White Estimation Research Articles

Comparison of four methods to estimate the scale parameter for Extended Poisson Exponential distribution

In this paper, it was obtained estimators of the scale parameter of Extended Poisson Exponential distribution by four methods using complete data, these methods are the Maximum Likelihood Estimator (MLE), the Least Squares Estimator (LSE), Plotting Position Estimator (PPE) and White Estimator (WE), these four methods have been compared by the criteria of Mean Square Error (MSE) using Monte Carlo simulation, and from the results on the samples in the simulation, the comparison in this study showed that Maximum Likelihood Estimator method is best from other methods followed by the White Estimator method then the Least Squares Estimator method.

Comparison of four non-Bayesian methods to estimate the scale parameter for Modified Weibull distribution by using the Simulation

In this paper, four methods were obtained to estimate the scale parameter of Modified Weibull distribution using complete data, which are the Modified Moments Estimator (MME), the Maximum Likelihood Estimator (MLE), White Estimator (WE) and Least Squares Estimator (LSE), Monte Carlo simulation is used to compare these four estimators with respect to the Mean Square Error criteria (MSE), and the results on simulated samples of the comparison showed that for all the varying sample size in this study, and in all cases for the four methods The MLE method is best followed by the OLSE method then the WE method and the MME method .

Empirical distribution function under heteroscedasticity

Neglecting heteroscedasticity of error terms may imply the wrong identification of a regression model (see appendix). Employment of (heteroscedasticity resistent) White's estimator of covariance matrix of estimates of regression coefficients may lead to the correct decision about the significance of individual explanatory variables under heteroscedasticity. However, White's estimator of covariance matrix was established for least squares (LS)-regression analysis (in the case when error terms are normally distributed, LS- and maximum likelihood (ML)-analysis coincide and hence then White's estimate of covariance matrix is available for ML-regression analysis, tool). To establish White's-type estimate for another estimator of regression coefficients requires Bahadur representation of the estimator in question, under heteroscedasticity of error terms. The derivation of Bahadur representation for other (robust) estimators requires some tools. As the key too proved to be a tight approximation of the empirical distribution function (d.f.) of residuals by the theoretical d.f. of the error terms of the regression model. We need the approximation to be uniform in the argument of d.f. as well as in regression coefficients. The present paper offers this approximation for the situation when the error terms are heteroscedastic.

A Class of Improved Heteroskedasticity-Consistent Covariance Matrix Estimators

The heteroskedasticity-consistent covariance matrix estimator proposed by White [White, H. A. (1980). Heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48:817–838], also known as HC0, is commonly used in practical applications and is implemented into a number of statistical software. Cribari–Neto et al. [Cribari–Neto, F., Ferrari, S. L. P., Cordeiro, G. M. (2000). Improved heteroscedasticity–consistent covariance matrix estimators. Biometrika 87:907–918] have developed a bias-adjustment scheme that delivers bias-corrected White estimators. There are several variants of the original White estimator that are also commonly used by practitioners. These include the HC1, HC2, and HC3 estimators, which have proven to have superior small-sample behavior relative to White's estimator. This paper defines a general bias-correction mechamism that can be applied not only to White's estimator, but to variants of this estimator as well, such as HC1, HC2, and HC3. Numerical evidence on the usefulness of the proposed corrections is also presented. Overall, the results favor the sequence of improved HC2 estimators.

Heteroskedasticity and Neglected Parameter Heterogeneity

The paper studies the consequences of neglecting parameter heterogeneity for the linear regression model and cross‐sectional data. Monte‐Carlo experiments are used to illustrate that neglected parameter heterogeneity typically leads to (a) regression coefficients that are economically meaningless and (b)significant test statistics for heteroskedasticity and, possibly non‐normality. The paper concludes that evidence for heteroskedasticity should not routinely lead to the use of White's well‐known heteroskedasticity‐consistent variance covariance matrix estimator. If heteroskedasticity is caused by neglected parameter heterogeneity or other causes of heteroskedasticity, such as wrong functional form, White's estimator will not serve any useful purpose.

Improved heteroscedasticity-consistent covariance matrix estimators

SUMMARY The heteroscedasticity-consistent covariance matrix estimator proposed by White (1980) is commonly used in practical applications and is implemented into a number of pieces of statistical software. However, although consistent, it can display substantial bias in small to moderately large samples, as shown by Monte Carlo simulations elsewhere. This paper defines modified White estimators which are approximately bias-free. Numerical results show that the modified estimators display much smaller bias than White's estimator in small samples. We also show that the bias correction leads to some variance inflation. In hypothesis testing based on heteroscedasticity-consistent covariance matrix estimators, numerical results suggest that tests based on the proposed bias-corrected estimators typically display smaller size distortions.

Jackknife Estimators of Variance for Parameter Estimates from Estimating Equations with Applications to Clustered Survival Data

An estimate of a parameter vector beta is often obtained by setting a "score" vector equal to zero and solving for beta. Estimating equations of this type include maximum likelihood, quasi-likelihood (McCullagh, 1983, Annals of Statistics 11, 59-67), and generalized estimating equations (Liang and Zeger, 1986, Biometrika 73, 13-22). White (1982, Econometrica 50, 1-26) proposed a variance estimator for beta that is robust to model misspecification. We show that a "one-step" jackknife estimator of variance is asymptotically equivalent to the variance estimator proposed by White. The one-step variance estimator may be preferred when the appropriate computer packages are not available to compute White's estimator directly. This jackknife estimator is very useful in our example with clustered survival data.