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1.
Intrinsic Dimensionality Estimation for Highdimensional Data Sets: New Approaches for the Computation of Correlation Dimension
Open Access
Title:
Intrinsic Dimensionality Estimation for Highdimensional Data Sets: New Approaches for the Computation of Correlation Dimension
Author:
Jochen Einbeck
;
Zakiah Kalantana
Jochen Einbeck
;
Zakiah Kalantana
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Description:
The analysis of high–dimensional data is usually challenging since many standard modelling approaches tend to break down due to the so–called “curse of dimensionality”. Dimension reduction techniques, which reduce the data set (explicitly or implicitly) to a smaller number of variables, make the data analysis more efficient and are furthermore u...
The analysis of high–dimensional data is usually challenging since many standard modelling approaches tend to break down due to the so–called “curse of dimensionality”. Dimension reduction techniques, which reduce the data set (explicitly or implicitly) to a smaller number of variables, make the data analysis more efficient and are furthermore useful for visualization purposes. However, most dimension reduction techniques require fixing the intrinsic dimension of the lowdimensional subspace in advance. The intrinsic dimension can be estimated by fractal dimension estimation methods, which exploit the intrinsic geometry of a data set. The most popular concept from this family of methods is the correlation dimension, which requires estimation of the correlation integral for a ball of radius tending to 0. In this paper we propose approaches to approximate the correlation integral in this limit. Experimental results on real world and simulated data are used to demonstrate the algorithms and compare to other methodology. A simulation study which verifies the effectiveness of the proposed methods is also provided.
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Publisher:
ACADEMY PUBLISHER
Year of Publication:
20130501T00:00:00Z
Source:
Journal of Emerging Technologies in Web Intelligence, Vol 5, Iss 2, Pp 9197 (2013)
Journal of Emerging Technologies in Web Intelligence, Vol 5, Iss 2, Pp 9197 (2013)
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Document Type:
article
Language:
English
Subjects:
intrinsic dimensionality ; fractalbased methods ; correlation dimension ; LCC:Science (General) ; LCC:Q1390 ; LCC:Science ; LCC:Q
intrinsic dimensionality ; fractalbased methods ; correlation dimension ; LCC:Science (General) ; LCC:Q1390 ; LCC:Science ; LCC:Q
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DDC:
310 Collections of general statistics
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http://ojs.academypublisher.com/index.php/jetwi/article/view/9970
URL:
http://doaj.org/search?source=%7B%22query%22%3A%7B%22bool%22%3A%7B%22must%22%3A%5B%7B%22term%22%3...
http://doaj.org/search?source=%7B%22query%22%3A%7B%22bool%22%3A%7B%22must%22%3A%5B%7B%22term%22%3...
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Directory of Open Access Journals: DOAJ Articles
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2.
Modelling beyond regression functions: an application of multimodal regression to speedflow data
Title:
Modelling beyond regression functions: an application of multimodal regression to speedflow data
Author:
Jochen Einbeck
;
Gerhard Tutz
Jochen Einbeck
;
Gerhard Tutz
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Description:
For speedflow data, which are intensively discussed in transportation science, common nonparametric regression models of the type "y"="m"("x")+noise turn out to be inadequate since simple functional models cannot capture the essential relationship between the predictor and response. Instead a more general setting is required, allowing for multi...
For speedflow data, which are intensively discussed in transportation science, common nonparametric regression models of the type "y"="m"("x")+noise turn out to be inadequate since simple functional models cannot capture the essential relationship between the predictor and response. Instead a more general setting is required, allowing for multifunctions rather than functions. The tool proposed is conditional modes estimation which, in the form of local modes, yields several branches that correspond to the local modes. A simple algorithm for computing the branches is derived. This is based on a conditional mean shift algorithm and is shown to work well in the application that is considered. Copyright 2006 Royal Statistical Society.
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Document Type:
article
URL:
http://www.blackwellsynergy.com/doi/abs/10.1111/j.14679876.2006.00547.x
http://www.blackwellsynergy.com/doi/abs/10.1111/j.14679876.2006.00547.x
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RePEc: Research Papers in Economics
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3.
LOCAL FITTING WITH A POWER BASIS Authors:
Open Access
Title:
LOCAL FITTING WITH A POWER BASIS Authors:
Author:
Jochen Einbeck
Jochen Einbeck
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Description:
Local polynomial modelling can be seen as a local fit of the data against a polynomial basis. In this paper we extend this method to the power basis, i.e. a basis which consists of the powers of an arbitrary function. Using an extended Taylor theorem, we derive asymptotic expressions for bias and variance of this estimator. We apply this method ...
Local polynomial modelling can be seen as a local fit of the data against a polynomial basis. In this paper we extend this method to the power basis, i.e. a basis which consists of the powers of an arbitrary function. Using an extended Taylor theorem, we derive asymptotic expressions for bias and variance of this estimator. We apply this method to a simulated data set for various basis functions and discuss situations where the fit can be improved by using a suitable basis. Finally, some remarks about bandwidth selection are given and the method is applied to real data. KeyWords: local polynomial fitting; Taylor expansion; power basis; bias reduction.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130720
Source:
http://www.ine.pt/revstat/pdf/rs040201.pdf
http://www.ine.pt/revstat/pdf/rs040201.pdf
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Document Type:
text
Language:
en
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.298.7302
http://www.ine.pt/revstat/pdf/rs040201.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.298.7302
http://www.ine.pt/revstat/pdf/rs040201.pdf
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4.
ON DESIGNWEIGHTED LOCAL FITTING AND ITS RELATION TO THE HORVITZTHOMPSON ESTIMATOR
Open Access
Title:
ON DESIGNWEIGHTED LOCAL FITTING AND ITS RELATION TO THE HORVITZTHOMPSON ESTIMATOR
Author:
Jochen Einbeck
Jochen Einbeck
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Description:
Abstract: Weighting is a widely used concept in many fields of statistics and has frequently caused controversies on its justification and benefit. In this paper, we analyze designweighted versions of the wellknown local polynomial regression estimators, derive their asymptotic bias and variance, and observe that the asymptotically optimal wei...
Abstract: Weighting is a widely used concept in many fields of statistics and has frequently caused controversies on its justification and benefit. In this paper, we analyze designweighted versions of the wellknown local polynomial regression estimators, derive their asymptotic bias and variance, and observe that the asymptotically optimal weights are in conflict with (practically motivated) weighting schemes previously proposed in the literature. We investigate this conflict using theory and simulation, and find that the problem has a surprising counterpart in sampling theory, leading us back to the discussion on the HorvitzThompson estimator and Basu’s (1971) elephants. In this light one might consider our results as an asymptotic and nonparametric version of the HorvitzThompson theorem. The crucial point is that biasminimizing weights can make estimators extremely vulnerable to outliers in the design space and have therefore to be used with particular care. Key words and phrases: Bias reduction, HorvitzThompson estimator, kernel smoothing, leverage values, local polynomial modelling, nonparametric smoothing, stratification.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130813
Source:
http://www.maths.dur.ac.uk/~dma0je/Preprints/dwlf4.pdf
http://www.maths.dur.ac.uk/~dma0je/Preprints/dwlf4.pdf
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Document Type:
text
Language:
en
DDC:
310 Collections of general statistics
(computed)
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Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.325.5781
http://www.maths.dur.ac.uk/~dma0je/Preprints/dwlf4.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.325.5781
http://www.maths.dur.ac.uk/~dma0je/Preprints/dwlf4.pdf
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5.
Modelling beyond Regression Functions: an Application of Multimodal Regression to SpeedFlow Data
Open Access
Title:
Modelling beyond Regression Functions: an Application of Multimodal Regression to SpeedFlow Data
Author:
Jochen Einbeck
;
Gerhard Tutz
;
Ludwig Maximilians Universität
Jochen Einbeck
;
Gerhard Tutz
;
Ludwig Maximilians Universität
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Description:
An enormous amount of publications deals with smoothing in the sense of nonparametric regression. However, nearly all of the literature treats the case where predictors and response are related in the form of a function y = m(x) + noise. In many situations this simple functional model does not capture adequately the essential relation between pr...
An enormous amount of publications deals with smoothing in the sense of nonparametric regression. However, nearly all of the literature treats the case where predictors and response are related in the form of a function y = m(x) + noise. In many situations this simple functional model does not capture adequately the essential relation between predictor and response. We show by means of speedflow diagrams, that a more general setting may be required, allowing for multifunctions instead of only functions. It turns out that in this case the conditional modes are more appropriate for the estimation of the underlying relation than the commonly used mean or the median. Estimation is achieved using a conditional meanshift procedure, which is adapted to the present situation.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130812
Source:
http://www.stat.unimuenchen.de/sfb386/papers/dsp/paper395.pdf
http://www.stat.unimuenchen.de/sfb386/papers/dsp/paper395.pdf
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Document Type:
text
Language:
en
Subjects:
Key Words ; Mean shift ; Conditional density ; Conditional mode ; Speedflow curves
Key Words ; Mean shift ; Conditional density ; Conditional mode ; Speedflow curves
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Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.323.7348
http://www.stat.unimuenchen.de/sfb386/papers/dsp/paper395.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.323.7348
http://www.stat.unimuenchen.de/sfb386/papers/dsp/paper395.pdf
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6.
License GPL (> = 2)
Open Access
Title:
License GPL (> = 2)
Author:
Jochen Einbeck
;
Ludger Evers
;
Lazyload Yes
Jochen Einbeck
;
Ludger Evers
;
Lazyload Yes
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Description:
Description Fitting multivariate data patterns with local principal curves; including simple tools for data compression (projection), bandwidth selection, and measuring goodnessoffit.
Description Fitting multivariate data patterns with local principal curves; including simple tools for data compression (projection), bandwidth selection, and measuring goodnessoffit.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20111113
Source:
http://cran.at.rproject.org/web/packages/LPCM/LPCM.pdf
http://cran.at.rproject.org/web/packages/LPCM/LPCM.pdf
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Document Type:
text
Language:
en
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.204.9194
http://cran.at.rproject.org/web/packages/LPCM/LPCM.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.204.9194
http://cran.at.rproject.org/web/packages/LPCM/LPCM.pdf
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7.
Repository CRAN
Open Access
Title:
Repository CRAN
Author:
Jochen Einbeck
;
Ross Darnell
;
John Hinde
;
Lazyload Yes
;
Needscompilation No
Jochen Einbeck
;
Ross Darnell
;
John Hinde
;
Lazyload Yes
;
Needscompilation No
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Description:
R topics documented: npmlregpackage. 2 alldist. 3 dkern. 10 fabric. 11 family.glmmNPML. 12 gqz. 13 hosp. 14 1 2 npmlregpackage irlsuicide. 15 missouri. 16 plot.glmmNPML. 17 post. 19 predict.glmmNPML. 20
R topics documented: npmlregpackage. 2 alldist. 3 dkern. 10 fabric. 11 family.glmmNPML. 12 gqz. 13 hosp. 14 1 2 npmlregpackage irlsuicide. 15 missouri. 16 plot.glmmNPML. 17 post. 19 predict.glmmNPML. 20
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20141205
Source:
http://cran.us.rproject.org/web/packages/npmlreg/npmlreg.pdf
http://cran.us.rproject.org/web/packages/npmlreg/npmlreg.pdf
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Document Type:
text
Language:
en
Subjects:
This program is free software ; you can redistribute it and/or mo
This program is free software ; you can redistribute it and/or mo
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Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.465.2608
http://cran.us.rproject.org/web/packages/npmlreg/npmlreg.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.465.2608
http://cran.us.rproject.org/web/packages/npmlreg/npmlreg.pdf
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8.
quadrature for overdispersed generalized linear models and variance component models License GPL (> = 2) Repository CRAN
Open Access
Title:
quadrature for overdispersed generalized linear models and variance component models License GPL (> = 2) Repository CRAN
Author:
Jochen Einbeck
;
Ross Darnell
;
John Hinde
;
Lazyload Yes
;
Needscompilation No
Jochen Einbeck
;
Ross Darnell
;
John Hinde
;
Lazyload Yes
;
Needscompilation No
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Description:
R topics documented: npmlregpackage. 2 alldist. 3 dkern. 10 fabric. 11 family.glmmNPML. 12 gqz. 13 hosp. 14 irlsuicide. 15 missouri. 16 1 2 npmlregpackage plot.glmmNPML. 17 post. 19 predict.glmmNPML. 20 summary.glmmNPML. 22 tolfind. 24 weightslogl.calc.w. 26 Index 28 npmlregpackage Nonparametric maximum likelihood estimation for random effect...
R topics documented: npmlregpackage. 2 alldist. 3 dkern. 10 fabric. 11 family.glmmNPML. 12 gqz. 13 hosp. 14 irlsuicide. 15 missouri. 16 1 2 npmlregpackage plot.glmmNPML. 17 post. 19 predict.glmmNPML. 20 summary.glmmNPML. 22 tolfind. 24 weightslogl.calc.w. 26 Index 28 npmlregpackage Nonparametric maximum likelihood estimation for random effect models
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130724
Source:
http://cran.at.rproject.org/web/packages/npmlreg/npmlreg.pdf
http://cran.at.rproject.org/web/packages/npmlreg/npmlreg.pdf
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Document Type:
text
Language:
en
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.1539
http://cran.at.rproject.org/web/packages/npmlreg/npmlreg.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.1539
http://cran.at.rproject.org/web/packages/npmlreg/npmlreg.pdf
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9.
astronomical
Open Access
Title:
astronomical
Author:
Jochen Einbeck
;
Ludger Evers
;
Coryn Bailerjones
Jochen Einbeck
;
Ludger Evers
;
Coryn Bailerjones
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Description:
Representing complex data using localized
Representing complex data using localized
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130817
Source:
http://www.stats.gla.ac.uk/~levers/publications/lpc_gaia.pdf
http://www.stats.gla.ac.uk/~levers/publications/lpc_gaia.pdf
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Document Type:
text
Language:
en
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Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.4361
http://www.stats.gla.ac.uk/~levers/publications/lpc_gaia.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.4361
http://www.stats.gla.ac.uk/~levers/publications/lpc_gaia.pdf
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10.
Representing Complex Data Using Localized Principal Components with Application to Astronomical Data
Open Access
Title:
Representing Complex Data Using Localized Principal Components with Application to Astronomical Data
Author:
Jochen Einbeck
;
Ludger Evers
;
Coryn BailerJones
Jochen Einbeck
;
Ludger Evers
;
Coryn BailerJones
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Description:
Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: “nonlinear”, “branched”, “disconnected”, “bended”, “curved”, “heterogeneous”, or, more general, “complex”. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. ...
Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: “nonlinear”, “branched”, “disconnected”, “bended”, “curved”, “heterogeneous”, or, more general, “complex”. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. Of the many alternative approaches proposed so far, local approximations of PCA are among the most promising. This paper will give a short review of localized versions of PCA, focusing on local principal curves and local partitioning algorithms. Furthermore we discuss projections other than the local principal components. When performing local dimension reduction for regression or classification problems it is important to focus not only on the manifold structure of the covariates, but also on the response variable(s). Local principal components only achieve the former, whereas localized regression approaches concentrate on the latter. Local projection directions derived from the partial least squares (PLS) algorithm offer an interesting tradeoff between these two objectives. We apply these methods to several real data sets. In particular, we consider
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20120228
Source:
http://pca.narod.ru/7MainGorbanKeglWunschZin.pdf
http://pca.narod.ru/7MainGorbanKeglWunschZin.pdf
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Document Type:
text
Language:
en
DDC:
310 Collections of general statistics
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Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.7641
http://pca.narod.ru/7MainGorbanKeglWunschZin.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.7641
http://pca.narod.ru/7MainGorbanKeglWunschZin.pdf
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(31) Einbeck, Jochen
(14) Jochen Einbeck
(10) The Pennsylvania State University CiteSeerX...
(6) Evers, Ludger
(4) Fried, Roland
(4) Gather, Ursula
(4) Tutz, Gerhard
(3) Lazyload Yes
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(3) Needscompilation No
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(2) Ben Oakley
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(2) Gerhard Tutz
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(2) Meintanis, Simos
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(1) BailerJones, Coryn
(1) Bowman, Adrian
(1) Box Cox Transformation
(1) Conesa, David
(1) Coryn BailerJones
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(1) Diva Saldiva de André, C.
(1) Dwyer, Jo
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(1) Einbeck, Jochen.
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(1) Hoad, Dominique
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(1) Kauermann, Göran
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(1) Lawson, Antony
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(1) Ludwig Maximilians Universität
(1) Morgan, Byron J. T.
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(1) Nagy, Stanislav
(1) Newell, John
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(1) Zayed, Mohammad
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(7) ddc 510
(7) sonderforschungsbereich 386
(3) ddc 310
(2) breakdown point
(2) mean shift
(2) outliers
(2) robust regression
(2) signal extraction
(1) astrophysics
(1) bias reduction
(1) bsl1 0
(1) conditional density
(1) conditional mode
(1) correlation dimension
(1) ddc 004
(1) ddc 330
(1) description
(1) fakultät für mathematik
(1) fractal based methods
(1) horvitz thompson theorem
(1) informatik und statistik
(1) intrinsic dimensionality
(1) kernel smoothing leverage values
(1) key words
(1) lazyload yes
(1) lcc q
(1) lcc q1 390
(1) lcc science
(1) lcc science general
(1) local polynomial modelling
(1) local principal curves c
(1) local smoothing
(1) nichtparametrisches verfahren
(1) nonparametric smoothing
(1) principal components
(1) principal curves
(1) qa mathematics
(1) qa mathematics inc computing science
(1) regression
(1) robustes verfahren
(1) sciences de l ingénieur
(1) speed flow curves
(1) stratification
(1) theorie
(1) this program is free software
(1) you can redistribute it and or mo
(1) zeitreihenanalyse
Subject:
Dewey Decimal Classification (DDC)
(8) Statistics [31*]
(1) Computer science, knowledge & systems [00*]
(1) Economics [33*]
(1) Mathematics [51*]
(1) Literature, rhetoric & criticism [80*]
Dewey Decimal Classification (DDC):
Year of Publication
(10) 2013
(5) 2011
(4) 2005
(4) 2012
(4) 2014
(3) 2003
(3) 2004
(3) 2010
(2) 2001
(2) 2002
(1) 2006
(1) 2007
(1) 2008
Year of Publication:
Content Provider
(13) Durham Univ.: Research Online
(10) CiteSeerX
(7) Munich LMU: Open Access
(4) EconStor
(3) RePEc.org
(1) ArXiv.org
(1) DataCite Metadata Store
(1) DOAJ Articles
(1) Kent Univ.
(1) Munich LMU: Digital theses
(1) Glasgow Univ.
(1) WallonieBruxelles Académie Univ.: DIfusion
(1) Dortmund TU: Eldorado
(1) Zenodo
Content Provider:
Language
(29) Unknown
(16) English
(1) Nauru
Language:
Document Type
(14) Article, Journals
(14) Reports, Papers, Lectures
(12) Text
(4) Books
(1) Theses
(1) Software
Document Type:
Access
(29) Unknown
(17) Open Access
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