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Optimality Properties (optimality + property)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Large-scale multiple testing under dependence

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2009
Wenguang Sun
Summary., The paper considers the problem of multiple testing under dependence in a compound decision theoretic framework. The observed data are assumed to be generated from an underlying two-state hidden Markov model. We propose oracle and asymptotically optimal data-driven procedures that aim to minimize the false non-discovery rate FNR subject to a constraint on the false discovery rate FDR. It is shown that the performance of a multiple-testing procedure can be substantially improved by adaptively exploiting the dependence structure among hypotheses, and hence conventional FDR procedures that ignore this structural information are inefficient. Both theoretical properties and numerical performances of the procedures proposed are investigated. It is shown that the procedures proposed control FDR at the desired level, enjoy certain optimality properties and are especially powerful in identifying clustered non-null cases. The new procedure is applied to an influenza-like illness surveillance study for detecting the timing of epidemic periods. [source]

Near-optimal designs for dual channel microarray studies

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 5 2005
Ernst Wit
Summary., Much biological and medical research employs microarray studies to monitor gene expression levels across a wide range of organisms and under many experimental conditions. Dual channel microarrays are a common platform and allow two samples to be measured simultaneously. A frequently used design uses a common reference sample to make conditions across different arrays comparable. Our aim is to formulate microarray experiments in the experimental design context and to use simulated annealing to search for near-optimal designs. We identify a subclass of designs, the so-called interwoven loop designs, that seems to have good optimality properties compared with the near-optimal designs that are found by simulated annealing. Commonly used reference designs and dye swap designs are shown to be highly inefficient. [source]

Improved Logrank-Type Tests for Survival Data Using Adaptive Weights

BIOMETRICS, Issue 1 2010
Song Yang
Summary For testing for treatment effects with time-to-event data, the logrank test is the most popular choice and has some optimality properties under proportional hazards alternatives. It may also be combined with other tests when a range of nonproportional alternatives are entertained. We introduce some versatile tests that use adaptively weighted logrank statistics. The adaptive weights utilize the hazard ratio obtained by fitting the model of Yang and Prentice (2005,,Biometrika,92, 1,17). Extensive numerical studies have been performed under proportional and nonproportional alternatives, with a wide range of hazard ratios patterns. These studies show that these new tests typically improve the tests they are designed to modify. In particular, the adaptively weighted logrank test maintains optimality at the proportional alternatives, while improving the power over a wide range of nonproportional alternatives. The new tests are illustrated in several real data examples. [source]

Robust location problems with pos/neg weights on a tree

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2001
Rainer E. Burkard
Abstract In this paper, we consider different aspects of robust 1-median problems on a tree network with uncertain or dynamically changing edge lengths and vertex weights which can also take negative values. The dynamic nature of a parameter is modeled by a linear function of time. A linear algorithm is designed for the absolute dynamic robust 1-median problem on a tree. The dynamic robust deviation 1-median problem on a tree with n vertices is solved in O(n2 ,(n) log n) time, where ,(n) is the inverse Ackermann function. Examples show that both problems do not possess the vertex optimality property. The uncertainty is modeled by given intervals, in which each parameter can take a value randomly. The absolute robust 1-median problem with interval data, where vertex weights might also be negative, can be solved in linear time. The corresponding deviation problem can be solved in O(n2) time. © 2001 John Wiley & Sons, Inc. [source]

On the construction of combined k -fault-tolerant Hamiltonian graphs

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2001
Chun-Nan Hung
Abstract A graph G is a combined k -fault-tolerant Hamiltonian graph (also called a combined k -Hamiltonian graph) if G , F is Hamiltonian for every subset F , (V(G) , E(G)) with |F| = k. A combined k -Hamiltonian graph G with |V(G)| = n is optimal if it has the minimum number of edges among all n -node k -Hamiltonian graphs. Using the concept of node expansion, we present a powerful construction scheme to construct a larger combined k -Hamiltonian graph from a given smaller graph. Many previous graphs can be constructed by the concept of node expansion. We also show that our construction maintains the optimality property in most cases. The classes of optimal combined k -Hamiltonian graphs that we constructed are shown to have a very good diameter. In particular, those optimal combined 1-Hamiltonian graphs that we constructed have a much smaller diameter than that of those constructed previously by Mukhopadhyaya and Sinha, Harary and Hayes, and Wang et al. © 2001 John Wiley & Sons, Inc. [source]

Maximum weight independent sets and matchings in sparse random graphs.

RANDOM STRUCTURES AND ALGORITHMS, Issue 1 2006
Exact results using the local weak convergence method
Let G(n,c/n) and Gr(n) be an n -node sparse random graph and a sparse random r -regular graph, respectively, and let I(n,r) and I(n,c) be the sizes of the largest independent set in G(n,c/n) and Gr(n). The asymptotic value of I(n,c)/n as n , ,, can be computed using the Karp-Sipser algorithm when c , e. For random cubic graphs, r = 3, it is only known that .432 , lim infnI(n,3)/n , lim supnI(n,3)/n , .4591 with high probability (w.h.p.) as n , ,, as shown in Frieze and Suen [Random Structures Algorithms 5 (1994), 649,664] and Bollabas [European J Combin 1 (1980), 311,316], respectively. In this paper we assume in addition that the nodes of the graph are equipped with nonnegative weights, independently generated according to some common distribution, and we consider instead the maximum weight of an independent set. Surprisingly, we discover that for certain weight distributions, the limit limnI(n,c)/n can be computed exactly even when c > e, and limnI(n,r)/n can be computed exactly for some r , 1. For example, when the weights are exponentially distributed with parameter 1, limnI(n,2e)/n , .5517, and limnI(n,3)/n , .6077. Our results are established using the recently developed local weak convergence method further reduced to a certain local optimality property exhibited by the models we consider. We extend our results to maximum weight matchings in G(n,c/n) and Gr(n). For the case of exponential distributions, we compute the corresponding limits for every c > 0 and every r , 2. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006 [source]