Robust estimation of fixed effect parameters and variances of linear mixed models: the minimum density power divergence approach

Many real-life data sets can be analyzed using linear mixed models (LMMs). Since these are ordinarily based on normality assumptions, under small deviations from the model the inference can be highly unstable when the associated parameters are estimated by classical methods. On the other hand, the d...

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Vydáno v:Advances in statistical analysis : AStA : a journal of the German Statistical Society Ročník 108; číslo 1; s. 127 - 157
Hlavní autoři: Saraceno, Giovanni, Ghosh, Abhik, Basu, Ayanendranath, Agostinelli, Claudio
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2024
Springer Nature B.V
Témata:
Asymptotic methods
Datasets
Divergence
Econometrics
Economics
Finance
Influence functions
Insurance
Management
Mathematical models
Mathematics and Statistics
Maximum likelihood estimators
Normality
Optimization
Original Paper
Parameter estimation
Probability density functions
Probability Theory and Stochastic Processes
Robustness
Statistics
Statistics for Business
62G05
Linear mixed models
Minimum density power divergence estimator
Robustness
62G35
ISSN:1863-8171, 1863-818X
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Shrnutí:Many real-life data sets can be analyzed using linear mixed models (LMMs). Since these are ordinarily based on normality assumptions, under small deviations from the model the inference can be highly unstable when the associated parameters are estimated by classical methods. On the other hand, the density power divergence (DPD) family, which measures the discrepancy between two probability density functions, has been successfully used to build robust estimators with high stability associated with minimal loss in efficiency. Here, we develop the minimum DPD estimator (MDPDE) for independent but non-identically distributed observations for LMMs according to the variance components model. We prove that the theoretical properties hold, including consistency and asymptotic normality of the estimators. The influence function and sensitivity measures are computed to explore the robustness properties. As a data-based choice of the MDPDE tuning parameter α is very important, we propose two candidates as “optimal” choices, where optimality is in the sense of choosing the strongest downweighting that is necessary for the particular data set. We conduct a simulation study comparing the proposed MDPDE, for different values of α , with S-estimators, M-estimators and the classical maximum likelihood estimator, considering different levels of contamination. Finally, we illustrate the performance of our proposal on a real-data example.
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ISSN:1863-8171
1863-818X
DOI:10.1007/s10182-023-00473-z