2026-09-20T18:53:05Zhttps://iris.unica.it/oai/requestoai:iris.unica.it:11584/2665872022-10-18T11:30:03Zcom_11584_207615com_11584_111066col_11584_265854
Parametric modeling of dependence of bivariate quantile regression residuals' signs
COLUMBU, SILVIA
bivariate
bivariato
dependence structure
dipendenza del segno dei residui
quantic regression
regressione quantica
residual signs dependence
struttura di dipendenza
Settore SECS-S/01 - Statistica
In this thesis, we propose a non-parametric method to study the dependence of the
quantiles of a multivariate response conditional on a set of covariates. We define a
statistic that measures the conditional probability of concordance of the signs of the
residuals of the conditional quantiles of each univariate response. The probability
of concordance is bounded from below by the value of largest possible negative
dependence and from above by that of largest possible positive dependence. The
value corresponding to the case of independence is contained in the interior of that
interval. We recommend two distinct regression methods to model the conditional
probability of concordance. The first is a logistic regression with a logit link modified.
The second one is a nonlinear regression method, where the outcome is modeled as
a polynomial function of the linear predictor. Both are conceived to constrain the
predicted probabilities to lie within the feasible range. The estimated probabilities
can be tested against the values of largest possible dependence and independence.
The method permits to capture important aspects of the dependence of multivariate
responses and assess possible effects of covariates on such dependence. We use data
on pulmonary disfunctions to illustrate the potential of the proposed method. We
suggest also graphical tools for a correct interpretation of results.
2015-04-16
info:eu-repo/semantics/doctoralThesis
http://hdl.handle.net/11584/266587
eng
numberofpages:136
info:eu-repo/semantics/openAccess
Università degli Studi di Cagliari
license:Non specificato