On Lindley-like mean correction in the improved estimation of linear regression models

The risks of estimators incorporating the correction to the sample mean in the spirit of Stein and Lindley are approximated in the case of small disturbances.     

Testing for normality in linear regression models using regression and scale equivariant estimators

In this paper we provide a general solution to the problem of controlling the probability of a type I error in normality tests for the disturbances in linear regressions when using robust-regression residuals. We show that many classes of well-known robust regression estimators belong to the class of regression and scale equivariant estimators. It is these equivariance properties that are used to reduce the nuisance parameter space under the null, from which we develop Monte Carlo and Maximized Monte Carlo tests for the null of disturbance normality. Finally, we illustrate in a simulation experiment the potential power gains from using robust-regression residuals in testing this null hypothesis.     

对云南林业发展面临的十大矛盾之思考

本文从分析云南林业发展所面临的十大矛盾的实质及其内在运动规律入手,提出如何处理这十大矛盾的具体方针和对策。     

Consistency ofs 2 in the linear regression model with correlated errors

We give a simple sufficient condition for consistency of the standard OLS-based estimate of the disturbance variance in the linear regression model with autocorrelated disturbances.Research supported by Deutsche Forschungsgemeinschaft (DFG). We are grateful to B. M. Poetscher for a generous supply of counterexamples.     

Econometrics and inconsistencies in the national accounts

Economic data are typically inconsistent with national accounting identities, contain measurement errors and are sometimes unavailable. A generalized conditioned least square procedure for the adjustment of data is proposed to deal with these problems. It is shown how the resulting data may be used for FIML estimation of the parameters of dynamic models (and the data themselves) with the aid of the Kalman-Bucy filter. An illustrative application of the proposed techniques to UK data is reported.     

Robust Bayesian analysis of a parameter change in linear regression

Robust Bayesian analyses in a conjugate normal framework have been developed by Learner (1978) and Polasek and Pötzelberger (1987). Fixing the prior mean and varying the prior covariance Matrix yields a so-called feasible ellipsoid for the posterior mean and robust HPD regions, also called HiFi-regions. This paper considers the application of this approach to gain robust Bayesian inference in case of a parameter change in regression models.     

Explanations of the inconsistencies in survey respondents’ forecasts

A comparison of the point forecasts and the probability distributions of inflation and output growth made by individual respondents to the US Survey of Professional Forecasters indicates that the two sets of forecasts are sometimes inconsistent. We evaluate a number of possible explanations, and find that not all forecasters update their histogram forecasts as new information arrives. This is supported by the finding that the point forecasts are more accurate than the histograms in terms of first-moment prediction.     

A more general class of biased estimators of the co-efficients in linear regression

In a recent paper, Ullah and Ullah (1978) proposed a class of biased estimators, namely double k-class (k₁, k₂) for the coefficients in a linear regression model. Even though, this set of estimators contains James and Stein (1961) as a special case, in its present form, it does not contain the ridge type estimators. The aim of this note is to extend Ullah and Ullah set of estimators and then establish a relationship with the various operational ridge estimators. The conditions under which the extended set of estimators dominates the ordinary least squares estimator are analyzed.     

Inadmissibility of the iterative Stein-rule estimator of the disturbance variance in a linear regression

In this paper, we consider the estimator of the disturbance variance in a linear regression when the Stein-rule estimator is used in place of the OLS estimator (the iterative Stein-rule estimator of the disturbance variance). It is shown that the iterative Stein-rule estimator of the disturbance variance is dominated by the usual estimator of the disturbance variance based on the OLS estimator under the squared error loss criterion, if the number of regressors is greater than or equal to five.     

On the use of better measured proxies in regression analysis

Improving the measurement of mismeasured regressors may cause the inconsistency in least-square coefficient estimators to rise. An explanation for this result is provided and a more comprehensive summary of the data that is free of this problem is proposed.     

Bootstrap LM tests for higher-order spatial effects in spatial linear regression models

This paper first extends the methodology of Yang (J Econom 185:33–59, 2015) to allow for non-normality and/or unknown heteroskedasticity in obtaining asymptotically refined critical values for the LM-type tests through bootstrap. Bootstrap refinements in critical values require the LM test statistics to be asymptotically pivotal under the null hypothesis, and for this we provide a set of general methods for constructing LM and robust LM tests. We then give detailed treatments for two general higher-order spatial linear regression models: namely the \(\mathtt{SARAR}(p,q)\) model and the \(\mathtt{MESS}(p,q)\) model, by providing a complete set of non-normality robust LM and bootstrap LM tests for higher-order spatial effects, and a complete set of LM and bootstrap LM tests robust against both unknown heteroskedasticity and non-normality. Monte Carlo experiments are run, and results show an excellent performance of the bootstrap LM-type tests.     

The asymptotic efficiency of semiparametric estimators for censored linear regression models

This paper presents numerical comparisons of the asymptotic mean square estimation errors of semiparametric generalized least squares (SGLS), quantite, symmetrically censored least squares (SCLS), and tobit maximum likelihood estimators of the slope parameters of censored linear regression models with one explanatory variable. The results indicate that the SCLS estimator is less efficient than the other two semiparametric estimators. The SGLS estimator is more efficient than quantile estimators when the tails of the distribution of the random component of the model are not too thick and the probability of censoring is not too large. The most efficient semiparametric estimators usually have smaller mean square estimation errors than does the tobit estimator when the random component of the model is not normally distributed and the sample size is 500–1,000 or more.     

On Liu estimators for the logit regression model

This paper introduces a shrinkage estimator for the logit model which is a generalization of the estimator proposed by Liu (1993) for the linear regression. This new estimation method is suggested since the mean squared error (MSE) of the commonly used maximum likelihood (ML) method becomes inflated when the explanatory variables of the regression model are highly correlated. Using MSE, the optimal value of the shrinkage parameter is derived and some methods of estimating it are proposed. It is shown by means of Monte Carlo simulations that the estimated MSE and mean absolute error (MAE) are lower for the proposed Liu estimator than those of the ML in the presence of multicollinearity. Finally the benefit of the Lie estimator is shown in an empirical application where different economic factors are used to explain the probability that municipalities have net increase of inhabitants.     

Inconsistency of estimate of the degree of freedom of multivariate student-t disturbances in linear regression models

A moment estimator for the degree of freedom of the jointly multivariate student-t distribution of the disturbances in a linear regression model has been suggested by Singh [Economic letters (1988) 27, 47–53]. In this paper we will show that the distribution of the moment estimate is independent of the true value of the degree of freedom and the estimate converges to infinite in probability as the sample size goes to infinite. Our results show that the moment estimate does not provide any information on the degree of freedom.     

Small sample properties of the two-step and three-step estimators in a heteroscedastic linear regression model and the Bayesian alternative

In this paper, we consider the heteroscedastic linear regression model in which the variance of the disturbance term is assumed to be proportional to one of the regressors raised to an unknown power. We first derive the Bayesian estimator, and compare the mean squared errors of the two-step, three-step and Bayesian estimates by Monte Carlo experiments.     

Age effects on consumer demand: an additive partially linear regression model

An additive partially linear regression model is used to estimate non-parametrically the effects of total expenditure and age in the context of Engel curves and to investigate the specification and welfare interpretation of the age effects in parametric models of consumer behaviour. Empirical analysis based on data drawn from the U.K. Family Expenditure Survey shows that modelling of the effects of age requires a more sophisticated approach than that generally adopted in parametric demand analysis. It also shows that failing to adequately capture these effects can have misleading welfare implications. JEL Classification: C14, D12
L'effet de l'âge sur la demande des consommateurs : un modèle de régression additif partiellement linéaire. On utilise un modèle de régression additif partiellement linéaire pour faire la calibration non paramétrique des effets de la dépense totale et de l'âge dans le contexte de courbes de Engel, et pour enquêter sur la spécification des effets d'âge et leur interprétation en termes de bien-être dans des modèles paramétriques de comportements du consommateur. L'analyse empirique est construite sur des données de la U.K. Family Expenditures Survey et montre que la modélisation des effets de l'âge réclame une approche plus sophistiquée que celle qui est généralement utilisée dans l'analyse paramétrique de la demande. On montre aussi que le manque à bien saisir ces effets peut conduire à des conclusions fausses pour ce qui est du niveau de bien-être.     

On ridge estimators for the negative binomial regression model

The negative binomial (NB) regression model is very popular in applied research when analyzing count data. The commonly used maximum likelihood (ML) estimator is very sensitive to highly intercorrelated explanatory variables. Therefore, a NB ridge regression estimator (NBRR) is proposed as a robust option of estimating the parameters of the NB model in the presence of multicollinearity. To investigate the performance of the NBRR and the traditional ML approach the mean squared error (MSE) is calculated using Monte Carlo simulations. The simulated result indicated that some of the proposed NBRR methods should always be preferred to the ML method.     

On the combination of exponential smoothing and diffusion forecasts: An application to broadband diffusion in the OECD area

The innovation diffusion literature has established that the spread of a successful innovation over time typically follows a sigmoid curve. Therefore, the forecasting in this area has been monopolized by the use of well known aggregate diffusion models. Time series forecasting has been surprisingly neglected, as it provides mainly accurate short term forecasts. In this work, a method of exponential smoothing, the Holt's damped trend with a modification, is applied in recent broadband diffusion data of two large regions after the reach of the inflection point. As validated with holdback sample data ranging from 6 up to 30 months, the key for successful forecasting is the use of the estimated saturation level calculated from a diffusion model, in order to specify the appropriate trend. The results indicate improved predictions compared to two popular diffusion models, the Gompertz and the Linear Logistic model. The paper concludes with the application of the proposed method in a 48-month forecasting horizon, as well as the suggestions for further research.     

On the estimation and testing of mixed geographically weighted regression models

Mixed geographically weighted regression (MGWR) model is a useful technique to explore spatial non-stationarity by allowing that some coefficients of the explanatory variables are constant and others are spatially varying, but its estimation and inference have not been systematically studied. This paper is concerned with estimation and testing of the model when there are certain linear constraints on the elements of constant coefficients. We propose a constrained two-step technique for estimating the constant coefficients and spatial varying coefficients, and develop a test procedure for the validity of the linear constraints. Finally, some simulations are conducted to examine the performance of our proposed procedure and the results are satisfactory.     

On the determination of maximum accuracy for regression processes with endogenous variable constraints

Optimal regression design is studied for a sequential problem in which the experimenter wishes to constrain the probable value of a dependent variable to the vicinity of a given target. In the context suggesting the problem, the dependent variable is an effluent, and the target arises from anti-pollution regulation.