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 -- - 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] Please don't print this e-mail unless you really need to. Please avoid sending me Word, Excel or PowerPoint attachments. Seehttp://www.gnu.org/philosophy/no-word-attachments.html. Per favore non stampate questo messaggio se non è proprio necessario. Per favore non mandatemi allegati in Word, Excel o PowerPoint. Le ragioni sono spiegate quihttp://www.gnu.org/philosophy/no-word-attachments.it.html