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$M$-estimation in nonlinear regression for longitudinal data
Kybernetika, Tome 43 (2007) no. 1, pp. 61-74 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The longitudinal regression model $Z_i^j=m(\theta _0,{\mathbb{X}}_i(T_i^j))+ \varepsilon _i^j,$ where $Z_i^j$ is the $j$th measurement of the $i$th subject at random time $T_i^j$, $m$ is the regression function, ${\mathbb{X}}_i(T_i^j)$ is a predictable covariate process observed at time $T_i^j$ and $\varepsilon _i^j$ is a noise, is studied in marked point process framework. In this paper we introduce the assumptions which guarantee the consistency and asymptotic normality of smooth $M$-estimator of unknown parameter $\theta _0$.
The longitudinal regression model $Z_i^j=m(\theta _0,{\mathbb{X}}_i(T_i^j))+ \varepsilon _i^j,$ where $Z_i^j$ is the $j$th measurement of the $i$th subject at random time $T_i^j$, $m$ is the regression function, ${\mathbb{X}}_i(T_i^j)$ is a predictable covariate process observed at time $T_i^j$ and $\varepsilon _i^j$ is a noise, is studied in marked point process framework. In this paper we introduce the assumptions which guarantee the consistency and asymptotic normality of smooth $M$-estimator of unknown parameter $\theta _0$.
Classification : 60G55, 62F10, 62F12, 62M10
Keywords: $M$-estimation; nonlinear regression; longitudinal data 
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     journal = {Kybernetika},
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     url = {http://geodesic.mathdoc.fr/item/KYB_2007_43_1_a4/}
}
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Orsáková, Martina. $M$-estimation in nonlinear regression for longitudinal data. Kybernetika, Tome 43 (2007) no. 1, pp. 61-74. http://geodesic.mathdoc.fr/item/KYB_2007_43_1_a4/

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