In this talk, we introduce a robust testing procedure — the Lq-likelihood ratio test (LqLR). We derive the asymptotic distribution of our test statistic and demonstrate its robustness properties both analytically and numerically.
The Statistics Department hosts weekly colloquia on a variety of statistcal subjects, bringing in speakers from around the world.
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Experimental costs are rising and it is important to use minimal resources to make statistical inference with maximal precision. Optimal design theory and ideas are increasingly applied to address design issues in a growing number of disciplines, and they include biomedicine, biochemistry, education, agronomy, manufacturing industry, toxicology and food science, to name a few.
We study behavior of the restricted maximum likelihood (REML) estimator under a misspecified linear mixed model (LMM) that has received much attention in recent gnome-wide association studies. The asymptotic analysis establishes consistency of the REML estimator of the variance of the errors in the LMM, and convergence in probability of the REML estimator of the variance of the random effects in the LMM to a certain limit, which is equal to the true variance of the random effects multiplied by the limiting proportion of the nonzero random effects present in the LMM.
Massively large data sets are routine and ubiquitous given modern computer capabilities. What is not so routine is how to analyse these data. One approach is to aggregate the data sets according to some scientific criteria. The resultant data are perforce symbolic data, i.e., lists, intervals, histograms, and so on. Applications abound, especially in the medical and social sciences. Other data sets (small or large in size) are naturally symbolic valued, such as species data, data with measurement uncertainties, confidential data, and the like.
Definitive Screening Designs (DSDs), discovered in 2011, are a new alternative to standard two-level screening designs. There are many desirable features of this family of designs. They require few runs while providing orthogonal main effects and avoiding any confounding of main effects by two-factor interactions. In addition they allow for estimating any quadratic effect of the continuous factors. The two-factor interactions are correlated but not confounded with each other. Moreover, in DSDs with 6 or more factors, it is possible to fit a full quadratic model in any three factors.
We collect the coauthor and citation data for all research papers published in four of the top journals in statistics between 2003 and 2012, analyze the data from several different perspectives (e.g., patterns, trends, community structures) and present an array of interesting findings. (1) Both the average numbers of papers per author published in these journals and the fraction of self citations have been decreasing, but the proportion of distant citations has been increasing.
Dimensional Analysis (DA) is a fundamental method in the engineering and physical sciences for analytically reducing the number of experimental variables prior to the experimentation. The principle use of dimensional analysis is to reduce from a study of the dimensions of the variables on the form of any possible relationship between those variables. The method is of great generality. In this talk, an overview/introduction of DA will be first given. A basic guideline for applying DA will be proposed, using examples for illustration. Some initial ideas on using DA for Data Analysis and
We propose sequential methods for obtaining approximate confidence limits and optimal sample sizes for the risk ratio (RR) of two independent binomial variates and a measure of reduction (MOR). The procedure is developed based on a modified maximum likelihood estimator (MLE) for the ratio. First-order asymptotic expansions are obtained for large-sample properties of the proposed procedure and we investigate its
finite sample behavior through numerical studies.
Data processing and source identification using lower dimensional hidden structure plays an essential role in many fields of applications, including image processing, neural networks, genome studies, signal processing and other areas where large datasets are often encountered. Representations of higher dimensional random vector using a lower dimensional vector provide a statistical framework to the identification and separation of the sources.
Latin Hypercube designs (LHD) are in standard use as plans for deterministic computer experiments. However, these designs depend on the ability of the investigator to set each factor independently of all the others. To be specific, the implied design region for an LHD is a square, cube or hypercube. However, there are cases where some parts of such a design region may be inaccessible or even nonsensical. In such cases it is useful to be able to produce a design that is both space-filling while obeying constraints on the design region.