Ανάρτηση Ερευνητικών Δοκιμίων των Στέλιου Αρβανίτη και Thierry Post

Ερευνητικό Δοκίμιο no 04 ǀ Μάρτιος 2022 με τίτλο "Ordering Arbitrage Portfolios and Finding Arbitrage Opportunities" των Στέλιου Αρβανίτη και Thierry Post

Περίληψη

We derive non‐asymptotic concentration inequalities for the uniform deviation between a multivariate density function and its non‐parametric kernel density estimator in stationary and uniform mixing time series framework. We derive analogous inequalities for their (first) Wasserstein distance, as well as for the deviations between integrals of bounded functions w.r.t. them. They can be used for the construction of confidence regions, the estimation of the finite sample probabilities of decision errors, etc. We employ the concentration results to the derivation of statistical guarantees and oracle inequalities in regularized prediction problems with expected costs exhibiting Lipschitz and strong convexity properties.
 

Ο Στέλιος Αρβανίτης είναι Αναπληρωτής Καθηγητής στο Τμήμα Οικονομικής Επιστήμης του Οικονομικού Πανεπιστημίου Αθηνών και ο Thierry Post είναι Καθηγητής στο Graduate School of Business του Nazarbayev University.

Ερευνητικό Δοκίμιο no 05 ǀ Μάρτιος 2022 με τίτλο "Concentration Inequalities for Kernel Density Estimators under Uniform Mixing" του Στέλιου Αρβανίτη 

Περίληψη

We derive non‐asymptotic concentration inequalities for the uniform deviation between a multivariate density function and its non‐parametric kernel density estimator in stationary and uniform mixing time series framework. We derive analogous inequalities for their (first)
Wasserstein distance, as well as for the deviations between integrals of bounded functions w.r.t. them. They can be used for the construction of confidence regions, the estimation of the finite sample probabilities of decision errors, etc. We employ the concentration results to the derivation of statistical guarantees and oracle inequalities in regularized prediction problems with expected costs exhibiting Lipschitz and strong convexity properties.Keywords: Non‐asymptotic concentration inequalities, Kernel Estimator, Density Estimation,
Uniform Mixing, Statistical Gaurantees, Lipschitz costs, Strong Convexity, Support Vector Machines,Hinge Costs.

Ο ΣτέλιοςΑρβανίτης είναι Αναπληρωτής Καθηγητής στο Τμήμα Οικονομικής Επιστήμης του Οικονομικού Πανεπιστημίου.