A generalized weighted likelihood estimator

TitreA generalized weighted likelihood estimator
Publication TypeConference Paper
Year of Publication2012
AuthorsAmiguet, M, Marazzi, A
Conference NameComputational and Financial Econometrics (CFE 2012) & ERCIM (European Research Consortium for Informatics and Mathematics) Working Group on Computing & Statistics (ERCIM 2012)
PublisherERCIM (European Research Consortium for Informatics and Mathematics)
Conference LocationOviedo, Spain

A new robust estimation method is proposed for regression in a wide framework including the GLM. Let Pα,μ(Y≤z) be a family of distributions depending on two parameters α and μ, where μ = E(Y) and α is a shape, a scale, or a dispersion parameter. Consider a general regression model where the response Y has cdf Pα0,μ0(x)(Y≤z), x is a covariate vector, E(Y|x) = μ0(x) = h(β0Tx), and h is a given link function. A specific example is the negative binomial (NB) regression model, where Y ∼ NB(α00(x)) and Var(y|x) = μ0(x)+α0μ0(x)2. Let (x1,y1), ... , (xn;yn) be a random sample and consider estimation of α0 and β0. If Y is continuous, the tail probabilities Pα0,μ0(xi)(Y≤yi) are a sample of a uniform distribution. If Y is discrete, generate m random samples (u11, ... , un1), ... ,(u1m, ... ,unm) from the uniform distribution on [0,1] and consider the "randomized tail probabilities" Pα0,μ0(xi)(zi,uij) = Pα0,μ0(xi)(Y≤yi) - uij Pα0,μ0(xi)(Y = yi), i = 1, ... ,n,  j = 1, ... ,m. For a given j, Pα0,μ0(xi)(z1,u1j) , ... , Pα0,μ0(xi)(zn,unj) is a sample from a uniform distribution. A set of weights is then derived from a measure of disparity between the empirical distribution of the (randomized or not) tail probabilities (or of a transformation of them) and their theoretical distribution under the model. These weights are used in a weighted likelihood procedure to estimate α0 and β0.


Abstract E383

6th CSDA International Conference on Computational and Financial Econometrics (CFE 2012) http://www.cfe-csda.org/cfe12 and 5th International Conference of the ERCIM (European Research Consortium for Informatics and Mathematics) Working Group on Computing & Statistics (ERCIM 2012) http://www.cfe-csda.org/ercim12

Conference Center “Ciudad de Oviedo”, Spain 1-3 December 2012

Citation Key / SERVAL ID6221


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