TY - JOUR
T1 - Estimation and Testing in M-quantile Regression with Applications to Small Area Estimation
AU - Bianchi, Annamaria
AU - Fabrizi, Enrico
AU - Salvati, Nicola
AU - Tzavidis, Nikos
PY - 2018
Y1 - 2018
N2 - In recent years, M-quantile regression has been applied to small area estimation to obtain reliable and outlier robust estimators without recourse to strong parametric assumptions. In this paper, after a review of M-quantile regression and its application to small area estimation, we cover several topics related to model specification and selection for M-quantile regression that received little attention so far. Specifically, a pseudo-R2goodness-of-fit measure is proposed, along with likelihood ratio and Wald type tests for model specification. A test to assess the presence of actual area heterogeneity in the data is also proposed. Finally, we introduce a new estimator of the scale of the regression residuals, motivated by a representation of the M-quantile regression estimation as a regression model with Generalised Asymmetric Least Informative distributed error terms. The Generalised Asymmetric Least Informative distribution, introduced in this paper, generalises the asymmetric Laplace distribution often associated to quantile regression. As the testing procedures discussed in the paper are motivated asymptotically, their finite sample properties are empirically assessed in Monte Carlo simulations. Although the proposed methods apply generally to M-quantile regression, in this paper, their use ar illustrated by means of an application to Small Area Estimation using a well known real dataset.
AB - In recent years, M-quantile regression has been applied to small area estimation to obtain reliable and outlier robust estimators without recourse to strong parametric assumptions. In this paper, after a review of M-quantile regression and its application to small area estimation, we cover several topics related to model specification and selection for M-quantile regression that received little attention so far. Specifically, a pseudo-R2goodness-of-fit measure is proposed, along with likelihood ratio and Wald type tests for model specification. A test to assess the presence of actual area heterogeneity in the data is also proposed. Finally, we introduce a new estimator of the scale of the regression residuals, motivated by a representation of the M-quantile regression estimation as a regression model with Generalised Asymmetric Least Informative distributed error terms. The Generalised Asymmetric Least Informative distribution, introduced in this paper, generalises the asymmetric Laplace distribution often associated to quantile regression. As the testing procedures discussed in the paper are motivated asymptotically, their finite sample properties are empirically assessed in Monte Carlo simulations. Although the proposed methods apply generally to M-quantile regression, in this paper, their use ar illustrated by means of an application to Small Area Estimation using a well known real dataset.
KW - Generalised Asymmetric Least Informative distribution
KW - Goodness-of-fit
KW - Likelihood ratio type test
KW - Loss function
KW - Robust regression
KW - Statistics and Probability
KW - Statistics, Probability and Uncertainty
KW - goodness-of-fit
KW - likelihood ratio type test
KW - loss function
KW - robust regression
KW - Generalised Asymmetric Least Informative distribution
KW - Goodness-of-fit
KW - Likelihood ratio type test
KW - Loss function
KW - Robust regression
KW - Statistics and Probability
KW - Statistics, Probability and Uncertainty
KW - goodness-of-fit
KW - likelihood ratio type test
KW - loss function
KW - robust regression
UR - http://hdl.handle.net/10807/121551
UR - http://www.interscience.wiley.com/jpages/0306-7734
U2 - 10.1111/insr.12267
DO - 10.1111/insr.12267
M3 - Article
SN - 0306-7734
VL - 86
SP - 541
EP - 570
JO - International Statistical Review
JF - International Statistical Review
ER -