More powerful sign test using median ranked set sample: Finite sample power comparison

Sign test using median ranked set samples (MRSS) is introduced and investigated. We show that, this test is more powerful than the sign tests based on simple random sample (SRS) and ranked set sample (RSS) for finite sample size. It is found that, when the set size of MRSS is odd, the null distribution of the MRSS sign test is the same as the sign test obtained by using SRS. The exact null distributions and the power functions, in case of finite sample sizes, of these tests are derived. Also, the asymptotic distribution of the MRSS sign tests are derived. Numerical comparison of the MRSS sign test power with the power of the SRS sign test and the RSS sign test is given. Illustration of the procedure, using real data set of bilirubin level in Jaundice babies who stay in neonatal intensive care is introduced.     

LSTAR-GARCH模型的单位根检验

LSTAR模型的单位根检验往往易忽视其条件方差的时变性,实际上,对许多经济变量尤其是金融变量建立LSTAR模型后,经常发现其条件方差存在GARCH效应。针对LSTAR-GARCH模型的平稳性检验,本文构建了检验统计量tNG,之后在极大似然估计的基础上,推导出tNG的渐近分布,通过蒙特卡洛模拟方法得到该统计量的渐近临界值,并在此基础上研究了tNG检验的检验功效。在与刘雪燕和张晓峒(2009)提出的tNL检验、Ling等(2003)提出的tLG检验以及DF单位根检验进行比较后,发现tNG检验具备明显优势。     

On improving the min test for the analysis of combination drug trials

In the analysis of clinical trials of combination therapies, the min test is often used to demonstrate a combination therapy's superiority to its components. Although uniformly most powerful within a class of monotone tests, this test is excessively conservative with low power at certain alternatives. This paperdemonstrates that more powerful tests may be found outside of this class. Some such alternative tests are suggested and compared with the min tests on the basis of their actual significance levels and powers. The proposed tests are observed to be less conservative and uniformly more powerful than the min test.     

Comparison op some two sample tests for equality of variances

The F-test, F max-test and Bartlett's test are compared on the basis of power for the purpose of testing the equality of variances in two normal populations. The power of each test is expressed as a linear combination of F-probabilities. Bartlett's test is noted to be unbiased, UMPU, consistent against all alterna¬tives and the test which yields minimum length confidence intervals on the ratio of the variancesλ=σ₁ ² /σ² ₂ The two samples Bartlett critical values, although not recognized as such, are found in the works of other authors. Tables of the powers of each test are given for various values of λ, levels of significance a and the respective sample sizes, n₁ and n₂.     

固定效应模型基于个体LM的新可混合性检验

对固定效应模型,本文基于拉格朗日乘数（LM）原理提出了一种新的可混合性检验。不同于已有的LM型可混合性检验,这里使用每个截面个体的LM统计量构建可混合性检验统计量。数理分析表明,本文所提的方法有着渐进正态性,对于扰动项的异方差和非正态均稳健,且与PY检验（Pesaran&Yamagata,2008）渐近等价。Monte Carlo模拟实验表明,相对于PY检验及另外两种LM型的可混合性检验,对于不同大小的 ,本文提出的方法有着良好的水平表现和更优越的检验势。     

A sequential testing procedure for outliers and structural change

In this paper a test for outliers based on externally studentized residuals is shown to be related to a test for predictive failure. The relationships between a test for outliers, a test for a correlated mean shift and a test for an intercept shift are developed. A sequential testing procedure for outliers and structural change is shown to be independent, so that the overall size of the joint test can be determined exactly. It is established that a joint test for outliers and constancy of variances cannot be performed.     

The Combination Test for Multivariate Normality

A basic graphical approach for checking normality is the Q - Q plot that compares sample quantiles against the population quantiles. In the univariate analysis, the probability plot correlation coefficient test for normality has been studied extensively. We consider testing the multivariate normality by using the correlation coefficient of the Q - Q plot. When multivariate normality holds, the sample squared distance should follow a chi-square distribution for large samples. The plot should resemble a straight line. A correlation coefficient test can be constructed by using the pairs of points in the probability plot. When the correlation coefficient test does not reject the null hypothesis, the sample data may come from a multivariate normal distribution or some other distributions. So, we use the following two steps to test multivariate normality. First, we check the multivariate normality by using the probability plot correction coefficient test. If the test does not reject the null hypothesis, then we test symmetry of the distribution and determine whether multivariate normality holds. This test procedure is called the combination test. The size and power of this test are studied, and it is found that the combination test, in general, is more powerful than other tests for multivariate normality.     

正交多项式逼近下非线性趋势序列单位根检验

 传统单位根检验方法常常假设带有线性的确定性趋势,但如果趋势是非线性的,通常将因为检验功效大幅下降而导致检验失败。本文研究用正交多项式逼近非线性趋势,然后对残差进行单位根检验的方法。研究了用正交多项式进行趋势逼近的性质,推导了这种方法进行单位根检验时统计量的极限分布,提出了正交多项式最高阶数的确定方法,仿真研究了残差相关与不相关时的检验功效。结果表明,检验方法是有效的。     

An efficient nonparametric test for bivariate two-sample location problem

We propose a new test for the two-sample bivariate location problem. The proposed test statistic has a U-statistic representation with a degenerate kernel. The limiting distribution is found for the proposed test statistic. The power of the test is compared using Monte Carlo simulation to the tests of Blumen [I. Blumen, A new bivariate sign-test for location, Journal of the American Statistical Association 53 (1958) 448–456], Mardia [K.V. Mardia, A non-parametric test for the bivariate two-sample location problem, Journal of the Royal Statistical Society, Series B 29 (1967) 320–342], Peters and Randles [D. Peters, R.H. Randles, A bivariate signed-rank test for the two-sample location problem, Journal of the Royal Statistical Society, Series B 53 (1991) 493–504], LaRocque, Tardif and van Eeden [D. LaRocque, S. Tardif, C. van Eeden, An affine-invariant generalization of the Wilcoxon signed-rank test for the bivariate location problem, Australian and New Zealand Journal of Statistics 45 (2003) 153–165], and Baringhaus and Franz [L. Baringhaus, C. Franz, On a new multivariate two-sample test, Journal of Multivariate Analysis 88 (2004) 190–206]. Under the bivariate normal and bivariate t distributions the proposed test was more powerful than the competitors for almost every change in location. Under the other distributions the proposed test reached the desired power of one at a faster rate than the other tests in the simulation study. Application of the test is presented using bivariate data from a synthetic and a real-life data set.     

STAR非线性平稳性检验中误设定的伪检验研究

本文通过理论分析和蒙特卡洛仿真模拟,研究平稳性检验中选用的统计量与数据生成过程不一致时,非线性ESTAR、LSTAR与线性DF检验法能否得出正确的结论.研究表明,二阶LSTAR与ESTAR模型可用相同的检验方法,但前者的非线性特征更强.当数据生成过程为线性AR,或非线性ESTAR、二阶LSTAR模型时,使用DF或ESTAR检验法可得出大致正确的结论,但LSTAR检验法完全失败.数据生成过程的非线性特征越强,ESTAR较DF检验方法的功效增益越高;线性特征越强,DF的功效增益越高.当转移函数F(θ,c,zt)中θ较大导致一阶泰勒近似误差较大或c非0时,标准ESTAR与LSTAR非线性检验法失去应用条件.θ较大或c偏离0较远时,数据生成过程中线性成分增强,用线性DF检验可获得更好的检验结果.     

Improved tests for homogeneity of variances

Equality of variances is one of the key assumptions of analysis of variances (ANOVA). There are several testing procedures available to validate this assumption, but it is rare to find a test procedure which controls the type I error rate while providing high statistical power. In this article, we introduce a bootstrap test based on the ratio of mean absolute deviances (RMD). We also propose a two-stage testing procedure where we first quantify the skewness of the distributions and then choose an appropriate test for homogeneity of variances. The performances of these test procedures are studied via a simulation study.     

Testing autocorrelation in a system perspective testing autocorrelation

The Breusch-Godfrey test for autocorrelated errors is generalised to cover systems of equations, and the properties of 18 versions of the test are studied using Monte Carlo methods. We show that only one group of tests regularly has actual size close to the nominal size; namely the likelihood ratio tests of the auxiliary regression system that are corrected in some manner for degrees-of-freedom. The Rao Ftest exhibits the best performance, whilst the commonly used TR2 test behaves badly even in single equations. However, the size and power properties of all tests deteriorate sharply as the number of equations increases, the system becomes more dynamic, the exogenous variables become more autocorrelated and the sample size decreases. This performance has, in general, an unknown degree since the interaction amongst these factors does not permit a predictive summary, as might be hoped for by response surface-type approaches.     

基于回归的时变偏度和时变峰度识别检验

资产收益率时变高阶矩建模的首要前提是资产收益率的偏度和峰度具有时变性,即资产收益率存在类似于异方差性的异偏度和异峰度特征。目前文献中的时变偏度和时变峰度识别检验存在适用性较差且检验功效较低等不足。本文提出基于回归的检验方法识别资产收益率偏度和峰度的时变性。该检验一方面利用概率积分变换缓解了拉格朗日乘数检验对资产收益率序列的高阶矩存在性的限制,另一方面考虑了检验统计量中参数估计的不确定性对其统计性质的影响,具有良好的渐近统计性质且适用性更广。蒙特卡洛模拟表明该检验具有良好的有限样本性质,具有合适的检验水平和较高的检验功效。最后,将基于回归的检验运用于上证综指和深圳成指收益率的时变建模研究中。     

Testing autocorrelation in a system perspective testing autocorrelation

The Breusch-Godfrey test for autocorrelated errors is generalised to cover systems of equations, and the properties of 18 versions of the test are studied using Monte Carlo methods. We show that only one group of tests regularly has actual size close to the nominal size; namely the likelihood ratio tests of the auxiliary regression system that are corrected in some manner for degrees-of-freedom. The Rao Ftest exhibits the best performance, whilst the commonly used TR2 test behaves badly even in single equations. However, the size and power properties of all tests deteriorate sharply as the number of equations increases, the system becomes more dynamic, the exogenous variables become more autocorrelated and the sample size decreases. This performance has, in general, an unknown degree since the interaction amongst these factors does not permit a predictive summary, as might be hoped for by response surface-type approaches.     

门限自回归下的单位根检验可靠性研究

在非对称的门限自回归模型下,由于传统单位根检验式的误设,会导致单位根检验势下降。本文通过一系列的Monte-Carlo模拟表明：非对称性对ADF和PP检验的检验势会产生较大影响,而对其他四种常用的单位根检验势产生的影响较小,也就是说,在非对称的门限自回归下,非对称性对退势单位根检验势产生的影响较小。模拟中也发现：NP单位根检验对TAR模型和持久性都具有稳健性。     

二元选择面板模型的设定检验

 本文将RESET检验扩展到二元选择面板数据模型的设定,考察了固定效应Probit模型和Logit模型的设定检验,包括异方差、遗漏变量和分布误设的检验。模拟结果表明Logit模型的RESET设定检验显示良好的水平和功效,而Probit模型的RESET检验可能由于估计方法的选择导致在某些方面的功效表现不好。但总体说来,在二元选择面板数据模型的设定检验上,RESET检验仍然是一个较好的选择。     

数据初始值对DF类IPS检验势的影响研究

 本文研究了DF类面板数据单位根IPS检验势受时序数据初始值的影响,推导了DF类面板单位根IPS检验统计量在局部备择假设下的极限分布和局部渐近势函数,发现了DF类面板数据单位根IPS检验统计量局部渐近势在异质性局部备择假设下是初始条件的单调递增函数;小样本Monte Carlo模拟分析结果表明,若假设初始条件为零,DF类IPS统计量的检验势将被低估。     

面板数据单位根似然比检验研究

本文采用似然比类检验统计量进行面板单位根检验（简称为LR检验）研究,在局部备择假设成立的条件下,推导了其在无确定项、仅含截距项以及存在线性时间趋势项三种模型下所对应的渐近分布与局部渐近势函数。Monte Carlo模拟结果显示,当面板数据中含确定项（截距项或时间趋势项）时,LR检验水平比LLC和IPS检验水平更接近于给定的显著性检验水平;此外,当面板数据中包含发散个体时,经水平修正后的LR检验势要远远高于经水平修正后的LLC与IPS检验势,其中,经水平修正后的LLC与IPS检验势接近于零。     

An alternative Wald type test for two linear restrictions with applications to non-linear models

This paper proposes a new test procedure called the rel test to resolve the problem of small-sample local biasedness and non-monotonic power behavior of the Wald test for two linear restrictions caused by inaccuracy of the estimated covariance matrix of the estimator. This new test procedure, which does not need the covariance matrix of the estimator, involves finding the critical region based on contour points of the percentile confidence limit of a rel utilizing the bootstrap in order to obtain a test with the desired size and good power properties. Simulation results indicate that this new test procedure, the rel test, performs rather well both with respect to controlling size and having monotonic increasing power.