On the Polynomial Measurement Error Model

This paper discusses point estimation of the coefficients of polynomial measurement error (errors-in-variables) models. This includes functional and structural models. The connection between these models and total least squares (TLS) is also examined. A compendium of existing as well as new results is presented

Extreme value analysis of Munich air pollution data

Three different approaches are presented to model extreme values of is fitted daily airpollution data. A generalized extreme values 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. To get information about the relationship of the exceedance of the air quality standard and possible predictors logistic regression is applied. 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. (orig.)Available from TIB Hannover: RR 6137(4) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Three estimators for the poisson regression model with measurement errors

Poisson regression model, measurement errors, corrected score estimator, structural quasi score estimator, naive estimator,

Different nonlinear regression models with incorrectly observed covariates

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. (orig.)Available from TIB Hannover: RR 6137(68) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Fitting a finite mixture distribution to a variable subject to heteroscedastic measurement error

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 distrubution parameters of X. (orig.)Available from TIB Hannover: RR 6137(48) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Fitting a finite mixture distribution to a variable subject to heteroscedastic measurement error

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 distrubution parameters of X. (orig.)Available from TIB Hannover: RR 6137(48) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

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

An adjusted least squares estimator, introduced by Cheng and Schneeweiss (1998) for consistently estimating a polynomial regression of any degree with errors in the variables, is modified such that it shows good results in small samples without losing its asymptotic properties for large samples. Simulation studies corroborate the theoretical findings. The new method is applied to analyse a geophysical law relating the depth of earthquakes to their distance from a trench where one of the earth's plates is submerged beneath another one. (orig.)Available from TIB Hannover: RR 6137(113) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman