M -estimation in nonlinear regression for longitudinal data

Martina Orsáková

Kybernetika (2007)

  • Volume: 43, Issue: 1, page 61-74
  • ISSN: 0023-5954

Abstract

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The longitudinal regression model Z i j = m ( θ 0 , 𝕏 i ( T i j ) ) + ε 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, 𝕏 i ( T i j ) is a predictable covariate process observed at time T i j and ε 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 θ 0 .

How to cite

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Orsáková, Martina. "$M$-estimation in nonlinear regression for longitudinal data." Kybernetika 43.1 (2007): 61-74. <http://eudml.org/doc/33840>.

@article{Orsáková2007,
abstract = {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 $\theta _0$.},
author = {Orsáková, Martina},
journal = {Kybernetika},
keywords = {$M$-estimation; nonlinear regression; longitudinal data},
language = {eng},
number = {1},
pages = {61-74},
publisher = {Institute of Information Theory and Automation AS CR},
title = {$M$-estimation in nonlinear regression for longitudinal data},
url = {http://eudml.org/doc/33840},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Orsáková, Martina
TI - $M$-estimation in nonlinear regression for longitudinal data
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 1
SP - 61
EP - 74
AB - 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 $\theta _0$.
LA - eng
KW - $M$-estimation; nonlinear regression; longitudinal data
UR - http://eudml.org/doc/33840
ER -

References

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