The use of multilevel modeling and the level two residual file to explore the relationship between middle years programme student performance and diploma programme student performance

Multilevel modeling has recently found a substantial niche in the context of educational research, although several details about the methodological application of these models have yet to be explored in an achievement data framework. This paper makes use of data provided by the International Baccalaureate (IB) in order to investigate modeling decisions and certain applications of the level two residual file in an effort to increase understanding about the way linear and logistic multilevel models function. The focus of this research is on the relationship between performances in two IB programmes: the Middle Years Programme (MYP) and the Diploma Programme (DP). The impact of predictors on the interpretation of the unconditional and conditional variance-covariance matrix as well as the reliability coefficients is discussed. Empirical findings suggest that students who perform better during MYP moderation tend to perform better on DP exams.     

相对论性理想流体熵密度的计算

求解自引力非辐射体系的熵结构，这个问题很有意义．本文一般地导出相对论性流体热力学第二定律的协变表达式．利用理想流体的熵流守恒和局域能量守恒等基本守恒律推导出熵密度的计算公式．     

"已实现"波动率理论研究与评价

"已实现"波动率是一种全新的金融波动率测量方法。"已实现"波动率在理论上没有测量误差的无偏估计量,在实证建模方面比其他模型更易于估计参数,同时最优频率的选取对于"已实现"波动率的测量精确度是很重要的。     

基于LD分解的空间谱估计技术

提出了一种基于对阵列协方差矩阵进行 LD 分解的空间谱估计算法。对一大类阵列来说,该算法对空间谱估计方法的工程实现问题具有十分重要的实际意义。文中证明了特殊Hernitian 矩阵 LD 分解的原理,给出了求分解因式的递推公式,然后,由 LD 分解找出的信号子空间,得出了估计信号源方向的空间谱计算公式。理论分析和模拟结果表明,LD 分解和原有的特征分解法相比,更易于用专用数字信号处理片实现,有更小的计算量,需更少的存储单元。     

Quotient spaces and statistical models

The purpose of this paper is to draw attention to the widespread occurrence of quotient spaces in statistical work. Quotient spaces are intrinsic to probability distributions, residuals and interaction in linear models, covariance functions and variograms of stochastic processes, etc. The theme is that explicit recognition of the quotient space can offer surprising conceptual simplification. The advantages of working directly with the quotient space are hard to describe in general. As the examples demonstrate, the answer lies partly in directness of approach.     

Parameterizations and Fitting of Bi-directed Graph Models to Categorical Data

Abstract.  We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi-directed graph models, under the global Markov property. Such models are useful data analytic tools especially if used in combination with other graphical models. The first parameterization, in the saturated case, is also known as thenation multivariate logistic transformation, the second is a variant that allows, in some (but not all) cases, variation-independent parameters. An algorithm for maximum likelihood fitting is proposed, based on an extension of the Aitchison and Silvey method.     

Principal Volatility Component Analysis

Many empirical time series such as asset returns and traffic data exhibit the characteristic of time-varying conditional covariances, known as volatility or conditional heteroscedasticity. Modeling multivariate volatility, however, encounters several difficulties, including the curse of dimensionality. Dimension reduction can be useful and is often necessary. The goal of this article is to extend the idea of principal component analysis to principal volatility component (PVC) analysis. We define a cumulative generalized kurtosis matrix to summarize the volatility dependence of multivariate time series. Spectral analysis of this generalized kurtosis matrix is used to define PVCs. We consider a sample estimate of the generalized kurtosis matrix and propose test statistics for detecting linear combinations that do not have conditional heteroscedasticity. For application, we applied the proposed analysis to weekly log returns of seven exchange rates against U.S. dollar from 2000 to 2011 and found a linear combination among the exchange rates that has no conditional heteroscedasticity.     

Variance Estimation and Asymptotic Confidence Bands for the Mean Estimator of Sampled Functional Data with High Entropy Unequal Probability Sampling Designs

For fixed size sampling designs with high entropy, it is well known that the variance of the Horvitz–Thompson estimator can be approximated by the Hájek formula. The interest of this asymptotic variance approximation is that it only involves the first order inclusion probabilities of the statistical units. We extend this variance formula when the variable under study is functional, and we prove, under general conditions on the regularity of the individual trajectories and the sampling design, that we can get a uniformly convergent estimator of the variance function of the Horvitz–Thompson estimator of the mean function. Rates of convergence to the true variance function are given for the rejective sampling. We deduce, under conditions on the entropy of the sampling design, that it is possible to build confidence bands whose coverage is asymptotically the desired one via simulation of Gaussian processes with variance function given by the Hájek formula. Finally, the accuracy of the proposed variance estimator is evaluated on samples of electricity consumption data measured every half an hour over a period of 1 week.     

Collinearity: revisiting the variance inflation factor in ridge regression

Ridge regression has been widely applied to estimate under collinearity by defining a class of estimators that are dependent on the parameter k. The variance inflation factor (VIF) is applied to detect the presence of collinearity and also as an objective method to obtain the value of k in ridge regression. Contrarily to the definition of the VIF, the expressions traditionally applied in ridge regression do not necessarily lead to values of VIFs equal to or greater than 1. This work presents an alternative expression to calculate the VIF in ridge regression that satisfies the aforementioned condition and also presents other interesting properties.