Selection of regressors in econometrics: parametric and nonparametric methods selection of regressors in econometrics

The present paper addresses the selection-of-regressors issue into a general discrimination framework. We show how this framework is useful in unifying various procedures for selecting regressors and helpful in understanding the different strategies underlying these procedures. We review selection of regressors in linear, nonlinear and nonparametric regression models. In each case we successively consider model selection criteria and hypothesis testing procedures.     

On tests of independence between stochastic regressors and disturbances

In this paper two tests for testing the hypothesis that the stochastic endogenous regressors in a structural equation, embedded in a system of simultaneous structural equations, are independent of the disturbances in that equation are presented.     

Indirect estimation of (latent) linear models with ordinal regressors A Monte Carlo study and some empirical illustrations

Summary This paper investigates the effects of ordinal regressors in linear regression models and in limited dependent variable models. Each ordered categorical variable is interpreted as a rough measurement of an underlying continuous variable as it is often done in microeconometrics for the dependent variable. It is shown that using ordinal indicators only leads to correct answers in a few special cases. In most situations, the usual estimators are biased. In order to estimate the parameters of the model consistently, the indirect estimation procedure suggested by Gourieroux et al. (1993) is applied. To demonstrate this method, first a simulation study is performed and then in a second step, two real data sets are used. In the latter case, continuous regressors are transformed into categorical variables to study the behavior of the estimation procedure. The method is extended to the case of limited dependent variable models. In general, the indirect estimators lead to adequate results. Received: March 27, 2000; revised version: March 6, 2001     

Estimation of semi-varying coefficient models with nonstationary regressors

We study a semivarying coefficient model where the regressors are generated by the multivariate unit root I(1) processes. The influence of the explanatory vectors on the response variable satisfies the semiparametric partially linear structure with the nonlinear component being functional coefficients. A semiparametric estimation methodology with the first-stage local polynomial smoothing is applied to estimate both the constant coefficients in the linear component and the functional coefficients in the nonlinear component. The asymptotic distribution theory for the proposed semiparametric estimators is established under some mild conditions, from which both the parametric and nonparametric estimators are shown to enjoy the well-known super-consistency property. Furthermore, a simulation study is conducted to investigate the finite sample performance of the developed methodology and results.     

Criterion and selection of optimal subsets in the linear regression,two stage procedures

In many practical situation the regression analysis with stochastic regressors is used. The estimations of this model are often influenced by a high degree of multicollinearity. For avoidance of this fact a criterion and a procedure for the selection of an optimal subset for regression will be derived on the base of the partition of the moments of the conditional normal distribution of the regressand under the condition of the regressors. Further two stage procedures improving the result of the subset regression. based also on the partition of the conditional moments will be given.     

Using simulation methods for bayesian econometric models: inference,development and communication: some comments

We extend the average derivatives estimator to the case of functionally dependent regressors. We show that the proposed estimator is consistent and has a limiting normal distribution. A consistent covariance matrix estimator for the proposed estimator is provided.     

A MODIFIED AVERAGE DERIVATIVES ESTIMATOR

We extend the average derivatives estimator to the case of functionally dependent regressors. We show that the proposed estimator is consistent and has a limiting normal distribution. A consistent covariance matrix estimator for the proposed estimator is provided.     

Bayesian model averaging for dynamic panels with an application to a trade gravity model

We extend the Bayesian Model Averaging (BMA) framework to dynamic panel data models with endogenous regressors using a Limited Information Bayesian Model Averaging (LIBMA) methodology. Monte Carlo simulations confirm the asymptotic performance of our methodology both in BMA and selection, with high posterior inclusion probabilities for all relevant regressors, and parameter estimates very close to their true values. In addition, we illustrate the use of LIBMA by estimating a dynamic gravity model for bilateral trade. Once model uncertainty, dynamics, and endogeneity are accounted for, we find several factors that are robustly correlated with bilateral trade. We also find that applying methodologies that do not account for either dynamics or endogeneity (or both) results in different sets of robust determinants.     

Influence measures based on confidence ellipsoids in general linear regression model with correlated regressors

In this paper, we investigated the Andrews–Pregibon (AP), COVRATIO and Cook–Weisberg (CW) statistics to determine the influential observations on the confidence ellipsoids in linear regression model with correlated errors and correlated regressors. A real example and a Monte Carlo simulation study are given to detect the effects of autocorrelation coefficient and ridge parameter on the AP, COVRATIO and CW statistics.     

Modified first-difference estimator in a panel data model with unobservable factors both in the errors and the regressors when the time dimension is small

Panel data models with factor structures in both the errors and the regressors have received considerable attention recently. In these models, the errors and the regressors are correlated and the standard estimators are inconsistent. This paper shows that, for such models, a modified first-difference estimator (in which the time and the cross-sectional dimensions are interchanged) is consistent as the cross-sectional dimension grows but the time dimension is small. Although the estimator has a non standard asymptotic distribution, t and F tests have standard asymptotic distribution under the null hypothesis.     

Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density

We investigate the issue of bandwidth estimation in a functional nonparametric regression model with function-valued, continuous real-valued and discrete-valued regressors under the framework of unknown error density. Extending from the recent work of Shang (2013 Shang, H.L. (2013), ‘Bayesian Bandwidth Estimation for a Nonparametric Functional Regression Model with Unknown Error Density’, Computational Statistics &; Data Analysis, 67, 185–198. doi: 10.1016/j.csda.2013.05.006[Crossref], [Web of Science ®] , [Google Scholar]) [‘Bayesian Bandwidth Estimation for a Nonparametric Functional Regression Model with Unknown Error Density’, Computational Statistics &; Data Analysis, 67, 185–198], we approximate the unknown error density by a kernel density estimator of residuals, where the regression function is estimated by the functional Nadaraya–Watson estimator that admits mixed types of regressors. We derive a likelihood and posterior density for the bandwidth parameters under the kernel-form error density, and put forward a Bayesian bandwidth estimation approach that can simultaneously estimate the bandwidths. Simulation studies demonstrated the estimation accuracy of the regression function and error density for the proposed Bayesian approach. Illustrated by a spectroscopy data set in the food quality control, we applied the proposed Bayesian approach to select the optimal bandwidths in a functional nonparametric regression model with mixed types of regressors.     

Tests of specification in econometrics

This survey of recent developments in testing for misspecification of econometric models reviews procedures based on a method due to Hausman. Particular attention is given to alternative forms of the test, its relationship to classical test procedures, and its role in pre-test estimation.     

Tests of specification in econometrics

This survey of recent developments in testing for misspecification of econometric models reviews procedures based on a method due to Hausman. Particular attention is given to alternative forms of the test, its relationship to classical test procedures, and its role in pre-test estimation.     

Robust methods in econometrics

This survey of recent developments in robust estimation and inference is directed primarily toward econometricians. It is argued that many of the techniques in common use in econometrics are highly sensitive to unverified hypotheses. Recent progress in designing alternative robust procedures is described and some prospects for future developments are discussed.     

Robust methods in econometrics

This survey of recent developments in robust estimation and inference is directed primarily toward econometricians. It is argued that many of the techniques in common use in econometrics are highly sensitive to unverified hypotheses. Recent progress in designing alternative robust procedures is described and some prospects for future developments are discussed.     

Bayes model averaging with selection of regressors

Summary. When a number of distinct models contend for use in prediction, the choice of a single model can offer rather unstable predictions. In regression, stochastic search variable selection with Bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors. Here we look at Bayes model averaging incorporating variable selection for prediction. This offers similar mean-square errors of prediction but with a vastly reduced predictor space. This can greatly aid the interpretation of the model. It also reduces the cost if measured variables have costs. The development here uses decision theory in the context of the multivariate general linear model. In passing, this reduced predictor space Bayes model averaging is contrasted with single-model approximations. A fast algorithm for updating regressions in the Markov chain Monte Carlo searches for posterior inference is developed, allowing many more variables than observations to be contemplated. We discuss the merits of absolute rather than proportionate shrinkage in regression, especially when there are more variables than observations. The methodology is illustrated on a set of spectroscopic data used for measuring the amounts of different sugars in an aqueous solution.     

A note on variable selection in functional regression via random subspace method

Variable selection problem is one of the most important tasks in regression analysis, especially in a high-dimensional setting. In this paper, we study this problem in the context of scalar response functional regression model, which is a linear model with scalar response and functional regressors. The functional model can be represented by certain multiple linear regression model via basis expansions of functional variables. Based on this model and random subspace method of Mielniczuk and Teisseyre (Comput Stat Data Anal 71:725–742, 2014), two simple variable selection procedures for scalar response functional regression model are proposed. The final functional model is selected by using generalized information criteria. Monte Carlo simulation studies conducted and a real data example show very satisfactory performance of new variable selection methods under finite samples. Moreover, they suggest that considered procedures outperform solutions found in the literature in terms of correctly selected model, false discovery rate control and prediction error.     

Developments and new dimensions in econometrics

Summary This special issue of the Journal of the German Statistical Society presents 14 papers with surveys on the development and new topics in econometrics. The articles aim to demonstrate how German econometricians see the discipline from their specific view. They briefly describe the main strands and emphasize some recent methods.     

Selection of Predictors in Distance-Based Regression

Distance-based regression is a prediction method consisting of two steps: from distances between observations we obtain latent variables which, in turn, are the regressors in an ordinary least squares linear model. Distances are computed from actually observed predictors by means of a suitable dissimilarity function. Being generally nonlinearly related with the response, their selection by the usual F tests is unavailable. In this article, we propose a solution to this predictor selection problem by defining generalized test statistics and adapting a nonparametric bootstrap method to estimate their p-values. We include a numerical example with automobile insurance data.     

On a method of identification of best subset model from full ar-model

An usual approach for selection of the best subset AR model of known maximal order is to use an appropriate information criterion, like AIC or SIC with an exhaustive selection of regressors and to choose the subset model that produces the optimum (minimum) value of AIC or SIC. This method is computationally intensive. Proposed is a method based on the use of singular value decomposition and QR with column pivoting factorization for extracting a reduced subset from the exhaustive candidate set of regressors and to use AIC or SIC on the reduced subset to obtain the best subset AR model. The result is substantially reduced domain of exhaustive search for the computation of the best subset AR model.