Quantile regression for longitudinal data with controlled within-individual variance
Abstract
The presence of heteroscedasticity in data can often throw statistical modeling into dis-
array. In the context of mixed models and longitudinal data, this paper directly addresses
this problem. We develop a quantile estimator based on the asymmetric Laplace distribu-
tion, which explains the heteroscedasticity between different groups of data. In addition to
developing this new model, our paper establishes the good asymptotic properties of this es-
timator under minimal assumptions on the data and verifies them using simulations. Instead
of improving performance point by point, our model focuses on the correct representation
of data dispersion. Using the permissive formalism of the asymmetric Laplace distribution,
we demonstrate the asymptotic properties of a class of estimators defined by a generalized
optimization problem inspired by maximum likelihood. A Ridge penalization is proposed to
address problems of variability overestimation. More generally, this paper presents a model
for handling volume estimation problems more accurately. An application to the diet diver-
sity of coral reef fish is proposed through the representation of isotopic niche sizes.
Keywords: Asymmetric Laplace Distribution, Linear Quantile Mixed Models, Gaussian Quadra-
ture, Ridge Regression, Penalized Linear Quantile Mixed Models
Domains
Statistics [math.ST]
Origin : Files produced by the author(s)