L-模糊集的L-模糊映射

引入L－模糊集的L－模糊映射,L－模糊单射,L－模糊满射及L－模糊双射等概念,并给出了它们的刻画。     

基于似然比族的一种渐近展开方法

研究假设检验问题中在适当的备选假设条件下基于似然比许愿 其计量的分布的渐近展开问题，当τ＝τ（ｎ）→０时，获得了形为Ｏ的收敛速度，并对独立同分布随机变量和与Ｌ统计量给出了其分布函数渐近展开式的具体形式。     

时间序列中向量自回归模型的拟合优度检验

本文提出并研究了一些诊断检验工具,用于一般参数型的时间序列向量自回归模型的拟合优度检验．该检验在零假设下渐近服从卡方分布,并能侦察到以参数速度收敛到零假设模型的备择模型．检验涉及到权函数,因此可以灵活地选择权函数以提高检验功效,尤其是在可能的偏离方向已知情形．如果备择不是方向型的,而只知道其属于某一个模型类中,此时可构造一个渐近分布自由的极大极小（maximin）检验．对于饱和备择,基于得分型思想给出了构造万能（omnibus）检验的可行性构想．本文对提出的检验从理论上进行了功效研究．另外,为提高检验在小样本情形的功效,本文把非参数Monte Carlo检验方法推广到相依数据情形．最后,通过模拟研究和实际数据分析进一步表明检验的有用性．     

基于纵向数据的Poisson-Gamma模型系数的随机性检验

应用随机系数化方法对纵向数据的Poisson-Gamma回归模型进行了研究,采用Laplace展开方法得到了关于响应变量的近似似然函数并得到模型系数的随机性检验的Score统计量.通过Monte Carlo模拟分析了检验的渐近功效.最后把得到的检验统计量应用到具体的数值实例分析中说明其有效性.     

具有随机删失数据的部分线性模型的拟合优度检验的渐近性质

研究随机删失部分线性回归模型的假设检验问题. 提出了一个检验统计量来检验数据是否满足一个部分线性回归模型, 它是基于残差的cusum过程的平方形式. 研究了零假设下和局部对立假设下检验统计量的渐近分布. 数值模拟表明该检验方法有好的检验功效.     

上界型拟合优度检验

对简单零假设情况,构造出一类上界型拟合优度检验.取不同的参数λ和不同的权函数,这类检验不仅包含许多已存在的检验,如Kolmogorov-Smirov检验,Berk-Jones检验等,而且还给出一些新的检验.众所周知,对不同的问题,"最优"的检验是不同的,有必要对这类检验的性质进行讨论.该文对任意给定的λ和较一般的权函数q(·),在较弱的条件下,导出了相应上界型检验统计量在零假设下的渐近分布,研究了它们的局部渐近功效;在若干固定备择假设下,对该类检验的功效进行了模拟研究.模拟结果表明,在不同的备择假设下,功效较优的检验是不同的,不存在对所有情况一致最优的检验.     

线性模型中自相关的经验似然比检验

研究线性回归模型中的自相关检验问题,用经验似然的方法构造检验统计量,得到了零假设下检验统计量的渐近分布,我们的检验方法不但可以检验一阶自相关,也可以检验高阶自相关,数值模拟表明检验方法具有良好的检验功效.     

关于L∞—模距离的二维带宽问题

二维宽带问题是将图G嵌入平面格子图,使其最长的连边尽可能短,迄今为止,在平面格子图中考虑的距离为矩线距离,即L1－模距离,在本文中,我们研究在L∞－模距离意义下的二维带宽问题。     

双诱导映射下的L-Fuzzy子环上的L-Fuzzy模

给出了L－Fuzzy子环的L－Fuzzy模概念，给出了它的若干刻画，并证明了在双诱导映射及逆映射下L－Fuzzy子环上的L－Fuzzy模仍L－Fuzzy环上的L－Fuzzy模。     

半参数回归模型L-估计的渐近展开

对妆参数回归模型Ｙ＝x^Tβ＋g（ｔ）＋ε,构造了参数向量β的Ｌ－估计量－／λn,获得了－／λn的渐近正态性及分布的Ｅdgeworth展开,其速度可达到Ｏ(n^-1)。     

Improved inference in dispersion models

We derive a general matrix Bartlett–type correction factor to the gradient statistic in the class of dispersion models. The correction improves the large–sample χ² approximation to the null distribution of the gradient statistic when the sample size is finite. We conduct Monte Carlo simulation experiments to evaluate and compare the performance of various different tests, namely the usual Wald, likelihood ratio, score, and gradient tests, the Bartlett–corrected versions of the likelihood ratio, score, and gradient tests, and bootstrap–based tests. The simulation results suggest that the analytical and computational corrections are effective in removing size distortions of the type I error probability with no power loss. The impact of the corrections in two real data applications is considered for illustrative purposes.     

季节调整对单位根检验的影响——基于蒙特卡罗模拟的研究

季节调整是使用季节数据进行经济分析的前提.但是季节调整是否会对单位根检验的结论造成影响却是一个存在争议的问题.本文扩展了Ghysels和Perron的分析框架,通过蒙特卡罗模拟考察了X-12-ARIMA季节调整对ADF和DF-GLS单位根检验的影响.结果表明,对于季节时间序列,使用季节调整后数据,只要滞后阶数选取合适,单位根检验的功效就不会发生严重损失.     

Interpreting Kullback-Leibler divergence with the Neyman-Pearson lemma

Kullback-Leibler divergence and the Neyman-Pearson lemma are two fundamental concepts in statistics. Both are about likelihood ratios: Kullback-Leibler divergence is the expected log-likelihood ratio, and the Neyman-Pearson lemma is about error rates of likelihood ratio tests. Exploring this connection gives another statistical interpretation of the Kullback-Leibler divergence in terms of the loss of power of the likelihood ratio test when the wrong distribution is used for one of the hypotheses. In this interpretation, the standard non-negativity property of the Kullback-Leibler divergence is essentially a restatement of the optimal property of likelihood ratios established by the Neyman-Pearson lemma. The asymmetry of Kullback-Leibler divergence is overviewed in information geometry.     

TESTING THE ADEQUACY OF GARCH-TYPE MODELS IN TIME SERIES

In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enhance power performance. The choice of weight functions and the power properties of the tests are studied. For a large number of alternatives, asymptotically distribution-free maximin test is constructed. The tests are asymptotically chi-squared under the null hypothesis and easy to implement. Simulation results indicate that the tests perform well.     

Likelihood ratio inequalities with applications to various mixtures

We give two simple inequalities on likelihood ratios. A first application is the consistency of the maximum-penalized marginal-likelihood estimator of the number of populations in a mixture with Markov regime. The second application is the derivation of the asymptotic power of the likelihood ratio test under loss of identifiability for contiguous alternatives. Finally, we propose self-normalized score tests that have exponentially decreasing level and asymptotic power 1.     

Diagnostic checking for conditional heteroscedasticity models

We suggest the score type tests for goodness-of-fit of conditional heteroscedasticity models in both univariate and multivariate time series. The tests can detect the alternatives converging to the null at a parametric rate. Weight functions are involved in the construction of the tests, which provides us with the flexibility to choose scores, especially under directional alternatives, for enhancing power performance. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. A possibility to construct score-based omnibus tests is discussed when the alternative is saturated. The power performance is also investigated. A simulation study is carried out and a real data is analyzed.     

正态分布方差变点的检验

本文讨论了正态分布方差只有一个变点的检验问题，我们构造了三个检验统计量，其中L检验基于非参数U统计量，B检验基于Bayes方法，R检验由极大似然比方法导出．本文给出了L、B、R检验的渐近临界值，并用MonteCarlo模拟方法研究了这三个检验与平方的CUSUM检验以及LM检验的势，并进行了比较。当变点在序列的前一半位置时，L和R检验较好，当变点在序列的后一半位置时，平方的CUSUM和B检验较好．     

Rank analogues of the likelihood ratio test for an ordered alternative in a two-way layout

Summary Distribution-free tests for no treatment effect against the simple order alternative in a two-way layout with equal number of observations per cell are considered. The nonparametric test statistics are constructed by the rank analogues of the likelihood ratio test statistic assuming normality (i) based on within-block rankings and (ii) based on combined rankings of all the observations after alignment within each block. The exact distributions are given and large sample properties are investigated. The asymptotic power of the test (i) as the number of observations per eell tends to infinity can be satisfied enough, and in the case that the number of blocks tends to infinity, the asymptotic power of the test (ii) is almost higher than that of the test (i). Also these rank tests are compared with linear rank tests and it is shown that these proposed tests are robust by a table.     

Nonlinearity tests for bilinear systems

The purpose of this paper is to develop nonlinearity tests for open-loop bilinear systems. Lagrange multiplier tests of linear systems against a bilinear alternative are proposed. A simulation study is performed to check the validity of the asymptotic null distributions of the test statistics and to investigate the power characteristics of the tests. Two recent nonlinearity tests in the time-series context are adapted to linear systems and compared with Lagrange multiplier tests. Simulation results show that the proposed Lagrange multiplier tests are more powerful than the other tests.     

Pattern classification by using improved wavelet Compressed Zernike Moments

In this paper, an improved Feature Extraction Method (FEM), which selects discriminative feature sets able to lead to high classification rates in pattern recognition tasks, is presented. The resulted features are the wavelet coefficients of an improved compressed signal, consisting of the Zernike moments amplitudes. By applying a straightforward methodology, it is aimed to construct optimal feature vectors in the sense of vector dimensionality and information content for classification purposes. The resulting surrogate feature vector is of lower dimensionality than the original Zernike moment feature vector and thus more appropriate for pattern recognition tasks.Appropriate validation tests have been arranged, in order to investigate the performance of the proposed algorithm by measuring the discriminative power of the new feature vectors despite the information loss.