A Note on a Partition of the Likelihood Ratio Test for Autoregressive Covariance Structure

A sequence of nested hypotheses is presented for the examination of the assumption of autoregressive covariance structure in, for example, a repeated measures experiment. These hypotheses arise naturally by specifying the joint density of the underlying vector random variable as a product of conditional densities and the density of a subset of the vector random variable. The tests for all but one of the nested hypotheses are well known procedures, namely analysis of variance F-tests and Bartlett's test of equality of variances. While the procedure is based on tests of hypotheses, it may be viewed as an exploratory tool which can lead to model identification. An example is presented to illustrate the method.     

The degree variance: An index of graph heterogeneity

In the analysis of empirically found graphs, the variance of the degrees can be used as a measure for the heterogeneity of (the points in) the graph. For several types of graphs, the maximum value of the degree variance is given, and the mean and variance of the degree variance under a simple stochastic null model are computed. These are used to produce normalized versions of the degree variance, which can be used as heterogeneity indices of graphs.     

ESTIMATING THE MAXIMUM (MINIMUM) OF A QUADRATIC FUNCTION UNDER CERTAIN CORRELATION PATTERNS

May nonidentity error correlation patterns encountered in regression theory allow computationally efficient techniques for modifying the usual procedures for constructing confidence intervals and performing F-tests so that valid inferences can be drawn. Such techniques are explored in light of the general theme of this note.     

Robust estimation of variance components

New robust estimates for variance components are introduced. Two simple models are considered: the balanced one-way classification model with a random factor and the balanced mixed model with one random factor and one fixed factor. However, the method of estimation proposed can be extended to more complex models. The new method of estimation we propose is based on the relationship between the variance components and the coefficients of the least-mean-squared-error predictor between two observations of the same group. This relationship enables us to transform the problem of estimating the variance components into the problem of estimating the coefficients of a simple linear regression model. The variance-component estimators derived from the least-squares regression estimates are shown to coincide with the maximum-likelihood estimates. Robust estimates of the variance components can be obtained by replacing the least-squares estimates by robust regression estimates. In particular, a Monte Carlo study shows that for outlier-contaminated normal samples, the estimates of variance components derived from GM regression estimates and the derived test outperform other robust procedures.     

Nonparametric and non-linear models and data mining in time series: a case-study on the Canadian lynx data

Nonparametric regression methods are used as exploratory tools for formulating, identifying and estimating non-linear models for the Canadian lynx data, which have attained bench-mark status in the time series literature since the work of Moran in 1953. To avoid the curse of dimensionality in the nonparametric analysis of this short series with 114 observations, we confine attention to the restricted class of additive and projection pursuit regression (PPR) models and rely on the estimated prediction error variance to compare the predictive performance of various (non-)linear models. A PPR model is found to have the smallest (in-sample) estimated prediction error variance of all the models fitted to these data in the literature. We use a data perturbation procedure to assess and adjust for the effect of data mining on the estimated prediction error variances; this renders most models fitted to the lynx data comparable and nearly equivalent. However, on the basis of the mean-squared error of out-of-sample prediction error, the semiparametric model X_t =1.08+1.37 X_{t −1}+ f ( X_{t −2})+ e_t and Tong's self-exciting threshold autoregression model perform much better than the PPR and other models known for the lynx data.     

Linearization of inequality indices in the design-based framework

Linearization methods are customarily adopted in sampling surveys to obtain approximated variance formulae for estimators of statistical functionals under the design-based approach. In the present paper, following the Deville [Variance estimation for complex statistics and estimators: linearization and residual techniques. Surv Methodol. 1999;25:193–203] approach stemming from the concept of design-based influence function, we provide a general result for linearizing a large family of population functionals which includes many of the inequality measures considered in social, economic and statistical studies, such as the Gini, Amato, Zenga, Atkinson and Generalized Entropy indices. The feasibility of our theoretical results is assessed by some simulation studies involving real and artificial data.     

Exponential GARCH Modeling With Realized Measures of Volatility

We introduce the realized exponential GARCH model that can use multiple realized volatility measures for the modeling of a return series. The model specifies the dynamic properties of both returns and realized measures, and is characterized by a flexible modeling of the dependence between returns and volatility. We apply the model to 27 stocks and an exchange traded fund that tracks the S&P 500 index and find specifications with multiple realized measures that dominate those that rely on a single realized measure. The empirical analysis suggests some convenient simplifications and highlights the advantages of the new specification.     

Efficiency comparison of M-estimates for scale at t-distributions

Using Fisher's information fort-distributions, the absolute asymptotic efficiency of some M-estimates for scale with known location parameter is calculated and graphically illustrated. The compared estimators are the standard deviationS _*, the mean absolute deviation, called mean deviationD _*, the median absolute deviation, called MAD_*, and some M-estimates for scale, one, which is very robust, and another one with high asymptotic efficiency fort-distributions close to the normal. The last one is considered with monotone (in the positive field) and with very late redescending χ-function too. Also the , an alternative and generalized excess measure defined as the double relative asymptotic variance of the underlying scale estimator in the previous paper, is calculated fort-distributions and graphically illustrated, because there is the relation that the higher the asymptotic efficiency of is, the lower is the corresponding .     

从法理角度看中国在联合国安理会的弃权行为(2000-2011)

弃权是产生法律效力的不成文规定,本身就是一种权利,也是一种态度,并非消极回避。中国的弃权是经过慎重考虑后的决策,充分尊重了《联合国宪章》的宗旨和原则,体现了原则性与灵活性的统一。中国在安理会投票中坚持反对霸权、捍卫主权、主张和平等原则。中国对1973号决议投弃权票正体现了这些原则。