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Monotone support vector quantile regression
Communications in Statistics - Theory and Methods, 2016ABSTRACTQuantile regression (QR) models have received a great deal of attention in both the theoretical and applied statistical literature. In this paper we propose support vector quantile regression (SVQR) with monotonicity restriction, which is easily obtained via the dual formulation of the optimization problem.
Jooyong Shim +2 more
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Generalized smooth monotonic regression
2005Common approaches to monotonic regression focus on the case of a unidimensional covariate and continuous dependent variable. Here a general approach is proposed that allows for additive and multiplicative structures where one or more variables have monotone influence on the dependent variable.
Tutz, Gerhard, Leitenstorfer, Florian
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Non-Euclidean locally monotonic regression
International Conference on Acoustics, Speech, and Signal Processing, 2002The concept of locally monotonic regression is extended by considering metrics on r/sup n/ that are different from the Euclidean metric. The existence of regressions for a large class of metrics is shown. Algorithms that show the computability of locally monotonic regressions are given.
A. Retrepo, I.W. Sandberg, A.C. Bovik
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The Reduced Monotonic Regression Method
Journal of the American Statistical Association, 1997Abstract Medical researchers often desire to categorize patients into monotonic response groups based on the relationship between continuous variables. Isotonic regression fits consist of level sets of increasing value, for which the estimated response is constant. However, the number of level sets obtained is often large, preventing simple description.
Michael J. Schell, Bahadur Singh
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A Method for Bayesian Monotonic Multiple Regression
Scandinavian Journal of Statistics, 2010Abstract. When applicable, an assumed monotonicity property of the regression function w.r.t. covariates has a strong stabilizing effect on the estimates. Because of this, other parametric or structural assumptions may not be needed at all. Although monotonic regression in one dimension is well studied, the question remains whether one can find ...
Saarela, Olli, Arjas, Elja
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2010
In some applications, we require a monotone estimate of a regression function. In others, we want to test whether the regression function is monotone. For solving the first problem, Ramsay's, Kelly and Rice's, as well as point-wise monotone regression functions in a spline space are discussed and their properties developed. Three monotone estimates are
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In some applications, we require a monotone estimate of a regression function. In others, we want to test whether the regression function is monotone. For solving the first problem, Ramsay's, Kelly and Rice's, as well as point-wise monotone regression functions in a spline space are discussed and their properties developed. Three monotone estimates are
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Monotone Regression: Continuity and Differentiability Properties
Psychometrika, 1971Least-squares monotone regression has received considerable discussion and use. Consider the residual sum of squares Q obtained from the least-squares monotone regression of yi on xi. Treating Q as a function of the yi, we prove that the gradient ▽Q exists and is continuous everywhere, and is given by a simple formula.
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Inverse boosting for monotone regression functions
Computational Statistics & Data Analysis, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kim, Yuwon, Koo, Ja-Yong
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Statistical optimality of locally monotonic regression
SPIE Proceedings, 1990We derive the maximum likelihood (ML) estimators for estimating locally monotonic signals embedded in white additive noise, when the noise is assumed to have a density function that is a member of a family of generalized exponential densities with parameter p that includes the Laplacian (p = 1), Gaussian (p = 2) and, as a limiting case, the uniform (p =
Alfredo Restrepo, Alan C. Bovik
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Spline estimation of generalised monotonic regression
Journal of Nonparametric Statistics, 2014We develop a simple and practical, yet flexible spline estimation method for semiparametric generalised linear models with monotonicity constraints. We propose to approximate the unknown monotone function by monotone B-splines, and employ generalised Rosen algorithm to compute the estimates.
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