Título: Estimation under shape constraints with log barrier penalty
Resumo: This is work in progress with Nianqing Liu (Xiamen), Mohamed Merabtine (QMUL) and Quang Vuong (NYU).A common belief is that imposing inequality constraints only improves estimation when the true parameter lies near the boundary. Indeed, when the true parameter is in the interior of the constraints, the constrained and unconstrained estimators are equivalent at any order. A popular method for estimation under shape constraint employs log barrier penalty, which maximises an objective function penalised with a log barrier constraining estimation. Classical numerical approaches reestimate the parameters decreasing the weight parameter until a convergence criterion is reached. We adopt a statistical interpretation of the penalty weight , which shrinks estimation towards the constraints. Under certain circumstances, the penalty weight can be chosen optimally minimising a Mean Squared Error criterion when the true parameter lies inside the constraints. The statistically optimised constrained estimator improves on the unconstrained and constrained estimators with a magnitude which is proportional to the distance to the constraints and a vanishing power of the sample size.
Palestrante: Prof. Dr. Emmanuel Guerre (Queen Mary University of London – UK)
Data: 15/10/2024
Horário: 13h30min
Local: Sala A101 do Instituto de Matemática e Estatística da UFRGS (Av. Bento Gonçalves, 9500 Prédio 43-111)