Statistics publications (MU)
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Items in this collection are the scholarly output of the Department of Statistics faculty, staff, and students, either alone or as co-authors, and which may or may not have been published in an alternate format. Items may contain more than one file type.
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Item On the de la Garza Phenomenon(Institute of Mathematical Statistics, 2010) Yang, Min, 1970 Oct. 28-; University of Missouri-Columbia. College of Arts and Sciences. Department of StatisticsDeriving optimal designs for nonlinear models is, in general, challenging. One crucial step is to determine the number of support points needed. Current tools handle this on a case-by-case basis. Each combination of model, optimality criterion and objective requires its own proof. The celebrated de la Garza Phenomenon states that under a (p − 1)th-degree polynomial regression model, any optimal design can be based on at most p design points, the minimum number of support points such that all parameters are estimable. Does this conclusion also hold for nonlinear models? If the answer is yes, it would be relatively easy to derive any optimal design, analytically or numerically. In this paper, a novel approach is developed to address this question. Using this new approach, it can be easily shown that the de la Garza phenomenon exists for many commonly studied nonlinear models, such as the Emax model, exponential model, three- and four-parameter log-linear models, Emax-PK1 model, as well as many classical polynomial regression models. The proposed approach unifies and extends many well-known results in the optimal design literature. It has four advantages over current tools: (i) it can be applied to many forms of nonlinear models; to continuous or discrete data; to data with homogeneous or nonhomogeneous errors; (ii) it can be applied to any design region; (iii) it can be applied to multiple-stage optimal design and (iv) it can be easily implemented.Item Universal Optimality in Balanced Uniform Crossover Design(Institute of Mathematical Statistics, 2003) Hedayat, A.; Yang, Min, 1970 Oct. 28-; University of Missouri-Columbia. College of Arts and Sciences. Department of StatisticsKunert [Ann. Statist. 12 (1984) 1006-1017] proved that, in the class of repeated measurement designs based on t treatments, p = t periods and n = λt experimental units, a balanced uniform design is universally optimal for direct treatment effects if t ≥ 3 and λ = 1, or if t ≥ 6 and λ = 2. This result is generalized to t ≥ 3 as long as λ ≤ (t −1)/2.Item Strong Consistency of MLE in Nonlinear Mixed-effects Models with Large Cluster Size(Indian Statistical Institute, 2005) Nie, Lei; Yang, Min, 1970 Oct. 28-; University of Missouri-Columbia. College of Arts and Sciences. Department of StatisticsThe search for conditions for the consistency of maximum likelihood estimators in nonlinear mixed effects models is difficult due to the fact that, in general, the likelihood can only be expressed as an integral over the random effects. For repeated measurements or clustered data, we focus on asymptotic theory for the maximum likelihood estimator for the case where the cluster sizes go to infinity, which is a minimum assumption required to validate most of the available methods of inference in nonlinear mixed-effects models. In particular, we establish sufficient conditions for the (strong) consistency of the maximum likelihood estimator of the fixed effects. Our results extend the results of Jennrich (1969) and Wu (1981) for nonlinear fixed-effects models to nonlinear mixed-effects models.Item Support Points of Locally Optimal Designs for Nonlinear Models with Two Parameters(Institute of Mathematical Statistics, 2009) Yang, Min, 1970 Oct. 28-; Stufken, John; University of Missouri-Columbia. College of Arts and Sciences. Department of StatisticsWe propose a new approach for identifying the support points of a locally optimal design when the model is a nonlinear model. In contrast to the commonly used geometric approach, we use an approach based on algebraic tools. Considerations are restricted to models with two parameters, and the general results are applied to often used special cases, including logistic, probit, double exponential and double reciprocal models for binary data, a loglinear Poisson regression model for count data, and the Michaelis-Menten model. The approach, which is also of value for multi-stage experiments, works both with constrained and unconstrained design regions and is relatively easy to implement.Item ComPhy: Prokaryotic Composite Distance Phylogenies Inferred from Whole-Genome Gene Sets(BioMed Central, 2009) Lin, Guan Ning, 1978-; Cai, Zhipeng; Lin, Guohui; Chakraborty, Sounak; Xu, Dong, 1965-; University of Missouri-Columbia. College of Arts and Sciences. Department of StatisticsWith the increasing availability of whole genome sequences, it is becoming more and more important to use complete genome sequences for inferring species phylogenies. We developed a new tool ComPhy, 'Composite Distance Phylogeny', based on a composite distance matrix calculated from the comparison of complete gene sets between genome pairs to produce a prokaryotic phylogeny. The composite distance between two genomes is defined by three components: Gene Dispersion Distance (GDD), Genome Breakpoint Distance (GBD) and Gene Content Distance (GCD). GDD quantifies the dispersion of orthologous genes along the genomic coordinates from one genome to another; GBD measures the shared breakpoints between two genomes; GCD measures the level of shared orthologs between two genomes. The phylogenetic tree is constructed from the composite distance matrix using a neighbor joining method. We tested our method on 9 datasets from 398 completely sequenced prokaryotic genomes. We have achieved above 90% agreement in quartet topologies between the tree created by our method and the tree from the Bergey's taxonomy. In comparison to several other phylogenetic analysis methods, our method showed consistently better performance. ComPhy is a fast and robust tool for genome-wide inference of evolutionary relationship among genomes.