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2004

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Articles 211 - 235 of 235

Full-Text Articles in Statistics and Probability

Oscillation Of Second Order Nonlinear Dynamic Equations On Time Scales, S. H. Saker, Martin Bohner Jan 2004

Oscillation Of Second Order Nonlinear Dynamic Equations On Time Scales, S. H. Saker, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

By means of Riccati transformation techniques, we establish some oscillation criteria for a second order nonlinear dynamic equation on time scales in terms of the coefficients. We give examples of dynamic equations to which previously known oscillation criteria are not applicable.

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Oscillation Theory For Second Order Dynamic Equations [Book Review], Martin Bohner Jan 2004

Oscillation Theory For Second Order Dynamic Equations [Book Review], Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

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Multiple Testing. Part Iii. Procedures For Control Of The Generalized Family-Wise Error Rate And Proportion Of False Positives, Mark J. Van Der Laan, Sandrine Dudoit, Katherine S. Pollard Jan 2004

Multiple Testing. Part Iii. Procedures For Control Of The Generalized Family-Wise Error Rate And Proportion Of False Positives, Mark J. Van Der Laan, Sandrine Dudoit, Katherine S. Pollard

U.C. Berkeley Division of Biostatistics Working Paper Series

The accompanying articles by Dudoit et al. (2003b) and van der Laan et al. (2003) provide single-step and step-down resampling-based multiple testing procedures that asymptotically control the family-wise error rate (FWER) for general null hypotheses and test statistics. The proposed procedures fundamentally differ from existing approaches in the choice of null distribution for deriving cut-offs for the test statistics and are shown to provide asymptotic control of the FWER under general data generating distributions, without the need for conditions such as subset pivotality. In this article, we show that any multiple testing procedure (asymptotically) controlling the FWER at level alpha …

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Cr Approximation On A Nonrigid Hypersurface Graph In Cⁿ, Al Boggess, Roman Dwilewicz Jan 2004

Cr Approximation On A Nonrigid Hypersurface Graph In Cⁿ, Al Boggess, Roman Dwilewicz

Mathematics and Statistics Faculty Research & Creative Works

Let M be a hypersurface in Cn that is the graph over a (2n - 1)-linear real space. the main result of the paper is that any CR function on M can be uniformly approximated on compact subsets by entire functions on Cn.

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The Independence Of Characters On Nonabelian Groups, David E. Grow, Kathryn E. Hare Jan 2004

The Independence Of Characters On Nonabelian Groups, David E. Grow, Kathryn E. Hare

Mathematics and Statistics Faculty Research & Creative Works

We show that there are characters of compact, connected, nonabelian groups that approximate random choices of signs. The work was motivated by Kronecker's theorem on the independence of exponential functions and has applications to thin sets.

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Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan Jan 2004

Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan

Articles and Preprints

In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDE's). The scheme has convergence order 1. In order to establish the scheme, we prove an infinite-dimensional Itô formula for "tame" functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires the use of the Malliavin calculus and the anticipating stochastic analysis of Nualart and Pardoux. Given the non-anticipating nature of the SDDE, the use of anticipating calculus methods appears to be novel.

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Evaluation Of Multiple Models To Distinguish Closely Related Forms Of Disease Using Dna Microarray Data: An Application To Multiple Myeloma, Johanna S. Hardin, Michael Waddell, C. David Page, Fenghuang Zhan, Bart Barlogie, John Shaughnessy, John J. Crowley Jan 2004

Evaluation Of Multiple Models To Distinguish Closely Related Forms Of Disease Using Dna Microarray Data: An Application To Multiple Myeloma, Johanna S. Hardin, Michael Waddell, C. David Page, Fenghuang Zhan, Bart Barlogie, John Shaughnessy, John J. Crowley

Pomona Faculty Publications and Research

Motivation: Standard laboratory classification of the plasma cell dyscrasia monoclonal gammopathy of undetermined significance (MGUS) and the overt plasma cell neoplasm multiple myeloma (MM) is quite accurate, yet, for the most part, biologically uninformative. Most, if not all, cancers are caused by inherited or acquired genetic mutations that manifest themselves in altered gene expression patterns in the clonally related cancer cells. Microarray technology allows for qualitative and quantitative measurements of the expression levels of thousands of genes simultaneously, and it has now been used both to classify cancers that are morphologically indistinguishable and to predict response to therapy. It is …

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Ua56/1 Fact Book, Wku Institutional Research Jan 2004

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

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Reconstructability Analysis With Fourier Transforms, Martin Zwick Jan 2004

Reconstructability Analysis With Fourier Transforms, Martin Zwick

Complex Systems Faculty Publications and Presentations

Fourier methods used in two‐ and three‐dimensional image reconstruction can be used also in reconstructability analysis (RA). These methods maximize a variance‐type measure instead of information‐theoretic uncertainty, but the two measures are roughly collinear and the Fourier approach yields results close to that of standard RA. The Fourier method, however, does not require iterative calculations for models with loops. Moreover, the error in Fourier RA models can be assessed without actually generating the full probability distributions of the models; calculations scale with the size of the data rather than the state space. State‐based modeling using the Fourier approach is also …

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Controlling Wound Healing Through Debridement, M. A. Jones, Baojun Song, D. M. Thomas Jan 2004

Controlling Wound Healing Through Debridement, M. A. Jones, Baojun Song, D. M. Thomas

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

The formation of slough (dead tissue) on a wound is widely accepted as an inhibitor to natural wound healing. In this article, a system of differential equations that models slough/wound interaction is developed. We prove a threshold theorem that provides conditions on the amount of slough to guarantee wound healing. As a state-dependent time scale, debridement (the periodic removal of slough) is used as a control. We show that closure of the wound can be reached in infinite time by debriding.

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การทดสอบสมมติฐานเกี่ยวกับความเป็นอิสระของตัวแบบล็อกการิทึมเชิงเส้นที่มีการแจกแจงพหุนาม, ประกาศิต สิงคะตีระ Jan 2004

การทดสอบสมมติฐานเกี่ยวกับความเป็นอิสระของตัวแบบล็อกการิทึมเชิงเส้นที่มีการแจกแจงพหุนาม, ประกาศิต สิงคะตีระ

Chulalongkorn University Theses and Dissertations (Chula ETD)

การวิจัยครั้งนี้มีวัตถุประสงค์ เพื่อเปรียบเทียบวิธีการทดสอบสมมติฐานเกี่ยวกับความเป็นอิสระของตัวแปรเชิงกลุ่ม 3 ตัวแปร ในตารางการณ์จร 3 ทาง ขนาด 2x2x2 และศึกษาความเป็นไปได้ที่จะนำวิธีการมอนติคาร์โลมาใช้แทนวิธีการทดสอบด้วยตัวสถิติอัตราส่วนภาวะน่าจะเป็น วิธีการทดสอบที่นำมาศึกษาเปรียบเทียบมี 3 วิธี ได้แก่ วิธีการทดสอบด้วยตัวสถิติอัตราส่วนภาวะน่าจะเป็น วิธีการทดสอบด้วยตัวสถิติของเซลเทอร์แมนและวิธีมอนติคาร์โล โดยวิธีการมอนติคาร์โลเป็นวิธีการทดสอบสมมติฐานที่ไม่อาศัยค่าวิกฤติของตัวสถิติทดสอบ แต่จะทำการเปรียบเทียบค่าสถิติที่คำนวณได้จากข้อมูลตัวอย่างที่ต้องการศึกษากับค่าสถิติที่คำนวณได้จากข้อมูลเทียมแต่ละชุดที่จำลองขึ้นโดยการสุ่มตัวอย่างซ้ำภายใต้ข้อกำหนดตามสมมติฐานว่าง เพื่อนำไปสู่การหาค่า P-value ผู้วิจัยได้ทำการศึกษาในแต่ละตัวแบบที่เป็นไปได้และเป็นตัวแบบที่มีรูปแบบปิดของค่าความถี่คาดหวัง เพื่อให้สามารถจำลองข้อมูลได้ถูกต้อง ซึ่งตัวแบบต่างๆ ประกอบด้วยตัวแบบที่เป็นอิสระอย่างสมบูรณ์ ตัวแบบความเป็นอิสระร่วม และตัวแบบความเป็นอิสระอย่างมีเงื่อนไข และได้กำหนดระดับความสัมพันธ์ให้กับตัวแปรร่วมที่มีความสัมพันธ์ร่วมกัน จากน้อยไปหามากคือ 0.25, 0.50 และ 0.75 ขนาดตัวอย่างที่ใช้คือ 40, 60, 80, 120, 160, 200 และ 240 และระดับนัยสำคัญที่ใช้คือ 0.05 และ 0.01 เกณฑ์ที่ใช้ในการเปรียบเทียบคือการพิจารณาความสามารถในการควบคุมความน่าจะเป็นของความผิดพลาดประเภทที่ 1 และ ค่าอำนาจการทดสอบ การวิจัยครั้งนี้ได้จำลองข้อมูลโดยกระทำซ้ำแบบเทคนิคมอนติคาร์โล (Monte Carlo simulation technique) จำนวน 500 ครั้ง ซึ่งในแต่ละครั้งจะกระทำซ้ำแบบมอนติคาร์โลอีก 500 ครั้ง เพื่อสร้างชุดข้อมูล 500 ชุด เพื่อคำนวณค่า P-value ของวิธีการทดสอบแบบมอนติคาร์โล ผลการวิจัยสามารถสรุปได้ดังนี้ วิธีการทดสอบทั้ง 3 วิธีสามารถควบคุมความน่าจะเป็นของความผิดพลาดประเภทที่ 1 ได้ในทุกสถานการณ์ วิธีการมอนติคาร์โลมีแนวโน้มที่จะให้ค่าอำนาจการทดสอบสูงที่สุด รองลงมาคือวิธีการทดสอบด้วยตัวสถิติอัตราส่วนภาวะน่าจะเป็น และวิธีการสอบด้วยตัวสถิติของเซลเทอร์แมน และโดยเฉพาะอย่างยิ่งในกรณีตัวอย่างขนาดเล็ก วิธีการมอนติคาร์โลจะมีค่าอำนาจการทดสอบสูงกว่าวิธีการอื่นอย่างชัดเจน ทั้งนี้เนื่องจากแนวคิดของวิธีการมอนติคาร์โลที่มีการจำลองข้อมูลเทียมหลายชุดภายใต้สมมติฐานว่างขึ้นมาพิจารณานั้นเสมือนเป็นการสร้างขอบเขตที่เป็นไปได้ของข้อมูลตามข้อกำหนดในสมมติฐานว่าง เพื่อเปรียบเทียบกับข้อมูลตัวอย่างที่ศึกษา จึงมีความถูกต้องมากกว่าการทดสอบสมมติฐานโดยทั่วไปซึ่งเป็นการเปรียบเทียบระหว่างค่าสถิติที่คำนวณได้กับค่าวิกฤติเพียงครั้งเดียว นอกจากนี้ยังพบว่าค่าอำนาจการทดสอบของวิธีการทดสอบทั้ง 3 วิธีแปรผันตามขนาดตัวอย่าง ระดับความสัมพันธ์ของตัวแปรร่วม และระดับนัยสำคัญ โดยสรุป ผู้วิจัยพบว่ามีความเป็นไปได้ที่จะนำเอาการทดสอบสมมติฐานด้วยวิธีการมอนติคาร์โลมาใช้ทดสอบสมมติฐานเกี่ยวกับความเป็นอิสระของตัวแบบล็อกการิทึมเชิงเส้น แทนการทดสอบทั้งสองวิธีดังกล่าวใน 3 ตัวแบบข้างต้นได้ โดยเฉพาะอย่างยิ่งในกรณีตัวอย่างขนาดเล็ก

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A Comparison Of Modified Reconstructability Analysis And Ashenhurst‐Curtis Decomposition Of Boolean Functions, Anas Al-Rabadi, Marek Perkowski, Martin Zwick Jan 2004

A Comparison Of Modified Reconstructability Analysis And Ashenhurst‐Curtis Decomposition Of Boolean Functions, Anas Al-Rabadi, Marek Perkowski, Martin Zwick

Complex Systems Faculty Publications and Presentations

Modified reconstructability analysis (MRA), a novel decomposition technique within the framework of set‐theoretic (crisp possibilistic) reconstructability analysis, is applied to three‐variable NPN‐classified Boolean functions. MRA is superior to conventional reconstructability analysis, i.e. it decomposes more NPN functions. MRA is compared to Ashenhurst‐Curtis (AC) decomposition using two different complexity measures: log‐functionality, a measure suitable for machine learning, and the count of the total number of two‐input gates, a measure suitable for circuit design. MRA is superior to AC using the first of these measures, and is comparable to, but different from AC, using the second.

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Grouped Data, Gudmund R. Iversen Jan 2004

Grouped Data, Gudmund R. Iversen

Mathematics & Statistics Faculty Works

No abstract provided.

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Multivariate Analysis Of Variance And Covariance (Manova And Mancova), Gudmund R. Iversen Jan 2004

Multivariate Analysis Of Variance And Covariance (Manova And Mancova), Gudmund R. Iversen

Mathematics & Statistics Faculty Works

No abstract provided.

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Random Error, Gudmund R. Iversen Jan 2004

Random Error, Gudmund R. Iversen

Mathematics & Statistics Faculty Works

No abstract provided.

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An Overview Of Reconstructability Analysis, Martin Zwick Jan 2004

An Overview Of Reconstructability Analysis, Martin Zwick

Complex Systems Faculty Publications and Presentations

This paper is an overview of reconstructability analysis (RA), a discrete multivariate modeling methodology developed in the systems literature; an earlier version of this tutorial is Zwick (2001). RA was derived from Ashby (1964), and was developed by Broekstra, Cavallo, Cellier Conant, Jones, Klir, Krippendorff, and others (Klir, 1986, 1996). RA resembles and partially overlaps log‐line (LL) statistical methods used in the social sciences (Bishop et al., 1978; Knoke and Burke, 1980). RA also resembles and overlaps methods used in logic design and machine learning (LDL) in electrical and computer engineering (e.g. Perkowski et al., 1997). Applications of RA, like …

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Uniqueness Theorems In Bioluminescence Tomography, Ge Wang, Yi Li, Ming Jiang Jan 2004

Uniqueness Theorems In Bioluminescence Tomography, Ge Wang, Yi Li, Ming Jiang

Mathematics and Statistics Faculty Publications

Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed in the University of Iowa. While the forward imaging model is described by the well-known diffusion equation, the inverse problem is to recover an internal bioluminescent source distribution subject to Cauchy data. Our primary goal in this paper is to establish the solution uniqueness for BLT under practical constraints despite the ill-posedness of the inverse problem in the general case. After a review on the inverse source literature, we demonstrate that in the general case …

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The Dual Spectral Set Conjecture, Steen Pedersen Jan 2004

The Dual Spectral Set Conjecture, Steen Pedersen

Mathematics and Statistics Faculty Publications

Suppose that Λ = (aZ + b) ∪ (cZ + d) where a, b, c, d are real numbers such that a ≠ 0 and c ≠ 0. The union is not assumed to be disjoint. It is shown that the translates Ω + λ, λ is an element of Λ, tile the real line for some bounded measurable set Ω if and only if the exponentials eλ(x) = ei2πλx, λ is an element of Λ, form an orthogonal basis for some bounded measurable set Ω'.

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Reliability Estimation Based On System Data With An Unknown Load Share Rule, Hyoungtae Kim, Paul H. Kvam Jan 2004

Reliability Estimation Based On System Data With An Unknown Load Share Rule, Hyoungtae Kim, Paul H. Kvam

Department of Math & Statistics Faculty Publications

We consider a multicomponent load-sharing system in which the failure rate of a given component depends on the set of working components at any given time. Such systems can arise in software reliability models and in multivariate failure-time models in biostatistics, for example. A load-share rule dictates how stress or load is redistributed to the surviving components after a component fails within the system. In this paper, we assume the load share rule is unknown and derive methods for statistical inference on load-share parameters based on maximum likelihood. Components with (individual) constant failure rates are observed in two environments: (1) …

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A Nonlinear Random Coefficients Model For Degradation Testing, Suk Joo Bae, Paul H. Kvam Jan 2004

A Nonlinear Random Coefficients Model For Degradation Testing, Suk Joo Bae, Paul H. Kvam

Department of Math & Statistics Faculty Publications

As an alternative to traditional life testing, degradation tests can be effective in assessing product reliability when measurements of degradation leading to failure can be observed. This article presents a degradation model for highly reliable light displays, such as plasma display panels and vacuum fluorescent displays (VFDs). Standard degradation models fail to capture the burn-in characteristics of VFDs, when emitted light actually increases up to a certain point in time before it decreases (or degrades) continuously. Random coefficients are used to model this phenomenon in a nonlinear way, which allows for a nonmonotonic degradation path. In many situations, the relative …

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Gamma-Set Domination Graphs. I: Complete Biorientations Of Q-Extended Stars And Wounded Spider Graphs, Kim A. S. Factor Jan 2004

Gamma-Set Domination Graphs. I: Complete Biorientations Of Q-Extended Stars And Wounded Spider Graphs, Kim A. S. Factor

Mathematics, Statistics and Computer Science Faculty Research and Publications

The domination number of a graph G, γ(G), and the domination graph of a digraph D, dom(D) are integrated in this paper. The γ-set domination graph of the complete biorientation of a graph G, domγ(G) is created. All γ-sets of specific trees T are found, and dom-γ(T) is characterized for those classes.

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Arbitration And Litigation Of Employment Claims: An Empirical Comparison, Theodore Eisenberg, Elizabeth Hill Jan 2004

Arbitration And Litigation Of Employment Claims: An Empirical Comparison, Theodore Eisenberg, Elizabeth Hill

Cornell Law Faculty Publications

The authors conducted empirical research comparing court case and arbitrated outcomes for employment disputes. In cases not involving civil rights claims, they found little evidence that arbitrated outcomes materially differed from trial outcomes where the claimant was a higher-paid employee. Moreover, they found no statistically significant differences between employee win rates or in the median or mean awards in arbitration and litigation. They also reported evidence indicating that arbitrated disputes conclude more quickly than litigated disputes.

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Wishartness And Independence Of Matrix Quadratic Forms For Kronecker Product Covariance Structures, Akhil K. Vaish, N. Rao Chaganty Jan 2004

Wishartness And Independence Of Matrix Quadratic Forms For Kronecker Product Covariance Structures, Akhil K. Vaish, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Let X be distributed as matrix normal with mean M and covariance matrix W⊗V, where W and V are nonnegative definite (nnd) matrices. In this paper we present a simple version of the Cochran’s theorem for matrix quadratic forms in X. The theorem is used to characterize the class of nnd matrices W such that the matrix quadratic forms that occur in multivariate analysis of variance are independent and Wishart except for a scale factor. © 2003 Elsevier Inc. All rights reserved.

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Deviance Information Criterion For Comparing Stochastic Volatility Models, Andreas Berg, Renate Meyer, Jun Yu Jan 2004

Deviance Information Criterion For Comparing Stochastic Volatility Models, Andreas Berg, Renate Meyer, Jun Yu

Research Collection School Of Economics

Bayesian methods have been efficient in estimating parameters of stochastic volatility models for analyzing financial time series. Recent advances made it possible to fit stochastic volatility models of increasing complexity, including covariates, leverage effects, jump components, and heavy-tailed distributions. However, a formal model comparison via Bayes factors remains difficult. The main objective of this article is to demonstrate that model selection is more easily performed using the deviance information criterion (DIC). It combines a Bayesian measure of fit with a measure of model complexity. We illustrate the performance of DIC in discriminating between various different stochastic volatility models using simulated …

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Forecasting The Equity Premium In The Australian Market, David E. Allen, Lurion Demello Jan 2004

Forecasting The Equity Premium In The Australian Market, David E. Allen, Lurion Demello

Research outputs pre 2011

This paper provides a forecasting methodology for estimating the market risk premium in Australia. We employ an in-sample and out-of-sample forecast estimate using various dividend yield measures. The lagged dividend yield model is used to predict future equity premia on a data series that includes the top 85 percent of the Australian stock market. An important concern in this paper is the accuracy of dividend yield in forecasting the equity premium in the Australian market. We find that the level of predictability in the later part of the series is very weak compared to in-sample prediction during the 70s and …

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