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267 269 o simplifica o problema de otimizao de

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Unformatted text preview: 2 e insere na função log-likelihood: função concentrada com respeito aos parâmetros . o Note que a solução para os estimadores dos parâmetros amostrais depende do parâmetro desconhecido ρ: e . No caso do modelo SAR: o Otimizando a função LL concentrada com respeito a ρ, encontra-se o estimador de ML de . o O passo seguinte consiste em estimar e . Vantagens em se trabalhar com LL concentrada: o Produz o mesmo resultado da full LL (D&M, 1993, p. 267-269) o Simplifica o problema de otimização de multivariada, para univariada. o Produz uma matriz de variância de covariância computacionalmente eficiente A função de LL para modelos SDM e SAR, assume a forma (Anselin, 1988): o • • • • mat r i x W . ln L = − ( n/ 2) l n( πσ2 ) + l n |I n − ρW | − e = y − ρW y − Z δ ee 2σ2 (3.6) ρ ∈ (min( ω) − 1 , max( ω) − 1 ) cont ai ns onl y real ei genval ues, a posi t i ve defi ni t e vari ance-covari ance ma onde y he co vetor n ρ 1 (min( ω) − 1 , max ω) matriz W. is ensur ed bω t...
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