Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances

We study the properties of the quasi-maximum likelihood estimator (QMLE) and related test statistics in dynamic models that jointly parameterize conditional means and conditional covariances, when a normal log-likelihood os maximized but the assumption of normality is violated. Because the score of the normal log-likelihood has the martingale difference property when the forst two conditional moments are correctly specified, the QMLE is generally Consistent and has a limiting normal destribution. We provide easily computable formulas for asymptotic standard errors that are valid under nonnormality. Further, we show how robust LM tests for the adequacy of the jointly parameterized mean and variance can be computed from simple auxiliary regressions. An appealing feature of these robyst inference procedures is that only first derivatives of the conditional mean and variance functions are needed. A monte Carlo study indicates that the asymptotic results carry over to finite samples. Estimation of several AR and AR-GARCH time series models reveals that in most sotuations the robust test statistics compare favorably to the two standard (nonrobust) formulations of the Wald and IM tests. Also, for the GARCH models and the sample sizes analyzed here, the bias in the QMLE appears to be relatively small. An empirical application to stock return volatility illustrates the potential imprtance of computing robust statistics in practice.     

Goodness of fit for the inverse Gaussian distribution

For testing the fit of the inverse Gaussian distribution with unknown parameters, the empirical distribution-function statistic A² is studied. Two procedures are followed in constructing the test statistic; they yield the same asymptotic distribution. In the first procedure the parameters in the distribution function are directly estimated, and in the second the distribution function is estimated by its Rao-Blackwell distribution estimator. A table is given for the asymptotic critical points of A². These are shown to depend only on the ratio of the unknown parameters. An analysis is provided of the effect of estimating the ratio to enter the table for A². This analysis enables the proposal of the complete operating procedure, which is sustained by a Monte Carlo study.     

No wonder social workers feel uncomfortable in court

The present article assesses the adversary systemper se and asks the question, Is there any place for courtroom antics and histrionics in cases involving children? Social workers are uncomfortable before the august body of thecourt, not because of any lack of education or knowledge on their part but because of the nature of the adversary process itself.     

The Pyramid Model: A Useful Tool in Career Counseling With University Students

Often university students are faced with career decisions and seek help from the university counseling center. The pyramid model is a useful tool to assist the counselor and the student in the decision-making process. The metaphor enables the student to understand the tasks that lie ahead in the career counseling process. It is holistic. A case study is included to illustrate the three-dimensional model of career counseling of university students.