Empirical likelihood for longitudinal partially linear model with α-mixing errors

In this paper, a partially linear model under longitudinal data is considered. In order to take into consideration the within-subject correlation structure of the repeated measurements, an empirical likelihood incorporating the correlation structure is developed. The asymptotic normality of the maximum empirical likelihood estimates of the regression coefficients is obtained. It also can be shown that the proposed empirical likelihood ratio is asymptotically standard chi-square. The results can be used directly to construct the asymptotic confidence regions of the regression coefficients. The convergence rate of the baseline function is derived.

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ON THE USE OF PARTIALLY LINEAR MODEL IN IDENTIFICATION OF ARCING-FAULT LOCATION ON OVERHEAD HIGH-VOLTAGE TRANSMISSION LINES

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127404010321 ◽

2004 ◽

Vol 14 (06) ◽

pp. 1975-1985

Author(s):

RASTKO ŽIVANOVIĆ

Keyword(s):

Linear Model ◽

Dynamic Behavior ◽

Nonlinear System Identification ◽

Identification Problem ◽

Parametric Modeling ◽

Partially Linear Model ◽

Practical Reasons ◽

Partially Linear ◽

Pull Out ◽

Arcing Fault

The task of locating an arcing-fault on overhead line using sampled measurements obtained at a single line terminal could be classified as a practical nonlinear system identification problem. The practical reasons impose the requirement that the solution should be with maximum possible precision. Dynamic behavior of an arc in open air is influenced by the environmental conditions that are changing randomly, and therefore the useful practically application of parametric modeling is out of question. The requirement to identify only one parameter is yet another specific of this problem. The parameter we need is the one that linearly correlates the voltage samples with the current derivative samples (inductance). The correlation between the voltage samples and the current samples depends on the unpredictable arc dynamic behavior. Therefore this correlation is reconstructed using nonparametric regression. A partially linear model combines both, parametric and nonparametric parts in one model. The fit of this model is noniterative, and provides an efficient way to identify (pull out) a single linear correlation from the nonlinear time series.

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Simultaneous inference of the partially linear model with a multivariate unknown function

Journal of Statistical Planning and Inference ◽

10.1016/j.jspi.2020.10.007 ◽

2021 ◽

Vol 213 ◽

pp. 93-105

Author(s):

Kun Ho Kim ◽

Shih-Kang Chao ◽

Wolfgang K. Härdle

Keyword(s):

Linear Model ◽

Unknown Function ◽

Partially Linear Model ◽

Simultaneous Inference ◽

Partially Linear

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Approximate Bayesian inference for joint linear and partially linear modeling of longitudinal zero-inflated count and time to event data

Statistical Methods in Medical Research ◽

10.1177/09622802211002868 ◽

2021 ◽

pp. 096228022110028

Author(s):

T Baghfalaki ◽

M Ganjali

Keyword(s):

Linear Model ◽

Joint Modeling ◽

Partially Linear Model ◽

Event Data ◽

Time To Event ◽

Data Set ◽

Partially Linear ◽

Time To Event Data ◽

Count Response ◽

Approximate Bayesian

Joint modeling of zero-inflated count and time-to-event data is usually performed by applying the shared random effect model. This kind of joint modeling can be considered as a latent Gaussian model. In this paper, the approach of integrated nested Laplace approximation (INLA) is used to perform approximate Bayesian approach for the joint modeling. We propose a zero-inflated hurdle model under Poisson or negative binomial distributional assumption as sub-model for count data. Also, a Weibull model is used as survival time sub-model. In addition to the usual joint linear model, a joint partially linear model is also considered to take into account the non-linear effect of time on the longitudinal count response. The performance of the method is investigated using some simulation studies and its achievement is compared with the usual approach via the Bayesian paradigm of Monte Carlo Markov Chain (MCMC). Also, we apply the proposed method to analyze two real data sets. The first one is the data about a longitudinal study of pregnancy and the second one is a data set obtained of a HIV study.

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