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Statistical Inference based on the Empirical Identity Process

Ivo Vincentius Stoepker

Statistical Inference based on the Empirical Identity Process.

Rel. Mauro Gasparini, Enrico Bibbona. Politecnico di Torino, Corso di laurea magistrale in Ingegneria Matematica, 2018

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The empirical identity process (Enrico Bibbona, Giovanni Pistone, and Mauro Gasparini. The Empirical Identity Process: asymptotics and applications. The Canadian Journal of Statistics, 2017) gives rise to a test statistic $d_n$ which can be used for statistical inference. In this thesis, a new statistic $o_n$ based on the process is devised, and two inference settings are studied; goodness-of-fit and parameter estimation. For the latter, minimum-distance estimators are constructed. In the goodness-of-fit setting, we show that the new statistics are powerful in uniform settings with alternatives containing clusters. However, they are outperformed in other cases if the parameters of the null distribution are estimated from the data. In the parameter estimation setting, the minimum-distance estimator based on $d_n$ is shown to have excellent performance, beating the maximum-likelihood estimator with the expectation-maximization algorithm in normal mixtures with high component overlap. Moreover, our minimum-distance estimators have excellent robustness properties, especially compared with the maximum-likelihood estimator which is shown not to be robust. However, the maximum-likelihood estimator is less sensitive to initialization.

Relators: Mauro Gasparini, Enrico Bibbona
Academic year: 2017/18
Publication type: Electronic
Number of Pages: 121
Corso di laurea: Corso di laurea magistrale in Ingegneria Matematica
Classe di laurea: New organization > Master science > LM-44 - MATHEMATICAL MODELLING FOR ENGINEERING
Aziende collaboratrici: UNSPECIFIED
URI: http://webthesis.biblio.polito.it/id/eprint/7675
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