| his thesis considers two different topics of econometric theory, the bootstrap and the semiparametric efficiency bound of the mixed proportional hazard model (MPH).;In Chapter II, it is shown that the bootstrap distribution of the quantile regression estimator is asymptotically normal with the asymptotic variance matrix equal to that of the quantile regression estimator itself. The quantile regression estimator in a linear regression minimizes the sum of an asymmetric absolute value function of the residuals. Its asymptotic variance-covariance matrix depends on the error density. Thus, this chapter proves that it is possible to assess the statistical accuracy of the quantile regression estimator by the bootstrap, thereby avoiding the need for density estimation.;In Chapter III, the semiparametric efficiency bound of the MPH is derived. The density of the MPH factors in such a way that there exists a complete sufficient statistic for the individual heterogeneity. The efficient score is shown to be the difference between the score in the parametric direction and its conditional expectation given the sufficient statistic. Applying this result to the single spell Weibull MPH, it is shown that its information matrix is singular and there cannot exist any ;In Chapter I, the... |
