Bias Correction in the Dynamic Panel Data Model with a Nonscalar Disturbance Covariance Matrix

Abstract

Approximation formulae are developed for the bias of ordinary and generalized Least Squares Dummy Variable (LSDV) estimators in dynamic panel data models. Results from Kiviet [Kiviet, J. F. (1995), on bias, inconsistency, and efficiency of various estimators in dynamic panel data models, J. Econometrics68:53–78; Kiviet, J. F. (1999), Expectations of expansions for estimators in a dynamic panel data model: some results for weakly exogenous regressors, In: Hsiao, C., Lahiri, K., Lee, L‐F., Pesaran, M. H., eds., Analysis of Panels and Limited Dependent Variables, Cambridge: Cambridge University Press, pp. 199–225] are extended to higher‐order dynamic panel data models with general covariance structure. The focus is on estimation of both short‐ and long‐run coefficients. The results show that proper modelling of the disturbance covariance structure is indispensable. The bias approximations are used to construct bias corrected estimators which are then applied to quarterly data from 14 European Union countries. Money demand functions for M1, M2 and M3 are estimated for the EU area as a whole for the period 1991: I–1995: IV. Significant spillovers between countries are found reflecting the dependence of domestic money demand on foreign developments. The empirical results show that in general plausible long‐run effects are obtained by the bias corrected estimators. Moreover, finite sample bias, although of moderate magnitude, is present underlining the importance of more refined estimation techniques. Also the efficiency gains by exploiting the heteroscedasticity and cross‐correlation patterns between countries are sometimes considerable.     

A Note on the Non-equivalence of the Neyman-Pearson and Generalized Likelihood Ratio Tests for Testing a Simple Null versus a Simple Alternative Hypothesis

Despite the great increase in the use of color in statistical graphics, we know very little about how color affects people's perception of the quantitative information on graphical displays. Perceptual psychologists have already demonstrated that color can cause optical illusions of various kinds. We ran a simple experiment to see if this can happen with a statistical map and found that an illusion did occur.     

On difference factor in assessment of dissolution similarity

In vitro dissolution similarity has been suggested as a surrogate for assessing equivalence between the pre-changed and post-changed formulations for postapproval changes of a drug. The difference factor f₁, based on the absolute mean difference, has been proposed as a criterion for evaluating similarity between dissolution profiles. Statistical properties including density function, bias, and asymptotic distribution of a consistent estimator are investigated. Due to complexity of the distribution of the estimator, we suggest the use of the confidence intervals obtained from the bootstrap method for evaluation of dissolution similarity. A simulation was conducted to examine the size and power of the proposed CI procedure. Comparisons with other criteria such as similarity factor are also provided. Numerical examples are used to illustrate the proposed CI procedure.     

Exponential-Bound Property of Estimators and Variable Selection in Generalized Additive Models

In this article, utilizing a scale mixture of skew-normal distribution in which mixing random variable is assumed to follow a mixture model with varying weights for each observation, we introduce a generalization of skew-normal linear regression model with the aim to provide resistant results. This model, which also includes the skew-slash distribution in a particular case, allows us to accommodate and detect outlying observations under the skew-normal linear regression model. Inferences about the model are carried out through the empirical Bayes approach. The conditions for propriety of the posterior and for existence of posterior moments are given under the standard noninformative priors for regression and scale parameters as well as proper prior for skewness parameter. Then, for Bayesian inference, a Markov chain Monte Carlo method is described. Since posterior results depend on the prior hyperparameters, we estimate them adopting the empirical Bayes method as well as using a Monte Carlo EM algorithm. Furthermore, to identify possible outliers, we also apply the Bayes factor obtained through the generalized Savage-Dickey density ratio. Examining the proposed approach on simulated instance and real data, it is found to provide not only satisfactory parameter estimates rather allow identifying outliers favorably.     

Some Second-Order Asymptotics for Extreme Value Linear Regression Models

ABSTRACT

In this article we derive finite-sample corrections in matrix notation for likelihood ratio and score statistics in extreme-value linear regression models. We consider three corrected score tests that perform better than the usual score test. We also derive general formulae for second-order biases of maximum likelihood estimates of the linear parameters. Some simulations are performed to compare the likelihood ratio and score statistics with their modified versions and to illustrate the bias correction.     

Estimation of P(Y < X) for Weibull Distribution Under Progressive Type-II Censoring

Based on progressively Type II censored samples, we consider the estimation of R = P(Y < X) when X and Y are two independent Weibull distributions with different shape parameters, but having the same scale parameter. The maximum likelihood estimator, approximate maximum likelihood estimator, and Bayes estimator of R are obtained. Based on the asymptotic distribution of R, the confidence interval of R are obtained. Two bootstrap confidence intervals are also proposed. Analysis of a real data set is given for illustrative purposes. Monte Carlo simulations are also performed to compare the different proposed methods.     

Compare diagnostic tests using transformation-invariant smoothed ROC curves()

Receiver operating characteristic (ROC) curve, plotting true positive rates against false positive rates as threshold varies, is an important tool for evaluating biomarkers in diagnostic medicine studies. By definition, ROC curve is monotone increasing from 0 to 1 and is invariant to any monotone transformation of test results. And it is often a curve with certain level of smoothness when test results from the diseased and non-diseased subjects follow continuous distributions. Most existing ROC curve estimation methods do not guarantee all of these properties. One of the exceptions is Du and Tang (2009) which applies certain monotone spline regression procedure to empirical ROC estimates. However, their method does not consider the inherent correlations between empirical ROC estimates. This makes the derivation of the asymptotic properties very difficult. In this paper we propose a penalized weighted least square estimation method, which incorporates the covariance between empirical ROC estimates as a weight matrix. The resulting estimator satisfies all the aforementioned properties, and we show that it is also consistent. Then a resampling approach is used to extend our method for comparisons of two or more diagnostic tests. Our simulations show a significantly improved performance over the existing method, especially for steep ROC curves. We then apply the proposed method to a cancer diagnostic study that compares several newly developed diagnostic biomarkers to a traditional one.     

A bootstrap test for time series linearity

A bootstrap algorithm is proposed for testing Gaussianity and linearity in stationary time series, and consistency of the relevant bootstrap approximations is proven rigorously for the first time. Subba Rao and Gabr (1980) and Hinich (1982) have formulated some well-known nonparametric tests for Gaussianity and linearity based on the asymptotic distribution of the normalized bispectrum. The proposed bootstrap procedure gives an alternative way to approximate the finite-sample null distribution of such test statistics. We revisit a modified form of Hinich's test utilizing kernel smoothing, and compare its performance to the bootstrap test on several simulated data sets and two real data sets—the S&P 500 returns and the quarterly US real GNP growth rate. Interestingly, Hinich's test and the proposed bootstrapped version yield substantially different results when testing Gaussianity and linearity of the GNP data.     

Generalized additive modelling of sample extremes

Summary.  We describe smooth non-stationary generalized additive modelling for sample extremes, in which spline smoothers are incorporated into models for exceedances over high thresholds. Fitting is by maximum penalized likelihood estimation, with uncertainty assessed by using differences of deviances and bootstrap simulation. The approach is illustrated by using data on extreme winter temperatures in the Swiss Alps, analysis of which shows strong influence of the north Atlantic oscillation. Benefits of the new approach are flexible and appropriate modelling of extremes, more realistic assessment of estimation uncertainty and the accommodation of complex dependence patterns.     

Calibrating the excess mass and dip tests of modality

Nonparametric tests of modality are a distribution-free way of assessing evidence about inhomogeneity in a population, provided that the potential sub populations are sufficiently well separated. They include the excess mass and dip tests, which are equivalent in univariate settings and are alternatives to the bandwidth test. Only very conservative forms of the excess mass and dip tests are available at presently, however, and for that reason they are generally not competitive with the bandwidth test. In the present paper we develop a practical approach to calibrating the excess mass and dip tests to improve their level accuracy and power substantially. Our method exploits the fact that the limiting distribution of the excess mass statistic under the null hypothesis depends on unknowns only through a constant, which may be estimated. Our calibrated test exploits this fact and is shown to have greater power and level accuracy than the bandwidth test has. The latter tends to be quite conservative, even in an asymptotic sense. Moreover, the calibrated test avoids difficulties that the bandwidth test has with spurious modes in the tails, which often must be discounted through subjective intervention of the experimenter.