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Title:

Statistical Analysis of Discontinuous . . .

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2013-01-03

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http://edoc.ub.uni-muenchen.de/2334/1/Kempe_Angela.pdf

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text

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en

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Title:

Consistencies and Rates of Convergence of Jump-PenalizedLeast Squares Estimators

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Abstract We study the asymptotics for jump-penalized least squares regression aiming at approx-imating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L2([0, 1)) our results cover other metricslike Skorokhod metric on the space of c`adl`ag functions and uniform met...

Abstract We study the asymptotics for jump-penalized least squares regression aiming at approx-imating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L2([0, 1)) our results cover other metricslike Skorokhod metric on the space of c`adl`ag functions and uniform metrics on C([0, 1]) aswell as convergence of the scale spaces, the family of estimates under varying smoothing parameter. We will show that the estimates used are in an adaptive sense rate optimal overthe class of functions of bounded variation, (piecewise) H"older continuous functions of order 1> = a> 0 and the class of step functions. In the latter setting, we will also deduce therates known from changepoint analysis for detecting the jumps. 1 Introduction We consider regression models of the form Y ni = f ni + xni, (i = 1,., n) (1) where xni are independent zero-mean sub-gaussian random variables and f ni is the mean valueof a square integrable function f 2 L2 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://ibb.gsf.de/preprints/2005/pp05-03.ps

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text

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en

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519 Probabilities & applied mathematics *(computed)*

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Title:

Imitation of binary random textures on the basis of Gaussian numerical models

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We present a method for binary texture synthesis based on thresholds of Gaussian random fields. The method enables us to reproduce the average value and correlation function of the observed texture. The method is comparatively simple, and it seems to be effective for a wide class of random binary textures. In the paper we discuss properties of t...

We present a method for binary texture synthesis based on thresholds of Gaussian random fields. The method enables us to reproduce the average value and correlation function of the observed texture. The method is comparatively simple, and it seems to be effective for a wide class of random binary textures. In the paper we discuss properties of the method and illustrate its performance in the statistically homogeneous and isotropic case. Key words: texture analysis and synthesis, binary texture simulation, numerical modeling of random fields, Gaussian threshold models. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://ibb.gsf.de/preprints/2007/pp07-24.pdf

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text

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en

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Title:

Consistencies and Rates of Convergence of Jump-Penalized Least Squares Estimators

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We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L 2 ([0,1)) our results cover other metrics like Skorokhod metric on the space of càdlàg functions and uniform metrics on C(...

We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L 2 ([0,1)) our results cover other metrics like Skorokhod metric on the space of càdlàg functions and uniform metrics on C([0,1]) as well as convergence of the scale spaces, the family of estimates under varying smoothing parameter. We will show that the estimates used are in an adaptive sense rate optimal over the class of functions of bounded variation, (piecewise) Hölder continuous functions of order 1 ≥ α> 0 and the class of step functions. In the latter setting, we will also deduce the rates known from changepoint analysis for detecting the jumps. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://ibb.gsf.de/preprints/2005/pp05-03.pdf

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text

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en

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Title:

and Mathematical Geophysics ‡

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We propose a new approach for model selection in mathematical statistics that is based not on the probability but on the ‘waiting time ’ of a sample. By waiting time of a sample we understand the average time of the first appearance of the sample in a sequence of independent identically distributed random variables. In the paper we consider a fe...

We propose a new approach for model selection in mathematical statistics that is based not on the probability but on the ‘waiting time ’ of a sample. By waiting time of a sample we understand the average time of the first appearance of the sample in a sequence of independent identically distributed random variables. In the paper we consider a few simple examples to illustrate the main idea and further mathematical problems related to the new approach. Key words: mathematical statistics, sample, model selection. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://ibb.gsf.de/preprints/2005/pp05-18.pdf

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text

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en

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Title:

Parsimonious segmentation of time series’ by Potts models

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Abstract. Typical problems in the analysis of data sets like time-series or images crucially rely on the extraction of primitive features based on segmentation. Variational approaches are a popular and convenient framework in which such problems can be studied. We focus on Potts models as simple nontrivial instances. The discussion proceeds alon...

Abstract. Typical problems in the analysis of data sets like time-series or images crucially rely on the extraction of primitive features based on segmentation. Variational approaches are a popular and convenient framework in which such problems can be studied. We focus on Potts models as simple nontrivial instances. The discussion proceeds along two data sets from brain mapping and functional genomics. 1 Minimize

Publisher:

Springer-Verlag

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-17

Source:

http://ibb.gsf.de/preprints/2003/pp03-03.ps

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text

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en

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Title:

Consistencies and Rates of Convergence of Jump-Penalized Least Squares Estimators

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We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L 2 ([0,1)) our results cover other metrics like Skorokhod metric on the space of càdlàg functions and uniform metrics on C(...

We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L 2 ([0,1)) our results cover other metrics like Skorokhod metric on the space of càdlàg functions and uniform metrics on C([0,1]) as well as convergence of the scale spaces, the family of estimates under varying smoothing parameter. We will show that the estimates used are in an adaptive sense rate optimal over the class of functions of bounded variation, (piecewise) Hölder continuous functions of order 1 ≥ α> 0 and the class of step functions. In the latter setting, we will also deduce the rates known from changepoint analysis for detecting the jumps. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-07

Source:

http://ibb.gsf.de/homepage/volkmar.liebscher/publications/pottsconsistency.pdf

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en

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Title:

Consistencies and Rates of Convergence of Jump-Penalized Least Squares Estimators

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We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L ([0, 1)) our results cover other metrics like Skorokhod metric on the space of c adl ag functions and uniform metrics on C...

We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L ([0, 1)) our results cover other metrics like Skorokhod metric on the space of c adl ag functions and uniform metrics on C([0,1]) as well as convergence of the scale spaces, the family of estimates under varying smoothing parameter. We will show that the estimates used are in an adaptive sense rate optimal over the class of functions of bounded variation, (piecewise) H older continuous functions of order a > 0 and the class of step functions. In the latter setting, we will also deduce the rates known from changepoint analysis for detecting the jumps. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-19

Source:

http://ibb.gsf.de/homepage/volkmar.liebscher/publications/pottsconsistency.ps

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Document Type:

text

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en

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Title:

Parsimonious segmentation of time series’ by Potts models

Author:

Description:

Abstract. Typical problems in the analysis of data sets like time-series or images crucially rely on the extraction of primitive features based on segmentation. Variational approaches are a popular and convenient framework in which such problems can be studied. We focus on Potts models as simple nontrivial instances. The discussion proceeds alon...

Abstract. Typical problems in the analysis of data sets like time-series or images crucially rely on the extraction of primitive features based on segmentation. Variational approaches are a popular and convenient framework in which such problems can be studied. We focus on Potts models as simple nontrivial instances. The discussion proceeds along two data sets from brain mapping and functional genomics. 1 Minimize

Publisher:

Springer-Verlag

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-17

Source:

http://ibb.gsf.de/preprints/2003/pp03-03.pdf

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Document Type:

text

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en

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Title:

Consistencies and rates of convergence of jump-penalized least squares estimators

Author:

Description:

We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L 2 ([0,1)) our results cover other metrics like Skorokhod metric on the space of càdlàg functions and uniform metrics on C(...

We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L 2 ([0,1)) our results cover other metrics like Skorokhod metric on the space of càdlàg functions and uniform metrics on C([0,1]). We will show that these estimators are in an adaptive sense rate optimal over certain classes of “approximation spaces.” Special cases are the class of functions of bounded variation (piecewise) Hölder continuous functions of order 0 < α ≤ 1 and the class of step functions with a finite but arbitrary number of jumps. In the latter setting, we will also deduce the rates known from change-point analysis for detecting the jumps. Finally, the issue of fully automatic selection of the smoothing parameter is addressed. 1. Introduction. We Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-26

Source:

http://arxiv.org/pdf/0902.4838v1.pdf

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en

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