Abstract: The log periodogram regression is widely used in empirical
applications because of its simplicity, since only a least squares
regression is required to estimate the memory parameter, d, its good
asymptotic properties and its robustness to misspecification of the
short term behavior of the series. However, the asymptotic distribution
is a poor approximation of the (unknown) finite sample distribution
if the sample size is small. Here the finite sample performance of different
nonparametric residual bootstrap procedures is analyzed when
applied to construct confidence intervals. In particular, in addition to
the basic residual bootstrap, the local and block bootstrap that might
adequately replicate the structure that may arise in the errors of the
regression are considered when the series shows weak dependence in
addition to the long memory component. Bias correcting bootstrap
to adjust the bias caused by that structure is also considered. Finally,
the performance of the bootstrap in log periodogram regression based
confidence intervals is assessed in different type of models and how
its performance changes as sample size increases.
Abstract: In this paper, penalized power-divergence test statistics have been defined and their exact size properties to test a nested sequence of log-linear models have been compared with ordinary power-divergence test statistics for various penalization, λ and main effect values. Since the ordinary and penalized power-divergence test statistics have the same asymptotic distribution, comparisons have been only made for small and moderate samples. Three-way contingency tables distributed according to a multinomial distribution have been considered. Simulation results reveal that penalized power-divergence test statistics perform much better than their ordinary counterparts.
Abstract: Bootstrapping has gained popularity in different tests of hypotheses as an alternative in using asymptotic distribution if one is not sure of the distribution of the test statistic under a null hypothesis. This method, in general, has two variants – the parametric and the nonparametric approaches. However, issues on reliability of this method always arise in many applications. This paper addresses the issue on reliability by establishing a reliability measure in terms of quantiles with respect to asymptotic distribution, when this is approximately correct. The test of hypotheses used is Ftest. The simulated results show that using nonparametric bootstrapping in F-test gives better reliability than parametric bootstrapping with relatively higher degrees of freedom.
Abstract: In recent years, the use of vector variance as a
measure of multivariate variability has received much attention in
wide range of statistics. This paper deals with a more economic
measure of multivariate variability, defined as vector variance minus
all duplication elements. For high dimensional data, this will increase
the computational efficiency almost 50 % compared to the original
vector variance. Its sampling distribution will be investigated to make
its applications possible.