Dear all,
we are glad to announce the following hybrid seminar
March 26, 2024, 12:15 PM
Where: Aula Delta 2C- edificio Delta (Campus Scientifico),
Via Torino, 155 Mestre (Venice, Italy)
Zoom: https://unive.zoom.us/j/85153268624?pwd=MzBhdlA2M1B2dThJQ2Y5T0EwUE5PZz09
Speaker: Philipp Sterzinger, University of Warwick
Title: Diaconis-Ylviskaer prior penalized likelihood in
high-dimensional logistic regression
Abstract:
In recent years, there has been a surge of interest in estimators
and inferential procedures that exhibit optimal asymptotic
properties in high-dimensional logistic regression when the number
of covariates grows proportionally as a fraction ($\kappa \in
(0,1)$) of the number of observations. In this seminar, we focus on
the behaviour of a class of maximum penalized likelihood estimators,
employing the Diaconis-Ylvisaker prior as the penalty.
Building on advancements in approximate message passing, we analyze
the aggregate asymptotic behaviour of these estimators when
covariates are normal random variables with arbitrary covariance.
This analysis enables us to eliminate the persistent asymptotic bias
of the estimators through straightforward rescaling for any value of
the prior hypertuning parameter. Moreover, we derive asymptotic
pivots for constructing inferences, including adjusted Z-statistics
and penalized likelihood ratio statistics.
Unlike the maximum likelihood estimate, which only asymptotically
exists in a limited region on the plane of $\kappa$ versus signal
strength, the maximum penalized likelihood estimate always exists
and is directly computable via maximum likelihood routines. As a
result, our asymptotic results remain valid even in regions where
existing maximum likelihood results are not obtainable, with no
overhead in implementation or computation.
The dependency of the estimators on the prior hyper-parameter
facilitates the derivation of estimators with zero asymptotic bias
and minimal mean squared error. We will explore these estimators'
shrinkage properties, substantiate our theoretical findings with
simulations and applications.
Visit this page https://www.unive.it/pag/41970/
for updates on our seminars.
Best regards,
Carlo Gaetan
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Dipartimento di Scienze Ambientali, Informatica e Statistica - DAIS
Università Ca' Foscari - Venezia
Z.A12 - Edificio Zeta
Via Torino, 155
I-30172 Mestre (VE)
ITALY
phone: ++39 041 234 8404
e-mail:[gaetan"at"unive"dot"it]
web:[http://www.dais.unive.it/~gaetan]
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