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.

scholarly journals A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 25 ◽  
Author(s):  
Ehab Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Eslam Hafez
Keyword(s):  
Statistical Model ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Likelihood Estimation ◽  
Linear Representation ◽  
Rate Function ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Least Squares Estimators ◽  
New Distribution

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

Functional least squares estimators in an additive effects outliers model

1990 ◽  
Vol 48 (2) ◽  
pp. 299-319 ◽  
Author(s):  
Sunil K. Dhar
Keyword(s):  
Asymptotic Behavior ◽  
Weak Convergence ◽  
Gaussian Process ◽  
Least Squares ◽  
Strong Consistency ◽  
Additive Effects ◽  
Uniform Consistency ◽  
Least Squares Estimators

AbstractConsider the additive effects outliers (A.O.) model where one observes , with The sequence of r.v.s is independent of and , are i.i.d. with d.f. , where the d.f.s Ln, n ≦ 0, are not necessarily known and εj's are i.i.d.. This paper discusses the asymptotic behavior of functional least squares estimators under the above model. Uniform consistency and uniform strong consistency of these estimators are proven. The weak convergence of these estimators to a Gaussian process and their asymptotic biases are also discussed under the above A.O. model.

scholarly journals Analysis of algebraic weighted least-squares estimators for enzyme parameters

1992 ◽  
Vol 288 (2) ◽  
pp. 533-538 ◽  
Author(s):  
M E Jones
Keyword(s):  
Least Squares ◽  
Coefficient Of Variation ◽  
Constant Coefficient ◽  
Weighted Least Squares ◽  
Simulated Data ◽  
Standard Errors ◽  
Parameter Estimates ◽  
Spreadsheet Program ◽  
Least Squares Estimators ◽  
Constant Coefficient Of Variation

An algorithm for the least-squares estimation of enzyme parameters Km and Vmax. is proposed and its performance analysed. The problem is non-linear, but the algorithm is algebraic and does not require initial parameter estimates. On a spreadsheet program such as MINITAB, it may be coded in as few as ten instructions. The algorithm derives an intermediate estimate of Km and Vmax. appropriate to data with a constant coefficient of variation and then applies a single reweighting. Its performance using simulated data with a variety of error structures is compared with that of the classical reciprocal transforms and to both appropriately and inappropriately weighted direct least-squares estimators. Three approaches to estimating the standard errors of the parameter estimates are discussed, and one suitable for spreadsheet implementation is illustrated.

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