apply our results to investigate the original returns for NO.1 SDS using a historical data set that covers the period 1999–2002.     

On the cusum of squares test for variance change in nonstationary and nonparametric time series models

In this paper we consider the problem of testing for a variance change in nonstationary and nonparametric time series models. The models under consideration are the unstable AR(q) model and the fixed design nonparametric regression model with a strong mixing error process. In order to perform a test, we employ the cusum of squares test introduced by Inclán and Tiao (1994,J. Amer. Statist. Assoc.,89, 913–923). It is shown that the limiting distribution of the test statistic is the sup of a standard Brownian bridge as seen in iid random samples. Simulation results are provided for illustration.     

在非线性回归模型中误差为AR(2)的相关性检验

本文讨论了在非线性回归模型中误差为AR(2)的相关性检验，得到了误差相关性检验的似然比检验统计量、Score检验统计量．对感兴趣参数和多余参数，利用Cox and Reid(1987)提出的正交化方法，给出了修正的似然比检验统计量和Score检验统计量．推广了胡跃清，韦博成(1994)讨论的在非线性回归模型中误差为AR(1)相关性检验的结果．     

m维AR(p)模型的统计诊断

统计诊断就是探查对统计推断（如估计或预测等）有较大影响的数据从而对全过程数据进行诊断．本文应用基于数据删除模型得到二维AR（1）模型的参数估计诊断公式,给出了Cook统计量的计算公式,进而推广到m维AR（p）模型的情形．