105,115 research outputs found
Generalized F-tests for the Multivariate Normal Mean
Based on Lauter\u27s (Biometrics, 1996) exact t test for biometrical studies related to the multivariate normal mean, we develop a generalized F-test for the multivariate normal mean and extend it to multiple comparison. The proposed generalized F- tests have simple approximate null distributions. A Monte Carlo study and two real examples show that the generalized F-test is at least as good as the optional individual LĂ„auter\u27s test and can improve its performance in some situations where the projection directions for the LĂ„auter\u27s test may not be suitably chosen. It is discussed that the generalized F-test could be superior to individual Lauter\u27s tests and the classical Hotelling T2-test for the general purpose of testing the multivariate normal mean. It is shown by Monte Carlo studies that the extended generalized F- test outperforms the commonly-used classical test for multiple comparison of normal means in the case of high dimension with small sample sizes. AMS Classification: 62F03; 62F0
Bayesian Model Choice of Grouped t-copula
One of the most popular copulas for modeling dependence structures is
t-copula. Recently the grouped t-copula was generalized to allow each group to
have one member only, so that a priori grouping is not required and the
dependence modeling is more flexible. This paper describes a Markov chain Monte
Carlo (MCMC) method under the Bayesian inference framework for estimating and
choosing t-copula models. Using historical data of foreign exchange (FX) rates
as a case study, we found that Bayesian model choice criteria overwhelmingly
favor the generalized t-copula. In addition, all the criteria also agree on the
second most likely model and these inferences are all consistent with classical
likelihood ratio tests. Finally, we demonstrate the impact of model choice on
the conditional Value-at-Risk for portfolios of six major FX rates
Flexible modelling in statistics: past, present and future
In times where more and more data become available and where the data exhibit
rather complex structures (significant departure from symmetry, heavy or light
tails), flexible modelling has become an essential task for statisticians as
well as researchers and practitioners from domains such as economics, finance
or environmental sciences. This is reflected by the wealth of existing
proposals for flexible distributions; well-known examples are Azzalini's
skew-normal, Tukey's -and-, mixture and two-piece distributions, to cite
but these. My aim in the present paper is to provide an introduction to this
research field, intended to be useful both for novices and professionals of the
domain. After a description of the research stream itself, I will narrate the
gripping history of flexible modelling, starring emblematic heroes from the
past such as Edgeworth and Pearson, then depict three of the most used flexible
families of distributions, and finally provide an outlook on future flexible
modelling research by posing challenging open questions.Comment: 27 pages, 4 figure
On high-dimensional sign tests
Sign tests are among the most successful procedures in multivariate
nonparametric statistics. In this paper, we consider several testing problems
in multivariate analysis, directional statistics and multivariate time series
analysis, and we show that, under appropriate symmetry assumptions, the
fixed- multivariate sign tests remain valid in the high-dimensional case.
Remarkably, our asymptotic results are universal, in the sense that, unlike in
most previous works in high-dimensional statistics, may go to infinity in
an arbitrary way as does. We conduct simulations that (i) confirm our
asymptotic results, (ii) reveal that, even for relatively large , chi-square
critical values are to be favoured over the (asymptotically equivalent)
Gaussian ones and (iii) show that, for testing i.i.d.-ness against serial
dependence in the high-dimensional case, Portmanteau sign tests outperform
their competitors in terms of validity-robustness.Comment: Published at http://dx.doi.org/10.3150/15-BEJ710 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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