Banca de QUALIFICAÇÃO: MAXIMILIAN UDO LACHMANN

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
DISCENTE: MAXIMILIAN UDO LACHMANN
DATA : 22/09/2025
LOCAL: Departamento de Estatística
TÍTULO:

Robust Estimation via Hellinger Distance: Theory and Applications in ARMA Time Series
and Symmetric Regression

 

PALAVRAS-CHAVES:

ARMA Models; Regression Models; Minimum Hellinger Distance; Minimum Profile Hellinger
Distance; Robust Estimation; Symmetric Distributions

 

PÁGINAS: 58
RESUMO:

This dissertation investigates robust estimation through Hellinger–distance methods in two
complementary parts.
First, we study a Minimum Profile Hellinger Distance Estimator (MPHDE) for ARMA models
with symmetric innovation densities. By profiling over the nuisance class of symmetric
densities and estimating the innovation density nonparametrically, the objective reduces to
maximizing a symmetricized L2 norm of the square-root kernel density estimator. We establish
consistency and asymptotic normality under standard regularity conditions. Extensive
simulations for AR(1) and ARMA(1,1) processes—both clean and contamination
scenarios—show lower bias and MSE and greater robustness to outliers compared with
Yule–Walker and maximum likelihood. An empirical study of Lake St. Clair water levels
demonstrates strong model diagnostics and forecasting gains in multi-step and rolling
horizons.
Second, we present a parametric Minimum Hellinger Distance Estimator for symmetric and
log-symmetric regression. We formalize the estimation functional, derive iteratively reweighted
least-squares (IRLS)–type estimating equations, and develop a framework for joint scale
estimation, where the variance is unknown and estimated simultaneously with the regression
coefficients. We also establish consistency under mild conditions, providing a rigorous
theoretical basis for applying Hellinger–distance estimation in regression models.

 

MEMBROS DA BANCA:
Presidente - 338043 - FRANCISCO JOSE DE AZEVEDO CYSNEIROS
Interno - 1137818 - JODAVID DE ARAUJO FERREIRA
Interno - 1651445 - RAYDONAL OSPINA MARTINEZ