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Asymptotic Properties and Variance Estimators of the M-quantile Regression Coefficients Estimators

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  • Annamaria Bianchi
  • Nicola Salvati

Abstract

M-quantile regression is defined as a “quantile-like” generalization of robust regression based on influence functions. This article outlines asymptotic properties for the M-quantile regression coefficients estimators in the case of i.i.d. data with stochastic regressors, paying attention to adjustments due to the first-step scale estimation. A variance estimator of the M-quantile regression coefficients based on the sandwich approach is proposed. Empirical results show that this estimator appears to perform well under different simulated scenarios. The sandwich estimator is applied in the small area estimation context for the estimation of the mean squared error of an estimator for the small area means. The results obtained improve previous findings, especially in the case of heteroskedastic data.

Suggested Citation

  • Annamaria Bianchi & Nicola Salvati, 2015. "Asymptotic Properties and Variance Estimators of the M-quantile Regression Coefficients Estimators," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(11), pages 2416-2429, June.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:11:p:2416-2429
    DOI: 10.1080/03610926.2013.791375
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    Cited by:

    1. Otto-Sobotka, Fabian & Salvati, Nicola & Ranalli, Maria Giovanna & Kneib, Thomas, 2019. "Adaptive semiparametric M-quantile regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 116-129.
    2. Marco Alfò & Maria Francesca Marino & Maria Giovanna Ranalli & Nicola Salvati & Nikos Tzavidis, 2021. "M‐quantile regression for multivariate longitudinal data with an application to the Millennium Cohort Study," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 122-146, January.
    3. Ranjbar, Setareh & Salvati, Nicola & Pacini, Barbara, 2023. "Estimating heterogeneous causal effects in observational studies using small area predictors," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    4. Merlo, Luca & Petrella, Lea & Salvati, Nicola & Tzavidis, Nikos, 2022. "Marginal M-quantile regression for multivariate dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).

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