Likelihood-based Inference for Multivariate Regression Models using Synthetic Data

110 Pages·2016·0.98 MB·English

by  Ricardo Pinto Moura

Ricardo Pinto Moura
Licenciado em Matemática - Ramo Educacional
Likelihood-based Inference for Multivariate
Regression Models using Synthetic Data
Dissertação para obtenção do Grau de Doutor em
Estatística e Gestão do Risco
Co-orientadores: Carlos Agra Coelho, Associate Professor with
Habilitation, Faculty of Sciences and Technology
NOVA University of Lisbon
Bimal K. Sinha, Presidential Research Professor,
University of Maryland Baltimore County
Júri
Presidente: Prof.DoutorJoséPauloBarbosaMota
Arguentes: Prof.a DoutoraMariaIvetteLealdeCarvalhoGomes
Prof.DoutorPedroJoséRamosMoreiradeCampos
Vogais: Prof.DoutorAntónioManuelPachecoPires
Prof.DoutorFilipeJoséGonçalvesPereiraMarques
Prof.DoutorBimalK.Sinha
December, 2016

Likelihood-based Inference for Multivariate Regression Models
using Synthetic Data
Copyright © Ricardo Pinto Moura, Faculty of Sciences and Technology, NOVA
University of Lisbon.
The Faculdade de Ciências e Tecnologia and the Universidade NOVA de Lisboa
havetheright,perpetualandwithoutgeographicalboundaries,tofileandpublish
this dissertation through printed copies reproduced on paper or on digital form,
orbyanyothermeansknownorthatmaybeinvented,andtodisseminatethrough
scientificrepositoriesandadmititscopyinganddistributionfornon-commercial,
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editor.
Estedocumentofoigeradoutilizandooprocessador(pdf)LATEX,combasenotemplate“unlthesis”[1]desen-
volvidonoDep.InformáticadaFCT-NOVA[2]. [1]https://github.com/joaomlourenco/unlthesis [2]
http://www.di.fct.unl.pt

To Veronica and Joel
for their love and full support.

Acknowledgements
Firstly, I would like to thank my adviser Prof. Dr. Carlos Agra Coelho for giving
me the honor of being his advisee, for trusting me, for his great friendship and
supportandforgivingthebrightestadviceseverytime. Iwouldliketoalsothank
my co-adviser Prof. Dr. Bimal Sinha for introducing me to the SDC world and to
themultipleimputationtechniquethatwouldbethefoundationofthisthesis,for
trusting me the task of developing this work, for sharing with me his expertise
and also for his friendship.
To my friends in the Centre of Mathematics and Aplications of the Nova Uni-
versity of Lisbon, for making me feel at home in the center and for their support.
ff
ToUMBCsta andstudentsforwelcomingmetotheirfamilyandtomakeme
a member of that family.
To Fulbright, by choosing me for the Research Grant which allowed me to
build the core work near the Prof. Dr. Bimal Sinha at UMBC and for allowing me
to experience the culture of the U.S.A..
ToDr. MartinKlein, forlettingmebeinhisStatisticalComputingclassesand
for his support.
To my parents, for their sacrifice in all the rough times showing that there’s
no gain without work.
Most importantly, I want to thank my brother Joel, for always making me
believe that I’m an hero, for looking at me with such pride that I could never
stop going further, and, finally, to my girlfriend Verónica, that pushed me into
makingthePhD,forbelievingthatmydestinywasyetnotdefinedandthatIwas
destined for greater accomplishments, for cheering me every time that I seemed
down and things were not running well and for making me believe that I would
always surpass the incoming problems.
vii

Abstract
Likelihood-based exact inference procedures are derived for the multivari-
ate regression model, for singly and multiply imputed synthetic data generated
via Posterior Predictive Sampling (PPS), via a newly proposed sampling method,
which will be called Fixed-Posterior Predictive Sampling (FPPS), and via Plug-in
sampling. By contemplating the single imputation case, the new developed pro-
cedures fill the gap in the existing literature where inferential methods are only
available for multiple imputation and, by being based in exact distributions, it
may even be applied to cases where the sample size is small. Simulation studies
compare the results obtained from all the proposed exact inferential procedures
and also compare these with the results obtained from the adaptation of Reiter’s
combination rule to multiply imputed synthetic datasets. An application using
U.S. 2000 Current Population Survey data is discussed and measures of privacy
are presented and compared among all methods.
Keywords: Finite sample inference, Maximum likelihood estimation, Pivotal
quantity, Partially syntheticdata, StatisticalDisclosure Control, Unbiased estima-
tors
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