A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo‐observations
Autor: | Martin Jacobsen, Torben Martinussen |
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Rok vydání: | 2016 |
Předmět: |
Statistics and Probability
Generalized linear model Minor (linear algebra) Estimator Regression analysis Function (mathematics) 01 natural sciences Term (time) 010104 statistics & probability 03 medical and health sciences 0302 clinical medicine Standard error Statistics Applied mathematics 030212 general & internal medicine 0101 mathematics Statistics Probability and Uncertainty Generalized estimating equation Mathematics |
Zdroj: | Scandinavian Journal of Statistics. 43:845-862 |
ISSN: | 1467-9469 0303-6898 |
Popis: | Pseudo-values have proven very useful in censored data analysis in complex settings such as multi-state models. It was originally suggested by Andersen et al., Biometrika, 90, 2003, 335 who also suggested to estimate standard errors using classical generalized estimating equation results. These results were studied more formally in Graw et al., Lifetime Data Anal., 15, 2009, 241 that derived some key results based on a second-order von Mises expansion. However, results concerning large sample properties of estimates based on regression models for pseudo-values still seem unclear. In this paper, we study these large sample properties in the simple setting of survival probabilities and show that the estimating function can be written as a U-statistic of second order giving rise to an additional term that does not vanish asymptotically. We further show that previously advocated standard error estimates will typically be too large, although in many practical applications the difference will be of minor importance. We show how to estimate correctly the variability of the estimator. This is further studied in some simulation studies. |
Databáze: | OpenAIRE |
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