Optimal Bias Bounds for Robust Estimation in Linear Models

AbstractA common goal of epidemiologic research is to study the association between a certain exposure and a certain outcome, while controlling for important covariates. This is often done by fitting a restricted mean model for the outcome, as in generalized linear models (GLMs) and in generalized estimating equations (GEEs). If the covariates are high-dimensional, then it may be difficult to well specify the model. This is an important concern, since model misspecification may lead to biased estimates. Doubly robust estimation is an estimation technique that offers some protection against model misspecification. It utilizes two models, one for the outcome and one for the exposure, and produces unbiased estimates of the exposure-outcome association if either model is correct, not necessarily both. Despite its obvious appeal, doubly robust estimation is not used on a regular basis in applied epidemiologic research. One reason for this could be the lack of up-to-date software. In this paper we describe a new

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Robust estimation in generalized linear models: the density power divergence approach

Test ◽

10.1007/s11749-015-0445-3 ◽

2015 ◽

Vol 25 (2) ◽

pp. 269-290 ◽

Cited By ~ 18

Author(s):

Abhik Ghosh ◽

Ayanendranath Basu

Keyword(s):

Robust Estimation ◽

Generalized Linear Models ◽

Linear Models ◽

Density Power Divergence ◽

Power Divergence

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Robust estimation of partially linear models for longitudinal data with dropouts and measurement error

Statistics in Medicine ◽

10.1002/sim.7062 ◽

2016 ◽

Vol 35 (29) ◽

pp. 5401-5416 ◽

Cited By ~ 3

Author(s):

Guoyou Qin ◽

Jiajia Zhang ◽

Zhongyi Zhu ◽

Wing Fung

Keyword(s):

Measurement Error ◽

Longitudinal Data ◽

Robust Estimation ◽

Linear Models ◽

Partially Linear Models ◽

Partially Linear

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On Outliers and Interventions in Count Time Series following GLMs

Austrian Journal of Statistics ◽

10.17713/ajs.v43i3.30 ◽

2014 ◽

Vol 43 (3) ◽

pp. 181-193 ◽

Cited By ~ 7

Author(s):

Roland Fried ◽

Tobias Liboschik ◽

Hanan Elsaied ◽

Stella Kitromilidou ◽

Konstantinos Fokianos

Keyword(s):

Time Series ◽

Parameter Estimation ◽

Robust Estimation ◽

Linear Models ◽

Sequential Testing ◽

Generalised Linear Models ◽

Count Time Series ◽

Different Types ◽

Robust Parameter ◽

Robust Parameter Estimation

We discuss the analysis of count time series following generalised linear models in the presence of outliers and intervention effects. Different modifications of such models are formulated which allow to incorporate, detect and to a certain degree distinguish extraordinary events (interventions) of different types in count time series retrospectively. An outlook on extensions to the problem of robust parameter estimation, identification of the model orders by robust estimation of autocorrelations and partial autocorrelations, and online surveillance by sequential testing for outlyingness is provided.

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