Regression model for surrogate data in high dimensional statistics

Abstract

This paper deals with the problem of estimating the regression of a surrogated scalar response variable given a functional random one. We construct an estimator of the regression operator by using, in addition to the available (true) response data, a surrogate data. We then establish some asymptotic properties of the constructed estimator in terms of the almost-complete and the quadratic mean convergences. Notice that the obtained results generalize a part of the results obtained in the finite dimensional framework. Finally, an illustration on the applicability of our results on both simulated data and a real dataset was realized. We have thus shown the superiority of our estimator on classical estimators when we are lacking complete data.     

Structure Learning of Contextual Markov Networks using Marginal Pseudo‐likelihood

Markov networks are popular models for discrete multivariate systems where the dependence structure of the variables is specified by an undirected graph. To allow for more expressive dependence structures, several generalizations of Markov networks have been proposed. Here, we consider the class of contextual Markov networks which takes into account possible context‐specific independences among pairs of variables. Structure learning of contextual Markov networks is very challenging due to the extremely large number of possible structures. One of the main challenges has been to design a score, by which a structure can be assessed in terms of model fit related to complexity, without assuming chordality. Here, we introduce the marginal pseudo‐likelihood as an analytically tractable criterion for general contextual Markov networks. Our criterion is shown to yield a consistent structure estimator. Experiments demonstrate the favourable properties of our method in terms of predictive accuracy of the inferred models.     

论广告语的伪诗歌化特征

为了吸引更多的受众,广告文案设计者在广告语创意时往往借用诗歌的艺术形式来表现,甚至也不排除一定意义上的诗歌精神的渗透,但它还不是真正的诗歌创作,广告语存在着伪诗歌化特征.广告语的伪诗歌化特征具体体现在伪情感、伪意境、伪节奏三个方面.     

GMM with Many Moment Conditions

This paper provides a first order asymptotic theory for generalized method of moments (GMM) estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak. Examples in which these asymptotics are relevant include instrumental variable (IV) estimation with many (possibly weak or uninformed) instruments and some panel data models that cover moderate time spans and have correspondingly large numbers of instruments. Under certain regularity conditions, the GMM estimators are shown to converge in probability but not necessarily to the true parameter, and conditions for consistent GMM estimation are given. A general framework for the GMM limit distribution theory is developed based on epiconvergence methods. Some illustrations are provided, including consistent GMM estimation of a panel model with time varying individual effects, consistent limited information maximum likelihood estimation as a continuously updated GMM estimator, and consistent IV structural estimation using large numbers of weak or irrelevant instruments. Some simulations are reported.     

Large‐sample tests of extreme‐value dependence for multivariate copulas

Starting from the characterization of extreme‐value copulas based on max‐stability, large‐sample tests of extreme‐value dependence for multivariate copulas are studied. The two key ingredients of the proposed tests are the empirical copula of the data and a multiplier technique for obtaining approximate p‐values for the derived statistics. The asymptotic validity of the multiplier approach is established, and the finite‐sample performance of a large number of candidate test statistics is studied through extensive Monte Carlo experiments for data sets of dimension two to five. In the bivariate case, the rejection rates of the best versions of the tests are compared with those of the test of Ghoudi et al. (1998) recently revisited by Ben Ghorbal et al. (2009). The proposed procedures are illustrated on bivariate financial data and trivariate geological data. The Canadian Journal of Statistics 39: 703–720; 2011. © 2011 Statistical Society of Canada     

Statistical Corrections of Invalid Correlation Matrices

Suppose estimates are available for correlations between pairs of variables but that the matrix of correlation estimates is not positive definite. In various applications, having a valid correlation matrix is important in connection with follow‐up analyses that might, for example, involve sampling from a valid distribution. We present new methods for adjusting the initial estimates to form a proper, that is, nonnegative definite, correlation matrix. These are based on constructing certain pseudo‐likelihood functions, formed by multiplying together exact or approximate likelihood contributions associated with the individual correlations. Such pseudo‐likelihoods may then be maximized over the range of proper correlation matrices. They may also be utilized to form pseudo‐posterior distributions for the unknown correlation matrix, by factoring in relevant prior information for the separate correlations. We illustrate our methods on two examples from a financial time series and genomic pathway analysis.     

Bayesian approach to change point problems

A Bayesian approach is considered to study the change point problems. A hypothesis for testing change versus no change is considered using the notion of predictive distributions. Bayes factors are developed for change versus no change in the exponential families of distributions with conjugate priors. Under vague prior information, both Bayes factors and pseudo Bayes factors are considered. A new result is developed which describes how the overall Bayes factor has a decomposition into Bayes factors at each point. Finally, an example is provided in which the computations are performed using the concept of imaginary observations.     

ON AN APPROXIMATE OPTIMALITY CRITERION FOR THE DESIGN OF FIELD EXPERIMENTS UNDER SPATIAL DEPENDENCE

The design of large‐scale field trials where the residuals are correlated has been of recent interest, in large part because of advances in statistical and computational methods of analysis. The construction of designs for correlated data has typically used A‐optimality and is computationally intensive. This involves calculating the inverse of the information matrix for treatments under the supervision of an optimization strategy that explores the design space. We propose an approximation to A‐optimality, using nearest‐neighbour balance, that is less computationally demanding and can achieve at least 95% efficiency relative to A‐optimality in many practical situations.     

云南境外的傣泐人

傣泐人又叫泐人(Lue),是傣族中的一支。在我国,傣泐人主要居住在云南的西双版纳,此外,思茅和红河地区也有少量分布。除了云南以外,境外的几个国家也居住有一些傣泐人。居住在境外各国的傣泐人,由于环境的改变,他们在文化、习俗等方面与云南的傣泐人已有了一些不同,在政治上也分别认同他们居住的国家。但是,另一方面,他们又仍然保持着对他们的故土西双版纳和他们傣泐人身份的认同。由于保持着这种认同,这个群体也就成为联系云南乃至中国与东南亚国家的一条天然纽带。