100 research outputs found
Testing linear hypotheses in high-dimensional regressions
For a multivariate linear model, Wilk's likelihood ratio test (LRT)
constitutes one of the cornerstone tools. However, the computation of its
quantiles under the null or the alternative requires complex analytic
approximations and more importantly, these distributional approximations are
feasible only for moderate dimension of the dependent variable, say .
On the other hand, assuming that the data dimension as well as the number
of regression variables are fixed while the sample size grows, several
asymptotic approximations are proposed in the literature for Wilk's \bLa
including the widely used chi-square approximation. In this paper, we consider
necessary modifications to Wilk's test in a high-dimensional context,
specifically assuming a high data dimension and a large sample size .
Based on recent random matrix theory, the correction we propose to Wilk's test
is asymptotically Gaussian under the null and simulations demonstrate that the
corrected LRT has very satisfactory size and power, surely in the large and
large context, but also for moderately large data dimensions like or
. As a byproduct, we give a reason explaining why the standard chi-square
approximation fails for high-dimensional data. We also introduce a new
procedure for the classical multiple sample significance test in MANOVA which
is valid for high-dimensional data.Comment: Accepted 02/2012 for publication in "Statistics". 20 pages, 2 pages
and 2 table
Bayes in the sky: Bayesian inference and model selection in cosmology
The application of Bayesian methods in cosmology and astrophysics has
flourished over the past decade, spurred by data sets of increasing size and
complexity. In many respects, Bayesian methods have proven to be vastly
superior to more traditional statistical tools, offering the advantage of
higher efficiency and of a consistent conceptual basis for dealing with the
problem of induction in the presence of uncertainty. This trend is likely to
continue in the future, when the way we collect, manipulate and analyse
observations and compare them with theoretical models will assume an even more
central role in cosmology.
This review is an introduction to Bayesian methods in cosmology and
astrophysics and recent results in the field. I first present Bayesian
probability theory and its conceptual underpinnings, Bayes' Theorem and the
role of priors. I discuss the problem of parameter inference and its general
solution, along with numerical techniques such as Monte Carlo Markov Chain
methods. I then review the theory and application of Bayesian model comparison,
discussing the notions of Bayesian evidence and effective model complexity, and
how to compute and interpret those quantities. Recent developments in
cosmological parameter extraction and Bayesian cosmological model building are
summarized, highlighting the challenges that lie ahead.Comment: Invited review to appear in Contemporary Physics. 41 pages, 6
figures. Expanded references wrt published versio
Effects of word-of-mouth versus traditional marketing: findings from an internet social networking site
The authors study the effect of word-of-mouth (WOM) marketing on member growth at an Internet social networking site and compare it with traditional marketing vehicles. Because social network sites record the electronic invitations from existing members, outbound WOM can be precisely tracked. Along with traditional marketing, WOM can then be linked to the number of new members subsequently joining the site (sign-ups). Because of the endogeneity among WOM, new sign-ups, and traditional marketing activity, the authors employ a vector autoregression (VAR) modeling approach. Estimates from the VAR model show that WOM referrals have substantially longer carryover effects than traditional marketing actions and produce substantially higher response elasticises. Based on revenue from advertising impressions served to a new member, the monetary value of a WOM referral can be calculated; this yields an upper-bound estimate for the financial incentives the firm might offer to stimulate WOM.pre-prin
Statistical strategies for avoiding false discoveries in metabolomics and related experiments
A generalization of the alias matrix
Abstract The investigation of aliases or biases is important for the interpretation of the results from factorial experiments. For two-level fractional factorials this can be facilitated through their group structure. For more general arrays the alias matrix can be used. This tool is traditionally based on the assumption that the error structure is that associated with ordinary least squares. For situations where that is not the case, we provide in this article a generalization of the alias matrix applicable under the generalized least squares assumptions. We also show that for the special case of split plot error structure, the generalized alias matrix simplifies to the ordinary alias matrix.
Statistics For Experimenters : An Introduction to Design, Data Analysis, and Model Building
Bayesian application to the two-stage near-saturated experimental design method with dispersion effects
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