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A small sample estimator for a polynomial regression with errors in the variables

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article

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Title:

Fitting a Finite Mixture Distribution to a Variable Subject to Heteroscedastic Measurement Error

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We consider the case where a latent variable X cannot be observed directly and instead a variable W = X + U with an heteroscedastic measurement error U is observed. It is assumed that the distribution of the true variable X is a mixture of normals and a type of the EM algorithm is applied to nd approximate ML estimates of the distribution parame...

We consider the case where a latent variable X cannot be observed directly and instead a variable W = X + U with an heteroscedastic measurement error U is observed. It is assumed that the distribution of the true variable X is a mixture of normals and a type of the EM algorithm is applied to nd approximate ML estimates of the distribution parameters of X. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-02-03

Source:

http://epub.ub.uni-muenchen.de/1445/1/paper_48.pdf

http://epub.ub.uni-muenchen.de/1445/1/paper_48.pdf Minimize

Document Type:

text

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en

Subjects:

Measurement error � EM algorithm � Finite mixture distribution

Measurement error � EM algorithm � Finite mixture distribution Minimize

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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. Minimize

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Title:

Extreme value analysis of Munich air pollution data

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We present three different approaches to model extreme values of daily air pollution data. We fitted a generalized extreme value distribution to the monthly maxima of daily concentration measures. For the exceedances of a high threshold depending on the data the parameters of the generalized Pareto distribution were estimated. Accounting for aut...

We present three different approaches to model extreme values of daily air pollution data. We fitted a generalized extreme value distribution to the monthly maxima of daily concentration measures. For the exceedances of a high threshold depending on the data the parameters of the generalized Pareto distribution were estimated. Accounting for autocorrelation clusters of exceedances were used. To get information about the relationship of the exceedance of the air quality standard and possible predictors we applied logistic regression. Results and their interpretation are given for daily average concentrations of O 3 and of NO 2 at two monitoring sites within the city of Munich. Keywords: air pollution, extreme values, generalized extreme value distribution, generalized Pareto distribution, logistic regression. 1 Introduction Peak concentrations of single air pollutants are of particular interest in the determination of the air quality. Extreme concentrations of harmful atmosph. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-14

Source:

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper04.ps.Z

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper04.ps.Z Minimize

Document Type:

text

Language:

en

Subjects:

air pollution ; extreme values ; generalized extreme value distribution ; generalized Pareto distribution ; logistic regression

air pollution ; extreme values ; generalized extreme value distribution ; generalized Pareto distribution ; logistic regression Minimize

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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. Minimize

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Title:

Modelling Count Data with Heteroscedastic Measurement Error in the Covariates

Description:

This paper is concerned with the estimation of the regression coefficients for a count data model when one of the explanatory variables is subject to heteroscedastic measurement error. The observed values W are related to the true regressor X by the additive error model W=X+U. The errors U are assumed to be normally distributed with zero mean bu...

This paper is concerned with the estimation of the regression coefficients for a count data model when one of the explanatory variables is subject to heteroscedastic measurement error. The observed values W are related to the true regressor X by the additive error model W=X+U. The errors U are assumed to be normally distributed with zero mean but heteroscedastic variances, which are known or can be estimated from repeated measurements. Inference is done by using quasi likelihood methods, where a model of the observed data is specified only through a mean and a variance function for the response Y given W and other correctly observed covariates. Although this approach weakens the assumption of a parametric regression model, there is still the need to determine the marginal distribution of the unobserved variable X, which is treated as a random variable. Provided appropriate functions for the mean and variance are stated, the regression parameters can be estimated consistently. We illust. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

Source:

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper58.ps.Z

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper58.ps.Z Minimize

Document Type:

text

Language:

en

Subjects:

measurement error ; quasi likelihood ; Poisson regression ; radon data

measurement error ; quasi likelihood ; Poisson regression ; radon data Minimize

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. Minimize

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Title:

Fitting a Finite Mixture Distribution to a Variable Subject to Heteroscedastic Measurement Error

Description:

We consider the case where a latent variable X cannot be observed directly and instead a variable W = X +U with an heteroscedastic measurement error U is observed. It is assumed that the distribution of the true variable X is a mixture of normals and a type of the EM algorithm is applied to find approximate ML estimates of the distribution param...

We consider the case where a latent variable X cannot be observed directly and instead a variable W = X +U with an heteroscedastic measurement error U is observed. It is assumed that the distribution of the true variable X is a mixture of normals and a type of the EM algorithm is applied to find approximate ML estimates of the distribution parameters of X . Keywords: Measurement error; EM algorithm; Finite mixture distribution 1 Introduction It is well known that measurement errors in the covariates of a regression model lead to biased parameter estimates. Most likelihood based methods that adjust for this effect treat the true predictor X as a stochastic variable and require an assumption about the marginal distribution of X, see e.g. Carroll, Ruppert and Stefanski (1995). Usually an unimodal distribution is assumed and without external knowledge its parameters have to be estimated from the observed data. But if the observations suggest that the underlying statistical population of . Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

Source:

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper48.ps.Z

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper48.ps.Z Minimize

Document Type:

text

Language:

en

Subjects:

Measurement error ; EM algorithm ; Finite mixture distribution

Measurement error ; EM algorithm ; Finite mixture distribution Minimize

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310 Collections of general statistics *(computed)*

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Title:

Different Nonlinear Regression Models with Incorrectly Observed Covariates

Description:

We present quasi-likelihood models for different regression problems when one of the explanatory variables is measured with heteroscedastic error. In order to derive models for the observed data the conditional mean and variance functions of the regression models are only expressed through functions of the observable covariates. The latent covar...

We present quasi-likelihood models for different regression problems when one of the explanatory variables is measured with heteroscedastic error. In order to derive models for the observed data the conditional mean and variance functions of the regression models are only expressed through functions of the observable covariates. The latent covariable is treated as a random variable that follows a normal distribution. Furthermore it is assumed that enough additional information is provided to estimate the individual measurement error variances, e.g. through replicated measurements of the fallible predictor variable. The discussion includes the polynomial regression model as well as the probit and logit model for binary data, the Poisson model for count data and ordinal regression models. Keywords: heteroscedastic measurement error, quasi-likelihood, polynomial regression, Poisson model, binary regression models, ordinal regression models 1 Introduction It is a familiar situation for pr. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

Source:

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper68.ps.Z

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper68.ps.Z Minimize

Document Type:

text

Language:

en

Subjects:

heteroscedastic measurement error ; quasi-likelihood ; polynomial regression ; Poisson model

heteroscedastic measurement error ; quasi-likelihood ; polynomial regression ; Poisson model Minimize

DDC:

310 Collections of general statistics *(computed)* ; 519 Probabilities & applied mathematics *(computed)*

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Title:

Fitting a Finite Mixture Distribution to a Variable Subject to Heteroscedastic Measurement Error

Description:

We consider the case where a latent variable X cannot be observed directly and instead a variable W=X+U with an heteroscedastic measurement error U is observed. It is assumed that the distribution of the true variable X is a mixture of normals and a type of the EM algorithm is applied to find approximate ML estimates of the distribution paramete...

We consider the case where a latent variable X cannot be observed directly and instead a variable W=X+U with an heteroscedastic measurement error U is observed. It is assumed that the distribution of the true variable X is a mixture of normals and a type of the EM algorithm is applied to find approximate ML estimates of the distribution parameters of X. Minimize

Year of Publication:

1996-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

Relations:

http://epub.ub.uni-muenchen.de/1445/1/paper_48.pdf ; Thamerus, Markus (1996): Fitting a Finite Mixture Distribution to a Variable Subject to Heteroscedastic Measurement Error. Sonderforschungsbereich 386, Discussion Paper 48

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Title:

Modelling Count Data with Heteroscedastic Measurement Error in the Covariates

Description:

This paper is concerned with the estimation of the regression coefficients for a count data model when one of the explanatory variables is subject to heteroscedastic measurement error. The observed values W are related to the true regressor X by the additive error model W=X+U. The errors U are assumed to be normally distributed with zero mean bu...

This paper is concerned with the estimation of the regression coefficients for a count data model when one of the explanatory variables is subject to heteroscedastic measurement error. The observed values W are related to the true regressor X by the additive error model W=X+U. The errors U are assumed to be normally distributed with zero mean but heteroscedastic variances, which are known or can be estimated from repeated measurements. Inference is done by using quasi likelihood methods, where a model of the observed data is specified only through a mean and a variance function for the response Y given W and other correctly observed covariates. Although this approach weakens the assumption of a parametric regression model, there is still the need to determine the marginal distribution of the unobserved variable X, which is treated as a random variable. Provided appropriate functions for the mean and variance are stated, the regression parameters can be estimated consistently. We illustrate our methods through an analysis of lung cancer rates in Switzerland. One of the covariates, the regional radon averages, cannot be measured exactly due to the strong dependency of radon on geological conditions and various other environmental sources of influence. The distribution of the unobserved true radon measure is modelled as a finite mixture of normals. Minimize

Year of Publication:

1997-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

DDC:

310 Collections of general statistics *(computed)*

Relations:

http://epub.ub.uni-muenchen.de/1452/1/paper_58.pdf ; Thamerus, Markus (1997): Modelling Count Data with Heteroscedastic Measurement Error in the Covariates. Sonderforschungsbereich 386, Discussion Paper 58

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Title:

Different Nonlinear Regression Models with Incorrectly Observed Covariates

Description:

We present quasi-likelihood models for different regression problems when one of the explanatory variables is measured with heteroscedastic error. In order to derive models for the observed data the conditional mean and variance functions of the regression models are only expressed through functions of the observable covariates. The latent covar...

We present quasi-likelihood models for different regression problems when one of the explanatory variables is measured with heteroscedastic error. In order to derive models for the observed data the conditional mean and variance functions of the regression models are only expressed through functions of the observable covariates. The latent covariable is treated as a random variable that follows a normal distribution. Furthermore it is assumed that enough additional information is provided to estimate the individual measurement error variances, e.g. through replicated measurements of the fallible predictor variable. The discussion includes the polynomial regression model as well as the probit and logit model for binary data, the Poisson model for count data and ordinal regression models. Minimize

Year of Publication:

1997-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

Relations:

http://epub.ub.uni-muenchen.de/1462/1/paper_68.pdf ; Thamerus, Markus (1997): Different Nonlinear Regression Models with Incorrectly Observed Covariates. Sonderforschungsbereich 386, Discussion Paper 68

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Title:

Extreme value analysis of Munich airpollution data

Author:

Description:

We present three different approaches to model extreme values of daily air pollution data. We fitted a generalized extreme value distribution to the monthly maxima of daily concentration measures. For the exceedances of a high threshold depending on the data the parameters of the generalized Pareto distribution were estimated. Accounting for aut...

We present three different approaches to model extreme values of daily air pollution data. We fitted a generalized extreme value distribution to the monthly maxima of daily concentration measures. For the exceedances of a high threshold depending on the data the parameters of the generalized Pareto distribution were estimated. Accounting for autocorrelation clusters of exceedances were used. To get information about the relationship of the exceedance of the air quality standard and possible predictors we applied logistic regression. Results and their interpretation are given for daily average concentrations of ozone and of nitrogendioxid at two monitoring sites within the city of Munich. Minimize

Year of Publication:

1995-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

Relations:

http://epub.ub.uni-muenchen.de/1408/1/paper_04.pdf ; Küchenhoff, Helmut und Thamerus, Markus (1995): Extreme value analysis of Munich airpollution data. Sonderforschungsbereich 386, Discussion Paper 4

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