检索结果-内蒙古大学图书馆

A segmentation-based algorithm for large-scale partially ordered monotonic regression

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2011年第8期55卷 2463-2476页

作者： Sysoev, O. Burdakov, O. Grimvall, A. Linkoping Univ Dept Comp & Informat Sci SE-58183 Linkoping Sweden Linkoping Univ Dept Math SE-58183 Linkoping Sweden

Monotonic regression (MR) is an efficient tool for estimating functions that are monotonic with respect to input variables. A fast and highly accurate approximate algorithm called the GPAV was recently developed for efficient solving large-scale multivariate MR problems. When such problems are too large, the GPAV becomes too demanding in terms of computational time and memory. An approach, that extends the application area of the GPAV to encompass much larger MR problems, is presented. It is based on segmentation of a large-scale MR problem into a set of moderate-scale MR problems, each solved by the GPAV. The major contribution is the development of a computationally efficient strategy that produces a monotonic response using the local solutions. A theoretically motivated trend-following technique is introduced to ensure higher accuracy of the solution. The presented results of extensive simulations on very large data sets demonstrate the high efficiency of the new algorithm. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Quadratic programming Large-scale optimization Least distance problem Monotonic regression Partially ordered data set pool-adjacent-violators algorithm

来源：评论

学校读者我要写书评

暂无评论

Bootstrap Confidence Intervals for Large-scale Multivariate Monotonic Regression Problems

引用

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2016年第3期45卷 1025-1040页

作者： Sysoev, Oleg Grimvall, Anders Burdakov, Oleg Linkoping Univ Dept Comp & Informat Sci S-58183 Linkoping Sweden Linkoping Univ Dept Math S-58183 Linkoping Sweden

Recently, the methods used to estimate monotonic regression (MR) models have been substantially improved, and some algorithms can now produce high-accuracy monotonic fits to multivariate datasets containing over a million observations. Nevertheless, the computational burden can be prohibitively large for resampling techniques in which numerous datasets are processed independently of each other. Here, we present efficient algorithms for estimation of confidence limits in large-scale settings that take into account the similarity of the bootstrap or jackknifed datasets to which MR models are fitted. In addition, we introduce modifications that substantially improve the accuracy of MR solutions for binary response variables. The performance of our algorithms is illustrated using data on death in coronary heart disease for a large population. This example also illustrates that MR can be a valuable complement to logistic regression.

关键词： Big data Bootstrap Confidence intervals Monotonic regression pool-adjacent-violators algorithm 62G08 62G09

来源：评论

学校读者我要写书评

暂无评论

Characterizing the optimal solutions to the isotonic regression problem for identifiable functionals

引用

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 2022年第3期74卷 489-514页

作者： Jordan, Alexander I. Muhlemann, Anja Ziegel, Johanna F. Heidelberg Inst Theoret Studies Computat Stat CST Grp Schloss Wolfsbrunnenweg 35 D-69118 Heidelberg Germany Univ Bern Inst Math Stat & Actuarial Sci Alpeneggstr 22 CH-3012 Bern Switzerland

In general, the solution to a regression problem is the minimizer of a given loss criterion and depends on the specified loss function. The nonparametric isotonic regression problem is special, in that optimal solutions can be found by solely specifying a functional. These solutions will then be minimizers under all loss functions simultaneously as long as the loss functions have the requested functional as the Bayes act. For the functional, the only requirement is that it can be defined via an identification function, with examples including the expectation, quantile, and expectile functionals. Generalizing classical results, we characterize the optimal solutions to the isotonic regression problem for identifiable functionals by rigorously treating these functionals as set-valued. The results hold in the case of totally or partially ordered explanatory variables. For total orders, we show that any solution resulting from the pool-adjacent-violators algorithm is optimal.

关键词： Order-restricted optimization problems Partial order Simultaneous optimality pool-adjacent-violators algorithm Consistent loss functions

来源：评论

学校读者我要写书评

暂无评论

Nonparametric Benchmark Dose Estimation with Continuous Dose-Response Data

引用

SCANDINAVIAN JOURNAL OF STATISTICS 2015年第3期42卷 713-731页

作者： Lin, Lizhen Piegorsch, Walter W. Bhattacharya, Rabi Univ Texas Austin Dept Stat & Data Sci Austin TX 78712 USA Univ Arizona Program Stat Tucson AZ 85721 USA Univ Arizona Dept Math Tucson AZ 85721 USA

We propose a new method for risk-analytic benchmark dose (BMD) estimation in a dose-response setting when the responses are measured on a continuous scale. For each dose level d, the observation X(d) is assumed to follow a normal distribution: N((d),sigma 2). No specific parametric form is imposed upon the mean (d), however. Instead, nonparametric maximum likelihood estimates of (d) and sigma are obtained under a monotonicity constraint on (d). For purposes of quantitative risk assessment, a hybrid' form of risk function is defined for any dose d as R(d) = P[X(d) < c], where c > 0 is a constant independent of d. The BMD is then determined by inverting the additional risk functionR(A)(d) = R(d) - R(0) at some specified value of benchmark response. Asymptotic theory for the point estimators is derived, and a finite-sample study is conducted, using both real and simulated data. When a large number of doses are available, we propose an adaptive grouping method for estimating the BMD, which is shown to have optimal mean integrated squared error under appropriate designs.

关键词： benchmark analysis benchmark dose bootstrap confidence limits dose-response analysis isotonic regression model uncertainty pool-adjacent-violators algorithm quantitative responses quantitative risk assessment

来源：评论

学校读者我要写书评

暂无评论

AN algorithm FOR ISOTONIC REGRESSION WITH ARBITRARY CONVEX DISTANCE FUNCTION

引用

COMPUTATIONAL STATISTICS & DATA ANALYSIS 1991年第2期11卷 205-219页

作者： STROMBERG, U UNIV LUND DEPT MATH STATS-22100 LUNDSWEDEN

In the present paper we consider the isotonic regression problem with an arbitrary convex distance function d(.), and the main purpose being to present an algorithm for obtaining all isotonic regressions under this reasonable assumption on d(.). Further, we consider a piece-wise linear distance function d(.) of the type d(t) = C-\t\ for t < 0 and d(t) = C+ \t\ for t greater-than-or-equal-to 0 and get an isotonic pth frctile regression by choosing p = C+ /(C- + C+).

关键词： ISOTONIC REGRESSION DISTANCE FUNCTION pool-adjacent-violators algorithm FRACTILE

来源：评论

学校读者我要写书评

暂无评论

Discrimination of locally stationary time series based on the excess mass functional

引用

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2006年第473期101卷 240-253页

作者： Chandler, G Polonik, W Connecticut Coll Dept Math New London CT 06320 USA Univ Calif Davis Dept Stat Davis CA 95616 USA

Discrimination of time series is an important practical problem with applications in various scientific fields. We propose and study a novel approach to this problem. Our approach is applicable to cases where time series in different categories have a different "shape." Although based on the idea of feature extraction, our method is not distance-based, and as such does not require aligning the time series. Instead, features are measured for each time series, and discrimination is based on these individual measures. An AR process with a time-varying variance is used as an underlying model. Our method then uses shape measures or, better, measures of concentration of the variance function, as a criterion for discrimination. It is this concentration aspect or shape aspect that makes the approach intuitively appealing. We provide some mathematical justification for our proposed methodology, as well as a simulation study and an application to the problem of discriminating earthquakes and explosions.

关键词： modulated AR process nonparametric estimation pool-adjacent-violators algorithm shape restrictions

来源：评论

学校读者我要写书评

暂无评论

Least squares and shrinkage estimation under bimonotonicity constraints

引用

STATISTICS AND COMPUTING 2010年第2期20卷 177-189页

作者： Beran, Rudolf Duembgen, Lutz Univ Bern Bern Switzerland Univ Calif Davis Davis CA 95616 USA

In this paper we describe active set type algorithms for minimization of a smooth function under general order constraints, an important case being functions on the set of bimonotone rxs matrices. These algorithms can be used, for instance, to estimate a bimonotone regression function via least squares or (a smooth approximation of) least absolute deviations. Another application is shrinkage estimation in image denoising or, more generally, regression problems with two ordinal factors after representing the data in a suitable basis which is indexed by pairs (i,j)a{1,aEuro broken vertical bar,r}x{1,aEuro broken vertical bar,s}. Various numerical examples illustrate our methods.

关键词： Active set algorithm Dynamic programming Estimated risk pool-adjacent-violators algorithm Regularization

来源：评论

学校读者我要写书评

暂无评论

OPTIMAL FALSE DISCOVERY RATE CONTROL FOR LARGE SCALE MULTIPLE TESTING WITH AUXILIARY INFORMATION

引用

ANNALS OF STATISTICS 2022年第2期50卷 807-857页

作者： Cao, Hongyuan Chen, Jun Zhang, Xianyang Florida State Univ Dept Stat Tallahassee FL 32306 USA Mayo Clin Dept Quantitat Hlth Sci Rochester MN USA Texas A&M Univ Dept Stat College Stn TX 77843 USA

Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are available. Exploiting such auxiliary information can boost statistical power. To this end, we propose a framework based on a two-group mixture model with varying probabilities of being null for different hypotheses a priori, where a shape-constrained relationship is imposed between the auxiliary information and the prior probabilities of being null. An optimal rejection rule is designed to maximize the expected number of true positives when average false discovery rate is controlled. Focusing on the ordered structure, we develop a robust EM algorithm to estimate the prior probabilities of being null and the distribution of p-values under the alternative hypothesis simultaneously. We show that the proposed method has better power than state-of-the-art competitors while controlling the false discovery rate, both empirically and theoretically. Extensive simulations demonstrate the advantage of the proposed method. Datasets from genome-wide association studies are used to illustrate the new methodology.

关键词： EM algorithm false discovery rate isotonic regression local false discovery rate multiple testing pool-adjacent-violators algorithm

来源：评论

学校读者我要写书评

暂无评论

A hierarchical active constraints search algorithm for optimal scaling of ordered categorical responses

引用

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 1995年第3-4期53卷 197-209页

作者： Lin, SP Tang, DI [a] Statistical Sciences and Epidemiology Division Nathan S. Kline Institute for Psychiatric Research Orangeburg New York U S A

We consider the problem of optimally quantifying the categories of an ordered response variable under a linear model. The mathematical formulation leads to the maximization of a ratio of quadratic forms subject to linear inequality constraints. The solution is given by a hierarchical active constraints search algorithm. We prove that the algorithm converges to the global optimum.

关键词： global optimality optimal scores ordered categories pool-adjacent-violators algorithm ratio of quadratic forms

来源：评论

学校读者我要写书评

暂无评论

Bootstrap estimation of the variance of the error term in monotonic regression models

引用

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2013年第4期83卷 625-638页

作者： Sysoev, O. Grimvall, A. Burdakov, O. Linkoping Univ Dept Comp & Informat Sci SE-58183 Linkoping Sweden Linkoping Univ Dept Math SE-58183 Linkoping Sweden

The variance of the error term in ordinary regression models and linear smoothers is usually estimated by adjusting the average squared residual for the trace of the smoothing matrix (the degrees of freedom of the predicted response). However, other types of variance estimators are needed when using monotonic regression (MR) models, which are particularly suitable for estimating response functions with pronounced thresholds. Here, we propose a simple bootstrap estimator to compensate for the over-fitting that occurs when MR models are estimated from empirical data. Furthermore, we show that, in the case of one or two predictors, the performance of this estimator can be enhanced by introducing adjustment factors that take into account the slope of the response function and characteristics of the distribution of the explanatory variables. Extensive simulations show that our estimators perform satisfactorily for a great variety of monotonic functions and error distributions.

关键词： uncertainty estimation bootstrap monotonic regression pool-adjacent-violators algorithm

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：