Unit:
Κατεύθυνση Στατιστική και Επιχειρησιακή ΈρευναLibrary of the School of Science
Author:
Zacharias Konstantinos
Supervisors info:
Μελιγκοτσίδου Λουκία, Αναπληρώτρια Καθηγήτρια, Τμήμα Μαθηματικών, ΕΚΠΑ
Σιάννης Φώτιος, Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Τρέβεζας Σάμης, Λέκτορας, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Literature Review of the Generalised Additive Model for location, scale and shape
Translated title:
Literature Review of the Generalised Additive Model for location, scale and shape
Summary:
The main objective of this study is to present different statistical models and discuss their contribution to data fit. The first model that is analysed is the Generalised Linear Model(GLM) which is a generalisation of the linear model assuming some member of the exponential family of distributions for the response variable. The nature of the data determines to a great extent the form of the generalised linear model that will be applied, through the choice of the link function of the model. The iterative methods which allow for the practical implementation of each particular model and the respective statistical inference procedures are discussed, as well.
The assumption of the exponential family distribution for the response is relaxed in the Generalised Additive Model(GAM). A general distribution is assumed for the dependent variable, with the introduction of smoothing functions that blend the inherent properties of the GLM with the additive models. The response variable depends linearly on unknown smooth functions of some predictor variables, and the inference is focused on these smoothers.
A general class of statistical models for a univariate response variable is presented, which is called the Generalized Additive Model for Location, Scale and Shape (GAMLSS). The choice of the distribution for the response variable in GAMLSS is made from a very general family of distributions including highly skewed or kurtotic continuous and discrete distributions. The GAMLSS systematic part is expanded to permit modelling of the mean (or location) and other distributional parameters of the response, as parametric and/or additive nonparametric (smooth) functions of explanatory variables and/or random-effects terms.
Main subject category:
Science
Keywords:
generalised additive model, centile estimation, non-parametric distribution
