Regression games

The solution of a TU cooperative game can be a distribution of the value of the grand coalition, i.e. it can be a distribution of the payoff (utility) all the players together achieve. In a regression model, the evaluation of the explanatory variables can be a distribution of the overall fit, i.e. the fit of the model every regressor variable is involved. Furthermore, we can take regression models as TU cooperative games where the explanatory (regressor) variables are the players. In this paper we introduce the class of regression games, characterize it and apply the Shapley value to evaluating the explanatory variables in regression models. In order to support our approach we consider Young’s (Int. J. Game Theory 14:65–72, 1985) axiomatization of the Shapley value, and conclude that the Shapley value is a reasonable tool to evaluate the explanatory variables of regression models.     

Financial Applications of a Tabu Search Variable Selection Model

We illustrate how a comparatively new technique, a Tabu search variable selection model [Drezner, Marcoulides and Salhi (1999)], can be applied efficiently within finance when the researcher must select a subset of variables from among the whole set of explanatory variables under consideration. Several types of problems in finance, including corporate and personal bankruptcy prediction, mortgage and credit scoring, and the selection of variables for the Arbitrage Pricing Model, require the researcher to select a subset of variables from a larger set. In order to demonstrate the usefulness of the Tabu search variable selection model, we: (1) illustrate its efficiency in comparison to the main alternative search procedures, such as stepwise regression and the Maximum R 2 procedure, and (2) show how a version of the Tabu search procedure may be implemented when attempting to predict corporate bankruptcy. We accomplish (2) by indicating that a Tabu Search procedure increases the predictability of corporate bankruptcy by up to 10 percentage points in comparison to Altman's (1968) Z-Score model.     

‘Model selection for generalized linear models with factor‐augmented predictors’

This paper considers generalized linear models in a data‐rich environment in which a large number of potentially useful explanatory variables are available. In particular, it deals with the case that the sample size and the number of explanatory variables are of similar sizes. We adopt the idea that the relevant information of explanatory variables concerning the dependent variable can be represented by a small number of common factors and investigate the issue of selecting the number of common factors while taking into account the effect of estimated regressors. We develop an information criterion under model mis‐specification for both the distributional and structural assumptions and show that the proposed criterion is a natural extension of the Akaike information criterion (AIC). Simulations and empirical data analysis demonstrate that the proposed new criterion outperforms the AIC and Bayesian information criterion. Copyright © 2009 John Wiley & Sons, Ltd.     

Estimation and Simulation of Autoregressive Hilbertian Processes with Exogenous Variables

We present the autoregressive Hilbertian with exogenous variables model (ARHX) which intends to take into account the dependence structure of random curves viewed as H-valued random variables, where H is a Hilbert space of functions, under the influence of explanatory variables. Limit theorems and consistent estimators are derived from an autoregressive representation. A simulation study illustrates the accuracy of the estimation by making a comparison on forecasts with other functional models.     

Forecasting the Development of the Market for Business Telephones in the UK

The problem of producing medium- to long-term forecasts of the market for business telephones is examined. Growth curves are generally appropriate for forecasting developing markets. However, this market is particularly sensitive to the state of business confidence and the feasibility of incorporating explanatory economic variables into the forecasting model is investigated. Three different model types are compared: growth curves with a fixed saturation level, multivariate linear models and growth curves with saturation levels determined by explanatory variables. The initial promise of models using explanatory variables is considerably diminished, once forecast rather than actual values of these variables are used. The market development model implicit in the growth curve is shown to be more robust than the linear model. Although the variable saturation level growth curve grants more insight into the maturity of the market, it does not produce significantly better forecasts than that with the fixed saturation level.     

Flexible regression models for carcinogenesis studies

Dynamic or flexible regression models are used more and more often in carcinogenesis studies to relate lifetime distribution to time-depending explanatory variables. In addition to the classical regression models, such as the Cox model, AFT model, Linear transformation model, Frailty model, etc., we expose so-called flexible regression models, which are well adapted to study cross-effects of survival functions. Such effects are sometimes observed in clinical trials. Classical examples are well-known data concerning effects of chemotherapy (CH) and chemotherapy plus radiotherapy (CH + R) on survival times of gastric cancers patients. In this paper, we give examples which illustrate possible applications of the Hsieh model (2001) and the SCE model proposed by Bagdonavicius and Nikulin and adapted to treat survival data with one crossing point. We compare both models. Biblipgraphy: 40 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 78–101.     

哈尔滨市冬季PM_(2.5)与影响要素的相关分析

运用相关性分析方法,研究哈尔滨市PM_(2.5)质量浓度与主要空气污染物及气象因素之间的相关关系.建立PM_(2.5)与影响其质量浓度变化的因素的单因变量的偏最小二乘回归分析(PLS1)模型,模型拟合良好,由模型知CO是导致PM_(2.5)质量浓度升高的主要因素.运用通径分析方法,研究解释变量对因变量的直接影响、通过其他解释变量对因变量的间接影响以及各解释变量的对因变量的协同作用.结果表明,各解释变量对PM_(2.5)质量浓度变化的总作用从大到小依次为:CO、PM_(10)、NO_2、风速、湿度、SO_2.     

An Extension of Least Angle Regression Based on the Information Geometry of Dually Flat Spaces

We extend the least angle regression algorithm using the information geometry of dually flat spaces. The extended least angle regression algorithm is used for estimating parameters in generalized linear regression, and it can be also used for selecting explanatory variables. We use the fact that a model manifold of an exponential family is a dually flat space. In estimating parameters, curves corresponding to bisectors in the Euclidean space play an important role. Originally, the least angle regression algorithm is used for estimating parameters and selecting explanatory variables in linear regression. It is an efficient algorithm in the sense that the number of iterations is the same as the number of explanatory variables. We extend the algorithm while keeping this efficiency. However, the extended least angle regression algorithm differs significantly from the original algorithm. The extended least angle regression algorithm reduces one explanatory variable in each iteration while the original algorithm increases one explanatory variable in each iteration. We show results of the extended least angle regression algorithm for two types of datasets. The behavior of the extended least angle regression algorithm is shown. Especially, estimates of parameters become smaller and smaller, and vanish in turn.     

2000年厦门港货物吞吐量预测

本文是《厦门港及附近水域交管系统应用研究》课题中关于港口货物吞吐量预测的部分。这一课题已通过专家鉴定。文中应用回归模型预测2000年厦门港货物吞吐量。通过从多个解释变量中选择合适的解释变量，可获得较好的预测结果。其结果说明在应用数学模型预测时，最为关键的是模型、变量和数据三者之间的相互适应，而不在于模型的复杂程度，特别是在历史数据不多的情况下更是如此。     

Tests de structure en régression sur variable fonctionnelle

In this Note we introduce a general approach to construct structural testing procedures in regression on functional variables. In the case of multivariate explanatory variables a well-known method consists in a comparison between a nonparametric estimator and a particular one. We adapt this approach to the case of functional explanatory variables. We give the asymptotic law of the proposed test statistic. The general approach used allows us to cover a large scope of possible applications as tests for no-effect, tests for linearity, …. To cite this article: L. Delsol, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Model selection method based on maximal information coefficient of residuals

The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this article, we give a new model selection criterion, based on the assumption that noise term in the model is independent with explanatory variables, of minimizing the association strength between regression residuals and the response, with fewer assumptions. Maximal Information Coefficient (MIC), a recently proposed dependence measure, captures a wide range of associations, and gives almost the same score to different type of relationships with equal noise, so MIC is used to measure the association strength. Furthermore, partial maximal information coefficient (PMIC) is introduced to capture the association between two variables removing a third controlling random variable. In addition, the definition of general partial relationship is given.     

Refining a Bayesian Network using a Chain Event Graph

The search for a useful explanatory model based on a Bayesian Network (BN) now has a long and successful history. However, when the dependence structure between the variables of the problem is asymmetric then this cannot be captured by the BN. The Chain Event Graph (CEG) provides a richer class of models which incorporates these types of dependence structures as well as retaining the property that conclusions can be easily read back to the client. We demonstrate on a real health study how the CEG leads us to promising higher scoring models and further enables us to make more refined conclusions than can be made from the BN. Further we show how these graphs can express causal hypotheses about possible interventions that could be enforced.     

Modeling first bid in retail secondary market online auctions: A Bayesian approach

We propose a Bayesian framework to model bid placement time in retail secondary market online business‐to‐business auctions. In doing so, we propose a Bayesian beta regression model to predict the first bidder and time to first bid, and a dynamic probit model to analyze participation. In our development, we consider both auction‐specific and bidder‐specific explanatory variables. While we primarily focus on the predictive performance of the models, we also discuss how auction features and bidders' heterogeneity could affect the bid timings, as well as auction participation. We illustrate the implementation of our models by applying to actual auction data and discuss additional insights provided by the Bayesian approach, which can benefit auctioneers.     

MODEL SELECTION METHOD BASED ON MAXIMAL INFORMATION COEFFICIENT OF RESIDUALS

The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this ar- ticle, we give a new model selection criterion, based on the assumption that noise term in the model is independent with explanatory variables, of minimizing the association strength between regression residuals and the response, with fewer assumptions. Maximal Information Coe~cient （MIC）, a recently proposed dependence measure, captures a wide range of associ- ations, and gives almost the same score to different type of relationships with equal noise, so MIC is used to measure the association strength. Furthermore, partial maximal information coefficient （PMIC） is introduced to capture the association between two variables removing a third controlling random variable. In addition, the definition of general partial relationship is given.     

Simultaneous variable selection for heteroscedastic regression models

In this paper, we propose a new criterion, named PICa, to simultaneously select explanatory variables in the mean model and variance model in heteroscedastic linear models based on the model structure. We show that the new criterion can select the true mean model and a correct variance model with probability tending to 1 under mild conditions. Simulation studies and a real example are presented to evaluate the new criterion, and it turns out that the proposed approach performs well.     

Modelling aesthetic variables in the valuation of paintings: an interval goal programming approach

The economic valuation of works of art is a decisive subject in the general field of valuation. Unlike in other areas of valuation, the explanatory power of the directly observable and quantifiable variables is very low, therefore, aesthetic criteria must be used to obtain valuation models with a greater explanatory power. Frequently, these aesthetic criteria are not always precise, and experts usually express them as an interval of values. This paper describes different valuation models that use the goal programming optimisation method to include explanatory variables of the closing price in the form of intervals of values. We have also modelled the possibility that an expert can determine the relevance of each observation in the formation of the valuation function depending on the degree of precision with which the variables have been defined.     

Localized Sliced Inverse Regression

We develop a supervised dimension reduction method that integrates the idea of localization from manifold learning with the sliced inverse regression framework. We call our method localized sliced inverse regression (LSIR) since it takes into account the local structure of the explanatory variables. The resulting projection from LSIR is a linear subspace of the explanatory variables that captures the nonlinear structure relevant to predicting the response. LSIR applies to both classification and regression problems and can be easily extended to incorporate the ancillary unlabeled data in semi-supervised learning. We illustrate the utility of LSIR on real and simulated data. Computer codes and datasets from simulations are available online.     

On statistical models for regression diagnostics

In regression diagnostics, the case deletion model (CDM) and the mean shift outlier model (MSOM) are commonly used in practice. In this paper we show that the estimates of CDM and MSOM are equal in a wide class of statistical models, which include LSE, MLE, Bayesian estimate andM-estimate in linear and nonlinear regression models; MLE in generalized linear models and exponential family nonlinear models; MLEs of transformation parameters of explanatory variables in a Box-Cox regression models and so on. Furthermore, we study some models, in which, the estimates are not exactly equal but are approximately equal for CDM and MSOM.     

Farmland appraisal based on the analytic network process

This paper presents an application of the Analytic Network Process (ANP) to farmland appraisal. The purpose of this new methodology is to solve some of the drawbacks found in comparative and capitalisation methods, called classical appraisal methods, which cannot deal with contexts where only partial information is available and/or qualitative variables are used. The ANP is a method based on the Multiple Criteria Decision Analysis (MCDA). Previous works have already applied other MCDA techniques to the appraisal context, such as the Analytic Hierarchy Process (AHP), however they have not been able to handle all the complexities of many real world appraisal problems. The ANP provides a more accurate approach for modelling complex environment because it allows the general study of the quantitative and qualitative explanatory variables of the price and the incorporation of feedback and interdependence relationships among variables. The new proposed methodology has been applied to a case study of a farm located in Valencia (Spain) in order to demonstrate its goodness. Both quantitative and qualitative variables, such as the age of the trees, productivity or water quality, have been considered to assess the market value of the farm. Six farms from the same region have been selected as reference assets. The appraisal problem has been solved in three different ways in order to study the influence of each model on the value of the problem farm. In this study it has been proved that the more information is incorporated into the model, the higher accuracy of the solution. From the results of this work we can conclude that the approach proposed stands out as a good alternative to current farmland appraisal approaches, as it has proven to be useful when data are only partially available, qualitative variables are used and influences among the explanatory variables are present.     

A primer on disease mapping and ecological regression using {\texttt{INLA}}

Spatial and spatio-temporal disease mapping models are widely used for the analysis of registry data and usually formulated in a hierarchical Bayesian framework. Explanatory variables can be included by a so-called ecological regression. It is possible to assume both a linear and a nonparametric association between disease incidence and the explanatory variable. Integrated nested Laplace approximations (INLA) can be used as a tool for Bayesian inference. INLA is a promising alternative to Markov chain Monte Carlo (MCMC) methods which provides very accurate results within short computational time. It is shown in this paper, how parameter estimates for well-known spatial and spatio-temporal models can be obtained by running INLA directly in R{\texttt{R}} using the package INLA{\texttt{INLA}}. Selected R{\texttt{R}} code is shown. An emphasis is given to the inclusion of an explanatory variable. Cases of Coxiellosis among Swiss cows from 2005 to 2008 are used for illustration. The number of stillborn calves is included as time-varying covariate. Additionally, various aspects of INLA such as model choice criteria, computer time, accuracy of the results and usability of the R{\texttt{R}} package are discussed.