Rate of Strong Consistency of Maximum Quasi-Likelihood Estimator in Multivariate Generalized Linear Models

In this article, we consider a multivariate generalized linear model with adaptive design matrix and general link function. The asymptotic singularity of design matrix of adaptive design presents challenge when establishing the large sample properties of the maximum quasi-likelihood estimate (MQLE). Under some mild conditions, we obtain a strong convergence rate of the MQLE.     

Asymptotic Behaviors of the Lorenz Curve for Censored Data Under Strong Mixing

In this article, we consider a nonparametric estimator of the Lorenz curve under censored dependent model. We show that this estimator is uniformly strongly consistent for the associated Lorenz curve. Also, a strong Gaussian approximation for the associated Lorenz process are established under appropriate assumptions. A law of the iterated logarithm for the Lorenz process is also derived.     

Consistency of Ridge Function Fields for Varying Nonparametric Regression

A nonparametric regression model proposed in Pelletier and Frouin (2006 Pelletier , B. , Frouin , R. ( 2006 ). Remote sensing of phytoplankton chlorophyll-a concentration by ridge function fields . App. Optics 45 : 784 – 798 . [Google Scholar]) as a solution to the geophysical problem of ocean color remote sensing is studied. The model, called ridge function field, combines a regression estimate in the form of a superposition of ridge functions, or which is equivalent to a neural network, with the idea pertaining to varying-coefficients models, where the parameters of a parametric family are allowed to vary with other variables. Under mild assumptions on the underlying distribution of the data, the strong universal consistency of the least-squares ridge function fields estimate is established.     

On the Strong Consistency of Ridge Estimates

In this article, we establish strong consistency of the ridge estimates using extended results for the strong consistency of the least squares estimates in multiple regression models which discard the usual assumption of null mean value for the errors and only requires them to be i.i.d. with absolute moment of order r (0 < r ? 1).     

Some comments on two-stage selection procedures

In this paper we study the procedures of Dudewicz and Dalal ( 1975 ), and the modifications suggested by Rinott ( 1978 ), for selecting the largest mean from k normal populations with unknown variances. We look at the case k = 2 in detail, because there is an optimal allocation scheme here. We do not really allocate the total number of samples into two groups, but we estimate this optimal sample size, as well, so as to guarantee the probability of correct selection (written as P(CS)) at least P^?, 1/2 < P^? < 1 . We prove that the procedure of Rinott is “asymptotically in-efficient” (to be defined below) in the sense of Chow and Robbins ( 1965 ) for any k  2. Next, we propose two-stage procedures having all the properties of Rinott's procedure, together with the property of “asymptotic efficiency” - which is highly desirable.     

Robust image segmentation via Bayesian type criterion

Image segmentation plays an important role in image processing before image recognition or compression. Many segmentation solutions follow the information theoretic criteria and often have excellent results; however, they are not robust to reduce the noise effect in contaminated image data. To guarantee the optimal segmentation with possible noise, a robust Bayesian information criterion is proposed to segment a grayscale image and it is less sensitive to noise. The asymptotic properties are also studied. Monte Carlo numerical experiments along with a brain magnetic resonance image are conducted to evaluate the performance of the new method.     

基于G1法的判断矩阵的一致性分析

应用层次分析法(AHP)法的难点在于构造判断矩阵,构造判断矩阵的难点在于其一致性问题,本文用G1法分析造成AHP判断矩阵不一致的原因,指出了G1法与构造判断矩阵的本质区别,解决了层次分析法的应用难题.同时对一些文献基于构造判断矩阵得出的值得商榷的结论进行了讨论.     

三维面板结构VAR模型的估计

文章构建了三维面板结构VAR模型,并提出参数估计的一致性方法,编制估计程序,仿真模拟有限样本性质。结果表明:在给定N₁、N₂的情况下,随着T的增加,参数的估计值与真值的偏差逐渐减少,并逼近于0;当T固定时,逐渐增大N₁、N₂,偏误逐渐减小,也都趋近于0。随着样本容量的增大,参数估计量的标准误均有逐渐减小的趋势。通过JB检验发现参数估计量都接受服从正态分布的原假设,具有较好的正态性。     

A class of one sample tests based on the Mann–Whitney–Wilcoxon functional

The main idea behind the proposed class of tests is rooted on an extension of the technique used in the derivation of the Mann–Whitney–Wilcoxon test. Just like the case of two-sample rank-based tests, the new class consists of tests defined through score functions. When properly selected, these score functions lead to consistent and often more powerful tests compared with classical goodness-of-fit tests. Theoretical results are supported by an extensive simulation study.