2011년 제 2회 통계 세미나 개최를 알려드리고자 합니다.
일시: 2011년 4월 13일(수) 오후 5시
장소: 고려대학교 정경관 508호
연사: Byungtae Seo
(Department of Statistics, Sungkyunkwan University)
"Semiparametric mixtures in GARCH
and Stochastic frontier models"
<Abstract>
Finite mixture models are attractive in capturing unseen underlying group structure in given data. These can be also used to construct flexible statistical models when a researcher is not sure if a chosen distributional assumption is appropriate. In this case, non- or semi-parametric mixtures would be more appropriate than finite mixtures. In this talk, I will present how we can use semi-parametric mixture models exemplified in two statistical problems. First, the GARCH model will be considered. In the GARCH model, the innovation is typically assumed to be normally distributed, which is clearly unrealistic in most cases. Although the normal assumption guarantees consistency of the estimators of GARCH parameters, it could cause bias and information loss for the estimators in a finite sample. Moreover, when a researcher wants to estimate Value-At-Risk, its estimator does not perform well due to improper distributional assumptions. A semi-parametric mixture model will be used to resolve this misspecification problem. Secondly, I will present another semi-parametric mixture approach for the stochastic frontier model with measurement error. In a stochastic frontier model, if a covariate also has a measurement error, the ordinary MLE will experience a serious bias. To correct this, we may need a certain distributional assumption for the true covariate. However, since the true covariate cannot be observed in practice, a typical parametric distributional assumption does not look plausible in many cases. For this problem, semi-parametric mixtures will be used to handle the unobserved covariate. This talk will also include some simulation studies and real data analysis for each application.