Consistent variable selection in large panels when factors are observable

In this paper we develop an econometric method for consistent variable selection in the context of a linear factor model with observable factors for panels of large dimensions. The subset of factors that best fit the data is sequentially determined. Firstly, a partial R² rule is used to show the existence of an optimal ordering of the candidate variables. Secondly, We show that for a given order of the regressors, the number of factors can be consistently estimated using the Bayes information criterion. The Akaike will asymptotically lead to overfitting of the model. The theory is established under approximate factor structure which allows for limited cross-section and serial dependence in the idiosyncratic term. Simulations show that the proposed two-step selection technique has good finite sample properties. The likelihood of selecting the correct specification increases with the number of cross-sections both asymptotically and in small samples. Moreover, the proposed variable selection method is computationally attractive. For K potential candidate factors, the search requires only 2K regressions compared to 2^K for an exhaustive search.     

Objective Bayesian model selection approach to the two way analysis of variance

An objective Bayesian procedure for testing in the two way analysis of variance is proposed. In the classical methodology the main effects of the two factors and the interaction effect are formulated as linear contrasts between means of normal populations, and hypotheses of the existence of such effects are tested. In this paper, for the first time these hypotheses have been formulated as objective Bayesian model selection problems. Our development is under homoscedasticity and heteroscedasticity, providing exact solutions in both cases. Bayes factors are the key tool to choose between the models under comparison but for the usual default prior distributions they are not well defined. To avoid this difficulty Bayes factors for intrinsic priors are proposed and they are applied in this setting to test the existence of the main effects and the interaction effect. The method has been illustrated with an example and compared with the classical method. For this example, both approaches went in the same direction although the large P value for interaction (0.79) only prevents us against to reject the null, and the posterior probability of the null (0.95) was conclusive.     

Decision functions for chain classifiers based on Bayesian networks for multi-label classification

Multi-label classification problems require each instance to be assigned a subset of a defined set of labels. This problem is equivalent to finding a multi-valued decision function that predicts a vector of binary classes. In this paper we study the decision boundaries of two widely used approaches for building multi-label classifiers, when Bayesian network-augmented naive Bayes classifiers are used as base models: Binary relevance method and chain classifiers. In particular extending previous single-label results to multi-label chain classifiers, we find polynomial expressions for the multi-valued decision functions associated with these methods. We prove upper boundings on the expressive power of both methods and we prove that chain classifiers provide a more expressive model than the binary relevance method.     

Estimation de facteurs de Bayes entre modèles dynamiques non linéaires à espace d'état

The use of nonlinear state space models in the study and control of stochastic dynamic systems is regularly growing. With the new generation of particle filters, efficient filtering methods are now available for the identification of these models. However their statistical selection is still an open problem because of the frequent nonaccessibility of the related likelihoods and the intricate estimation of the latter. This rules out all the usual model comparison information criteria as Akaïke's and unfavour also the efficient methods relying on Bayes factor estimation by MCMC simulations.This Note shows how a convergent nonparametric Bayes factor estimator can be built and used advantageously, as direct application of these new particle filters themselves. To cite this article: J.-P. Vila, I. Saley, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

On the admissibility of an estimator of a normal mean vector under a linex loss function

For ap-variate normal mean with known variances, the model proposed by Zellner (1986,J. Amer. Statist. Assoc.,81, 446–451) is discussed in a slightly different framework. A generalized Bayes estimate is derived from a three-stage Bayes point of view under the asymmetric loss function, and the admissibility of such estimators is proved.     

Suboptimality of M-step back strategies in Bayesian games

We consider the Bayes optimal strategy for repeated two player games where moves are made simultaneously. In these games we look at models where one player assumes that the other player is employing a strategy depending only on the previousm-move pairs (as discussed in Wilson, 1986). We show that, under very unrestrictive conditions, such an assumption is not consistent with the assumption of rationality of one's opponent. Indeed, we show that by employing such a model a player is implicitly assuming that his opponent is not playing rationally,with probability one. We argue that, in the context of experimental games, thesem-step back models must be inferior to models which are consistent with the assumption that an opponent can be rational.     

More on the inadmissibility of step-up

Cohen and Sackrowitz [Characterization of Bayes procedures for multiple endpoint problems and inadmissibility of the step-up procedure, Ann. Statist. 33 (2005) 145-158] proved that the step-up multiple testing procedure is inadmissible for a multivariate normal model with unknown mean vector and known intraclass covariance matrix. The hypotheses tested are each mean is zero vs. each mean is positive. The risk function is a 2×1 vector where one component is average size and the other component is one minus average power. In this paper, we extend the inadmissibility result to several different models, to two-sided alternatives, and to other risk functions. The models include one-parameter exponential families, independent t-variables, independent χ²-variables, t-tests arising from the analysis of variance, and t-tests arising from testing treatments against a control. The additional risk functions are linear combinations where one component is the false discovery rate (FDR).     

带有不可忽略缺失数据的半参数再生散度模型的贝叶斯分析

半参数再生散度模型是再生散度模型和半参数回归模型的推广,包括了半参数广义线性模型和广义部分线性模型等特殊类型.讨论的是该模型在响应变量和协变量均存在非随机缺失数据情形下参数的Bayes估计和基于Bayes因子的模型选择问题.在分析中,采用了惩罚样条来估计模型中的非参数成分,并建立了Bayes层次模型;为了解决Gibbs抽样过程中因参数高度相关带来的混合性差以及因维数增加导致出现不稳定性的问题,引入了潜变量做为添加数据并应用了压缩Gibbs抽样方法,改进了收敛性;同时,为了避免计算多重积分,利用了M-H算法估计边缘密度函数后计算Bayes因子,为模型的选择比较提供了一种准则.最后,通过模拟和实例验证了所给方法的有效性.     

Objective Bayesian testing on the common mean of several normal distributions under divergence-based priors

This paper considers the problem of testing on the common mean of several normal distributions. We propose a solution based on a Bayesian model selection procedure in which no subjective input is considered. We construct the proper priors for testing hypotheses about the common mean based on measures of divergence between competing models. This method is called the divergence-based priors (Bayarri and García-Donato in J R Stat Soc B 70:981–1003, 2008). The behavior of the Bayes factors based DB priors is compared with the fractional Bayes factor in a simulation study and compared with the existing tests in two real examples.     

Joint modelling of the total amount and the number of claims by conditionals

In the risk theory context, let us consider the classical collective model. The aim of this paper is to obtain a flexible bivariate joint distribution for modelling the couple (S,N), where N is a count variable and S=X₁+?+X_N is the total claim amount. A generalization of the classical hierarchical model, where now we assume that the conditional distributions of S|N and N|S belong to some prescribed parametric families, is presented. A basic theorem of compatibility in conditional distributions of the type S given N and N given S is stated. Using a known theorem for exponential families and results from functional equations new models are obtained. We describe in detail the extension of two classical collective models, which now we call Poisson-Gamma and the Poisson-Binomial conditionals models. Other conditionals models are proposed, including the Poisson-Lognormal conditionals distribution, the Geometric-Gamma conditionals model and a model with inverse Gaussian conditionals. Further developments of collective risk modelling are given.     

Nonlinear multigrid method for solving the anisotropic image denoising models

In this paper, we study a nonlinear multigrid method for solving a general image denoising model with two L ¹-regularization terms. Different from the previous studies, we give a simpler derivation of the dual formulation of the general model by augmented Lagrangian method. In order to improve the convergence rate of the proposed multigrid method, an improved dual iteration is proposed as its smoother. Furthermore, we apply the proposed method to the anisotropic ROF model and the anisotropic LLT model. We also give the local Fourier analysis (LFAs) of the Chambolle’s dual iterations and a modified smoother for solving these two models, respectively. Numerical results illustrate the efficiency of the proposed method and indicate that such a multigrid method is more suitable to deal with large-sized images.     

An efficient gradient method with approximate optimal stepsize for large-scale unconstrained optimization

In this paper, we introduce a new concept of approximate optimal stepsize for gradient method, use it to interpret the Barzilai-Borwein (BB) method, and present an efficient gradient method with approximate optimal stepsize for large unconstrained optimization. If the objective function f is not close to a quadratic on a line segment between the current iterate x _k and the latest iterate x _k?1, we construct a conic model to generate the approximate optimal stepsize for gradient method if the conic model is suitable to be used. Otherwise, we construct a new quadratic model or two other new approximation models to generate the approximate optimal stepsize for gradient method. We analyze the convergence of the proposed method under some suitable conditions. Numerical results show the proposed method is very promising.     

Noise sensitivity in continuum percolation

We prove that the Poisson Boolean model, also known as the Gilbert disc model, is noise sensitive at criticality. This is the first such result for a Continuum Percolation model, and the first which involves a percolation model with critical probability p _c ≠ 1/2. Our proof uses a version of the Benjamini-Kalai-Schramm Theorem for biased product measures. A quantitative version of this result was recently proved by Keller and Kindler. We give a simple deduction of the non-quantitative result from the unbiased version. We also develop a quite general method of approximating Continuum Percolation models by discrete models with p _c bounded away from zero; this method is based on an extremal result on non-uniform hypergraphs.     

带有缺失数据的结构方程模型中的模型选择问题

结构方程模型在社会学、教育学、医学、市场营销学和行为学中有很广泛的应用。在这些领域中,缺失数据比较常见,很多学者提出了带有缺失数据的结构方程模型,并对此模型进行过很多研究。在这一类模型的应用中,模型选择非常重要,本文将一个基于贝叶斯准则的统计量,称为L_v测度,应用到此类模型中进行模型选择。最后,本文通过一个模拟研究及实例分析来说明L_v测度的有效性及应用,并在实例分析中给出了根据贝叶斯因子进行模型选择的结果,以此来进一步说明该测度的有效性。     

Adaptive neural network model for time-series forecasting

In this study, a novel adaptive neural network (ADNN) with the adaptive metrics of inputs and a new mechanism for admixture of outputs is proposed for time-series prediction. The adaptive metrics of inputs can solve the problems of amplitude changing and trend determination, and avoid the over-fitting of networks. The new mechanism for admixture of outputs can adjust forecasting results by the relative error and make them more accurate. The proposed ADNN method can predict periodical time-series with a complicated structure. The experimental results show that the proposed model outperforms the auto-regression (AR), artificial neural network (ANN), and adaptive k-nearest neighbors (AKN) models. The ADNN model is proved to benefit from the merits of the ANN and the AKN through its’ novel structure with high robustness particularly for both chaotic and real time-series predictions.     

Using Bayesian networks for bankruptcy prediction: Some methodological issues

This study provides operational guidance for building naïve Bayes Bayesian network (BN) models for bankruptcy prediction. First, we suggest a heuristic method that guides the selection of bankruptcy predictors. Based on the correlations and partial correlations among variables, the method aims at eliminating redundant and less relevant variables. A naïve Bayes model is developed using the proposed heuristic method and is found to perform well based on a 10-fold validation analysis. The developed naïve Bayes model consists of eight first-order variables, six of which are continuous. We also provide guidance on building a cascaded model by selecting second-order variables to compensate for missing values of first-order variables. Second, we analyze whether the number of states into which the six continuous variables are discretized has an impact on the model’s performance. Our results show that the model’s performance is the best when the number of states for discretization is either two or three. Starting from four states, the performance starts to deteriorate, probably due to over-fitting. Finally, we experiment whether modeling continuous variables with continuous distributions instead of discretizing them can improve the model’s performance. Our finding suggests that this is not true. One possible reason is that continuous distributions tested by the study do not represent well the underlying distributions of empirical data. Finally, the results of this study could also be applicable to business decision-making contexts other than bankruptcy prediction.     

Bayesian inference in spherical linear models: robustness and conjugate analysis

The early work of Zellner on the multivariate Student-t linear model has been extended to Bayesian inference for linear models with dependent non-normal error terms, particularly through various papers by Osiewalski, Steel and coworkers. This article provides a full Bayesian analysis for a spherical linear model. The density generator of the spherical distribution is here allowed to depend both on the precision parameter φ and on the regression coefficients β. Another distinctive aspect of this paper is that proper priors for the precision parameter are discussed.The normal-chi-squared family of prior distributions is extended to a new class, which allows the posterior analysis to be carried out analytically. On the other hand, a direct joint modelling of the data vector and of the parameters leads to conjugate distributions for the regression and the precision parameters, both individually and jointly. It is shown that some model specifications lead to Bayes estimators that do not depend on the choice of the density generator, in agreement with previous results obtained in the literature under different assumptions. Finally, the distribution theory developed to tackle the main problem is useful on its own right.     

A family of new, high order NS-α models arising from helicity correction in Leray turbulence models

This report gives a reinterpretation of the NS-α model which leads to a family of high order NS-α-deconvolution models with NS-α as the zeroth order case. First, we show that the Navier-Stokes-α model arises by adding helicity correction to Leray-α model. Higher order Leray models have recently been proposed in [W. Layton, R. Lewandowski, A high accuracy Leray-deconvolution model of turbulence and its limiting behavior, Anal. Appl. 6 (1) (2008); W. Layton, C. Manica, M. Neda, L. Rebholz, Numerical analysis and computational testing of a high-accuracy Leray-deconvolution model of turbulence, Numer. Methods Partial Differential Equations, in press]: the so-called Leray-deconvolution models, that employ van Cittert approximate deconvolution to decrease consistency error. We use an analogous helicity correction idea to develop a family of higher order accurate NS-α type models, the NS-α-deconvolution models. We prove several mathematical and physical properties for this new family of models and discuss the design of efficient algorithms for them.     

Approximate Bayesian shrinkage estimation

A Bayesian shrinkage estimate for the mean in the generalized linear empirical Bayes model is proposed. The posterior mean under the empirical Bayes model has a shrinkage pattern. The shrinkage factor is estimated by using a Bayesian method with the regression coefficients to be fixed at the maximum extended quasi-likelihood estimates. This approach develops a Bayesian shrinkage estimate of the mean which is numerically quite tractable. The method is illustrated with a data set, and the estimate is compared with an earlier one based on an empirical Bayes method. In a special case of the homogeneous model with exchangeable priors, the performance of the Bayesian estimate is illustrated by computer simulations. The simulation result shows as improvement of the Bayesian estimate over the empirical Bayes estimate in some situations.     

A general criterion to determine the number of change-points

A general criterion is proposed to determine the number K of the change-points in a parametric nonlinear multi-response model. Schwarz criterion is a particular case. The change-points depend on regressor values and not on instant of measure. We prove that the proposed estimator for K is consistent. Simulation results, using Monte Carlo technique, for nonlinear models which have numerous applications, support the relevance of the theory.