Ditulis oleh dhin di/pada 27 April 2009
Applied Nonparametric Regression
Wolfgang Hardle
Humboldt-Universitat zu Berlin
Wirtschaftswissenschaftliche Fakultat
Institut fur Statistik und Okonometrie
Spandauer Str. 1
D{10178 Berlin1994}
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Applied Nonparametric Regression
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Ditulis oleh dhin di/pada 27 April 2009
Nonparametric Bayesian Data Analysis.
Peter Muller Fernando A. Quintana
Abstract
We review the current state of nonparametric Bayesian inference. The discussion follows a list of important statistical inference problems, including density estimation, regression, survival analysis, hierarchical models and model validation. For each inference problem we review relevant nonparametric Bayesian models and approaches including Dirichlet process (DP) models and variations, Polya trees, wavelet based models, neural network models, spline regression, CART, dependent DP models, and model validation with DP and Polya tree extensions of parametric models.
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Nonparametric Bayesian Data Analysis
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Ditulis oleh dhin di/pada 27 April 2009
Kajian Teori Regresi Parametrik Normal dan Regresi Non Parametrik
(Theory Presentation of Normal Parametric Regression and
Nonparametric Regression)
Yulia, S1, IM Tirta2 dan Rita Ratih T2
1Mahasiswa Jurusan Matematika FMIPA Universitas Jember
2Staf Pengajar Jurusan Matematika FMIPA Universitas Jember
ABSTRAK
In this paper, observation of the analysis normal parametric regression by least square method and non parametric regression by Theil method. Tulisan ini mempelajari atau mengkaji analisis regresi parametrik dengan menggunakan metode kuadarat terkecil dan Regresi Non parametrik dengan menggunakan metode Theil. Hasil kajian teoritis diilustrasikan dengan menggunakan data simulasi. Hasil analisis menunjukkan bahwa untuk data yang diketahui bentuk distribusinya, uji parametrik dengan menggunakan metode kudarta terkecil memberikan hasil yang sedikit lebih baik daripada uji non parametrik dengan metode theil.
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Kajian Teori Regresi Parametrik Normal dan Regresi Non Parametrik
(Theory Presentation of Normal Parametric Regression and
Nonparametric Regression)
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Ditulis oleh dhin di/pada 26 April 2009
About Regression Estimators
with High Breakdown Point
Vandev, D.L.
Inst. of Mathematics., Bulg. Acad. Sciences,
P.O.Box 373,1113 Sofia, Bulgaria
and Neykov, N.M. 1
Inst. of Meteorology and Hydrology, Bulg. Acad.Sciences,
66 Tsarigradsko chaussee, 1784 Sofia, Bulgaria
Abstract
A generalisation of a theorem by Vandev (1993) concerning the finite sample breakdown point is given. Using this result the breakdown point properties of the LMS and LTS estimators of Rousseeuw (1984) and the rank-based regression estimator of Hossjer (1994) are studied. Moreover, the breakdown point properties of the weighted least trimmed estimators of order k in the case of grouped logistic regression are investigated, as well as linear regression with an exponential q-th power distribution. 1991 Mathematics Subject Classification: Primary 62J05; Secondary 62F35. Keywords: Breakdown point, Least Median of Squares, Least Trimmed Squares, Modified maximum likelihood, R-estimators, Robust regression estimators, Logistic regression
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About Regression Estimators with High Breakdown Point
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Ditulis oleh dhin di/pada 26 April 2009
High Breakdown Point Multivariate M-Estimation
D. E. Tyler
1 Department of Statistics
Hill Center, Busch Campus
Rutgers, The State University of New Jersey
110 Frelinghuysen Road
Piscataway, NJ 08854-8019
Abstract:
In this talk, a general study of the properties of the M-estimates of multivariate location and scatter with auxiliary scale proposed in Tatsuoka and Tyler (2000) is presented. This study provides a unifying treatment for some of the high breakdown point methods develop for multivariate statistics, as well as a unifying framework for comparing these methods. The multivariate M-estimates with auxiliary scale include as special cases the minimum volume ellipsoid estimates [Rousseeuw (1985)], the multivariate S-estimates [Davies (1987)], the multivariate constrained M-estimates [Kent and Tyler (1996)], and the recently introduced multivariate MM-estimates [Tatsuoka and Tyler (2000)]. The results obtained for the multivariate MM-estimates, such as its breakdown point, its inuence function and its asymptotic distribution, are entirely new. The breakdown points of the M-estimates of multivariate location and scatter for _xed scale are also derived. This generalizes the results on the breakdown points of the univariate redescending M-estimates of location with fixed scale given by Huber (1984).
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High Breakdown Point Multivariate M-Estimation
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Ditulis oleh dhin di/pada 26 April 2009
High Breakdown Estimation Methods for
Phase I Multivariate Control Charts
Willis A. Jensen, Jeffrey B. Birch, and William H. Woodall
Abstract
The goal of Phase I monitoring of multivariate data is to identify multivariate outliers and step changes so that the estimated control limits are sufficiently accurate for Phase II monitoring. High breakdown estimation methods based on the minimum volume ellipsoid (MVE) or the minimum covariance determinant (MCD) are well suited to detecting multivariate outliers in data. However, they are difficult to implement in practice due to the extensive computation required to obtain the estimates. Based on previous studies, it is not clear which of these two estimation methods is best for control chart applications. The comprehensive simulation study here gives guidance for when to use which estimator, and control limits are provided. High breakdown estimation methods such as MCD and MVE, can be applied to a wide variety of multivariate quality control data.
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High Breakdown Estimation Methods for Phase I Multivariate Control Charts
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Ditulis oleh dhin di/pada 26 April 2009
Fast algorithms fo r computing high breakdown
covariance matrices with missing data
Samuel Copt and Maria-Pia Victoria-Feser
No 2003.04
Abstract
Robust estimation of covariance matrices when some of the data at hand are missing is an important problem. It has been studied by Little and Smith (1987) and more recently by Cheng and Victoria-Feser (2002). The latter propose the use of high breakdown estimators and so-called hybrid algorithms (see e.g. Woodruff and Rocke 1994). In particular, the minimum volume ellipsoid of Rousseeuw (1984) is adapted to the case of missing data. To compute it, they use (a modified version of) the forward search algorithm (see e.g. Atkinson 1994). In this paper, we propose to use instead a modification of the C-step algorithm proposed by Rousseeuw and Van Driessen (1999) which is actually a lot faster. We also adapt the orthogonalized Gnanadesikan-Kettering (OGK) estimator proposed by Maronna and Zamar (2002) to the case of missing data and use it as a starting point for an adapted Sestimator. Moreover, we conduct a simulation study to compare different robust estimators in terms of their efficiency and breakdown and use them to analyse real datasets.
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Fast algorithms fo r computing high breakdown
covariance matrices with missing data
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Ditulis oleh dhin di/pada 26 April 2009
Breakdown points of trimmed likelihood estimators and related estimators
in generalized linear models
By CHRISTINE H. MULLER and NEYKO NEYKOV March 2001
Summary
Lower bounds for breakdown points of trimmed likelihood (TL) estimators in a general setup are expressed by the fullness parameter of Vandev (1993), where results of Vandev and Neykov (1998) are extended. A special application of the general result are the breakdown points of TL estimators and related estimators as the S estimators in generalized linear models. For the generalized linear models, a connection between the fullness parameter and the quantity N(X) of Muller (1995) is derived for the case that the explanatory variables may be not in general position which happens in particular in designed experiments. These results are in particular applied to logistic regression and log-linear models where also upper bounds for the breakdown points are derived.
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Breakdown points of trimmed likelihood estimators and related estimators
in generalized linear models
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Ditulis oleh dhin di/pada 26 April 2009
Breakdown Point Theory Notes
Charles J. Geyer
February 2, 2006
Introduction
These are class notes for Stat 5601 (nonparametrics) taught at the University of Minnesota, Spring 2006. This not a theory course, so the bit of theory we do here is very simple, but very important. Without some notion of robustness we have no way to say why nonparametrics is a good idea, or, at least, no quantitative way. We could say (and
sometimes do say) that the assumptions for the sign test are weaker than the assumptions for the signed rank test, which in turn are weaker than the assumptions for Student’s t test. But what does that say? We know that no data are exactly normal, so
either no one should ever use Student’s t test or one should use Student’s t test so long as the population distribution isn’t too non-normal but what does the latter statement mean? What is too non-normal when we have no way to quantitate non-normality?
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Breakdown Point Theory Notes
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