Improved maximum likelihood estimators in a heteroskedastic errors-in-variables model (original) (raw)
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The linear heteroskedastic regression model, for which the variance of the response is given by a suitable function of a set of linear exogenous variables, is very useful in econometric applications. We derive a simple matrix formula for the n −1 biases of the maximum likelihood estimators of the parameters in the variance of the response, where n is the sample size. These biases are easily obtained as a vector of regression coefficients in a simple weighted least squares regression. We use simulation to compare the uncorrected estimators with the bias-corrected ones to conclude the superiority of the corrected estimators over the uncorrected ones with regard to the normal approximation. The practical use of such biases is illustrated in two applications to real data sets.
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Statistics in Medicine, 2008
In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the model's goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease. Copyright © 2008 John Wiley & Sons, Ltd.
A sequence of improved standard errors under heteroskedasticity of unknown form
Fuel and Energy Abstracts, 2011
The linear regression model is commonly used by practitioners to model the relationship between the variable of interest and a set of explanatory variables. The assumption that all error variances are the same (homoskedasticity) is oftentimes violated. Consistent regression standard errors can be computed using the heteroskedasticity-consistent covariance matrix estimator proposed by White (1980). Such standard errors, however, typically display nonnegligible systematic errors in finite samples, especially under leveraged data. Cribari-Neto et al. (2000) improved upon the White estimator by defining a sequence of bias-adjusted estimators with increasing accuracy. In this paper, we improve upon their main result by defining an alternative sequence of adjusted estimators whose biases vanish at a much faster rate. Hypothesis testing inference is also addressed. An empirical illustration is presented.
Statistics in Medicine, 2002
It is common in the analysis of aggregate data in epidemiology that the variances of the aggregate observations are available. The analysis of such data leads to a measurement error situation, where the known variances of the measurement errors vary between the observations. Assuming multivariate normal distribution for the 'true' observations and normal distributions for the measurement errors, we derive a simple EM algorithm for obtaining maximum likelihood estimates of the parameters of the multivariate normal distributions. The results also facilitate the estimation of regression parameters between the variables as well as the 'true' values of the observations. The approach is applied to reestimate recent results of the WHO MONICA Project on cardiovascular disease and its risk factors, where the original estimation of the regression coe cients did not adjust for the regression attenuation caused by the measurement errors.
Improved estimators in some linear errors-in-variables models in finite samples
Economics Letters, 1986
The paper uses a Monte Carlo study to demonstrate the dominance under mean squared errors or quadratic loss of a new improved estimator for some linear errors-in-variables models in finite samples. The new estimator is non-linear and biased in a conventional sense and has a smaller risk than the least squares and the Stein estimators. Standard errors for this estimator can be conveniently obtained by bootstrapping methods. 0165-1765/86/$3.50 0 1986, Elsevier Science Publishers B.V. (North-Holland)
Influence Assessment in an Heteroscedastic Errors-in-Variables Model
Communications in Statistics - Theory and Methods, 2012
The main goal of this article is to consider influence assessment in models with error-prone observations and variances of the measurement errors changing across observations. The techniques enable to identify potential influential elements and also to quantify the effects of perturbations in these elements on some results of interest. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease.