scholarly journals Partially linear model estimation for missing response data

2021 ◽  
Vol 2106 (1) ◽  
pp. 012013
Author(s):  
N Salam
Keyword(s):  
Asymptotic Variance ◽  
Partially Linear Model ◽  
Asymptotically Normal ◽  
Missing Responses ◽  
Response Data ◽  
Partially Linear ◽  
Point Estimates ◽  
Special Cases ◽  
Approach Method ◽  
The Mean

Abstract This paper will discuss the estimation of a partially linear (semiparametric) model with missing responses using the normal approach. An estimator class is defined which includes special cases, namely the partially linear imputation estimator, the marginal mean estimator and the trend score weighted estimator. The estimator class is asymptotically normal. The three special estimators have the same asymptotic variance. Based on the above conditions, the mean F will be estimated, say θ. The three special estimators above will be used to estimate the mean F, namely in the form of point estimates and confidence intervals with some missing responses using the normal approach method.

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.

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.

Estimation of the marginal location under a partially linear model with missing responses

2010 ◽  
Vol 54 (2) ◽  
pp. 546-564 ◽  
Author(s):  
Ana Bianco ◽  
Graciela Boente ◽  
Wenceslao González-Manteiga ◽  
Ana Pérez-González
Keyword(s):  
Linear Model ◽  
Partially Linear Model ◽  
Missing Responses ◽  
Partially Linear

Decoration technique and surface physics

1978 ◽  
Vol 36 (1) ◽  
pp. 436-437 ◽  
Author(s):  
H. Bethge
Keyword(s):  
Diffusion Path ◽  
Special Importance ◽  
Surface Physics ◽  
Step Structure ◽  
Initial Stage ◽  
Special Cases ◽  
Atomic Surface ◽  
The Mean ◽  
Bulk Structure ◽  
Decoration Technique

Besides the atomic surface structure, diverging in special cases with respect to the bulk structure, the real structure of a surface Is determined by the step structure. Using the decoration technique /1/ it is possible to image step structures having step heights down to a single lattice plane distance electron-microscopically. For a number of problems the knowledge of the monatomic step structures is important, because numerous problems of surface physics are directly connected with processes taking place at these steps, e.g. crystal growth or evaporation, sorption and nucleatlon as initial stage of overgrowth of thin films.To demonstrate the decoration technique by means of evaporation of heavy metals Fig. 1 from our former investigations shows the monatomic step structure of an evaporated NaCI crystal. of special Importance Is the detection of the movement of steps during the growth or evaporation of a crystal. From the velocity of a step fundamental quantities for the molecular processes can be determined, e.g. the mean free diffusion path of molecules.

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.

scholarly journals A New Class of Estimators Based on a General Relative Loss Function

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1138
Author(s):  
Tao Hu ◽  
Baosheng Liang
Keyword(s):  
Loss Function ◽  
Asymptotically Normal ◽  
New Class ◽  
Statistical Inferences ◽  
Relative Loss ◽  
Special Cases ◽  
Class Of Estimators ◽  
Box Cox Transformation ◽  
Loss Estimator ◽  
Prostate Cancer Study

Motivated by the relative loss estimator of the median, we propose a new class of estimators for linear quantile models using a general relative loss function defined by the Box–Cox transformation function. The proposed method is very flexible. It includes a traditional quantile regression and median regression under the relative loss as special cases. Compared to the traditional linear quantile estimator, the proposed estimator has smaller variance and hence is more efficient in making statistical inferences. We show that, in theory, the proposed estimator is consistent and asymptotically normal under appropriate conditions. Extensive simulation studies were conducted, demonstrating good performance of the proposed method. An application of the proposed method in a prostate cancer study is provided.

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 Thermodynamic and Elastic Properties of Interstitial Alloy FeC with BCC Structure at Zero Pressure

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Bui Duc Tinh ◽  
Nguyen Quang Hoc ◽  
Dinh Quang Vinh ◽  
Tran Dinh Cuong ◽  
Nguyen Duc Hien
Keyword(s):  
Nearest Neighbor ◽  
Young Modulus ◽  
Thermodynamic Quantities ◽  
Atom Concentration ◽  
Main Metal ◽  
Special Cases ◽  
Analytic Expressions ◽  
Rigidity Modulus ◽  
Bcc Structure ◽  
The Mean

The analytic expressions for the thermodynamic and elastic quantities such as the mean nearest neighbor distance, the free energy, the isothermal compressibility, the thermal expansion coefficient, the heat capacities at constant volume and at constant pressure, the Young modulus, the bulk modulus, the rigidity modulus, and the elastic constants of binary interstitial alloy with body-centered cubic (BCC) structure, and the small concentration of interstitial atoms (below 5%) are derived by the statistical moment method. The theoretical results are applied to interstitial alloy FeC in the interval of temperature from 100 to 1000 K and in the interval of interstitial atom concentration from 0 to 5%. In special cases, we obtain the thermodynamic quantities of main metal Fe with BCC structure. Our calculated results for some thermodynamic and elastic quantities of main metal Fe and alloy FeC are compared with experiments.

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