scholarly journals The Consistency of Estimators in a Heteroscedastic Partially Linear Model with ρ−-Mixing Errors

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1188
Author(s):  
Yu Zhang ◽  
Xinsheng Liu
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Unknown Parameter ◽  
Strong Consistency ◽  
Weighted Least Squares ◽  
Partially Linear Model ◽  
Random Errors ◽  
Partially Linear ◽  
Special Cases ◽  
Theoretical Results

This paper studies a heteroscedastic partially linear model based on ρ − -mixing random errors, stochastically dominated and with zero mean. Under some suitable conditions, the strong consistency and p -th ( p > 0 ) mean consistency of least squares (LS) estimators and weighted least squares (WLS) estimators for the unknown parameter are investigated, and the strong consistency and p -th ( p > 0 ) mean consistency of the estimators for the non-parametric component are also studied. These results include the corresponding ones of independent, negatively associated (NA), and ρ * -mixing random errors as special cases. At last, two simulations are presented to support the theoretical results.

scholarly journals Strong Consistency of Estimators in a Partially Linear Model with Asymptotically Almost Negatively Associated Errors

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Yu Zhang ◽  
Xinsheng Liu ◽  
Mohamed Sief
Keyword(s):  
Least Squares ◽  
Strong Consistency ◽  
Weighted Least Squares ◽  
Partially Linear Model ◽  
Random Errors ◽  
Negatively Associated ◽  
Partially Linear ◽  
Least Squares Estimators ◽  
Special Cases ◽  
Asymptotically Almost Negatively Associated

This paper studies a heteroscedastic partially linear regression model in which the errors are asymptotically almost negatively associated (AANA, in short) random variables with not necessarily identical distribution and zero mean. Under some mild conditions, we establish the strong consistency of least squares estimators, weighted least squares estimators, and the ultimate weighted least squares estimators for the unknown parameter, respectively. In addition, the strong consistency of the estimator for nonparametric component is also investigated. The results derived in the paper include the corresponding ones of independent random errors and some dependent random errors as special cases. At last, two simulations are carried out to study the numerical performance of the strong consistency for least squares estimators and weighted least squares estimators of the unknown parametric and nonparametric components in the model.

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

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.

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

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.

scholarly journals New Restricted Liu Estimator in a Partially Linear Model

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Jibo Wu ◽  
Yong Li
Keyword(s):  
Asymptotic Normality ◽  
Linear Model ◽  
Simulation Study ◽  
Linear Constraints ◽  
Partially Linear Model ◽  
Liu Estimator ◽  
Numerical Example ◽  
Partially Linear

In this paper, we introduce a new restricted Liu estimator in a partially linear model when addition linear constraints are assumed to hold. We also consider the asymptotic normality of the new estimator. Finally, a numerical example and a simulation study are listed to illustrate the performance of the new estimator.

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