EV Regression Model Research Articles

Strong convergence for weighted sums of (α, β)-mixing random variables and application to simple linear EV regression model

Abstract In this article, the complete convergence and the Kolmogorov strong law of large numbers for weighted sums of ( α , β ) \left(\alpha ,\beta ) -mixing random variables are presented. An application to simple linear errors-in-variables model is provided. Simulation studies are also carried out to support the theoretical results.

Complete f-moment convergence for arrays of random variables and its applications in semiparametric and EV regression models

Complete f-moment convergence for arrays of random variables and its applications in semiparametric and EV regression models

Strong laws for weighted sums of some dependent random variables and applications

Let {Xn, n ? 1} be a sequence of random variables satisfying a generalized Rosenthal type inequality and stochastically dominated by a random variable X. Let {ani, 1 ? i ? n, n ? 1} be an array of constants. We study the Marcinkiewicz-Zygmund type strong laws for weighted sums ?n i=1 aniXi under the condition that the exponential moment of the random variable X exists. These results are the interesting supplements for some known results. As statistical applications, we provide the strong consistency of LS estimators in simple linear EV regression models with widely orthant dependent random errors.

Sufficient and necessary conditions for the strong consistency of LS estimators in simple linear EV regression models

ABSTRACT In this paper, the sufficient and necessary conditions for the strong consistency of least squares estimators in simple linear EV regression models are proved under widely orthant dependent random errors. The results obtained in the paper improve and extend some existing ones in the literature. Simulation studies are also carried out to support the consistency of the estimators under dependence assumption and finite samples.

Complete q-th moment convergence for the maximum of partial sums of -negatively associated random variables and its application to the EV regression model*

In this article, we prove the complete q-th moment convergence for the maximum of partial sums of -negatively associated random variables under some general conditions. The results obtained in this article are extensions of previous studies for -negatively associated random variables. In addition, we investigate the strong consistency of the least squares estimator in the simple linear errors-in-variables model based on -negatively associated random variables, and provide some simulations to assess the finite sample performance of the theoretical results.

Strong Law of Large Numbers for Weighted Sums of Random Variables and Its Applications in EV Regression Models

This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent (END, for short) random variables. Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided. In particular, the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product. The results that the authors obtained generalize the corresponding ones for independent random variables and some dependent random variables. As an application, the authors investigate the errors-in-variables (EV, for short) regression models and establish the strong consistency for the least square estimators. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.

Strong consistency of LS estimators in simple linear EV regression models with WOD errors

Strong consistency of LS estimators in simple linear EV regression models with WOD errors

Strong consistency of LS estimator in simple linear EV regression models

Strong consistency of LS estimator in simple linear EV regression models

Strong and weak consistency of least squares estimators in simple linear EV regression models

For a simple linear errors-in-variables regression model, we obtain a necessary and sufficient condition for the convergence rate in the strong consistency of the least squares estimator for each of the unknown parameters. We also obtain a necessary and sufficient condition for the convergence rate in the weak consistency.

Complete f-moment convergence for Sung’s type weighted sums and its application to the EV regression models

In this paper, we establish a general result on the complete f-moment convergence for Sung’s type weighted sums of extended negatively dependent random variables under some general assumptions. As applications, we investigate the strong consistency of the least square estimator in the simple linear errors-in-variables models, and provide some simulations to verify the validity of our theoretical results.

Complete and complete moment convergence with applications to the EV regression models

ABSTRACTIn this paper, the complete convergence and complete moment convergence for arrays of rowwise m-extended negatively dependent (m-END, for short) random variables are established. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for m-END random variables is also achieved. By using the results that we established, we further investigate the strong consistency of the least square estimator in the simple linear errors-in-variables models, and provide some simulations to verify the validity of our theoretical results.

Asymptotic properties of LS estimators in the errors-in-variables model with MD errors

In this paper, the complete convergence for weighted sums of a class of random variables is established. By using the complete convergence, we further investigate the complete consistency of LS estimators in the EV regression model with martingale difference (in short) errors. In addition, the mean consistency of LS estimators is also studied. The results obtained in the paper generalize the corresponding ones for independent random variables and some dependent random variables.

On consistency of least square estimators in the simple linear EV model with negatively orthant dependent errors

In this paper, we mainly study the asymptotic properties of least square (LS, for short) estimators in the simple linear errors-in-variables (EV, for short) regression model with negatively orthant dependent (NOD, for short) errors. Under some suitable conditions, the strong consistency, weak consistency and complete consistency of the LS estimators in the EV regression model with NOD errors are obtained, which generalize or improve the corresponding ones for independent random variables and negatively associated random variables in some sense.

Strong and weak consistency of LS estimators in the EV regression model with negatively superadditive-dependent errors

In this paper, the strong laws of large numbers for partial sums and weighted sums of negatively superadditive-dependent (NSD, in short) random variables are presented, especially the Marcinkiewicz–Zygmund type strong law of large numbers. Using these strong laws of large numbers, we further investigate the strong consistency and weak consistency of the LS estimators in the EV regression model with NSD errors, which generalize and improve the corresponding ones for negatively associated random variables. Finally, a simulation is carried out to study the numerical performance of the strong consistency result that we established.

Complete convergence for weighted sums of NSD random variables and its application in the EV regression model

In this paper, some basic properties for negatively superadditive-dependent (NSD, in short) random variables are presented, such as the Rosenthal-type inequality and the Kolmogorov-type exponential inequality. Using these properties, we further study the complete convergence for weighted sums of NSD random variables, which generalizes and improves some corresponding ones for independent random variables and negatively associated random variables. Some sufficient conditions to prove the complete convergence for weighted sums of NSD random variables are provided. As an application, the complete consistency of LS estimators in the EV regression model with NSD errors is investigated under mild conditions, which generalizes and improves the corresponding one for negatively associated random variables.

Consistency of LS estimators in the EV regression model with martingale difference errors

In this paper, we consider the following simple linear errors in variables modelwhere θ, β, x1, x2, … are unknown constants (parameters) and ξi, ηi, i=1, 2, … are observable. The consistency of the least square estimators for the unknown parameters β and θ is established, while the errors { ϵi}, {δi} are sequences of martingale difference. In order to obtain our results, some limit theorems for weighted sums of martingale differences are proved.

MDP for estimators in EV regression models with α-mixing errors

In this paper, we consider the following simple linear errors-in-variables regression model:where θ and β are the unknown parameters, ηi, ξi’s are observable and xi’s are unobservable. We assume the error variables {(ε1, δi), 1≤i≤n} form a L2 stationary α-mixing sequences. In this paper, we obtained the moderate deviation principles for the least-square estimators of the unknown parameters θ and β.

Consistency for the LS estimator in the linear EV regression model with replicate observations

In this paper, we consider the following linear errors-in-variables regression model: ξij=xi+δij,ηij=yi+εij=θ+βxi+εij, with independent identically distributed errors (εij,δij),(j=1,2,…,ni;i=1,2,…). The strong and weak consistency for the LS estimators βˆ and θˆ of the unknown parameters β,θ in this model are obtained, which weaken some known conditions and improve some known results.

Asymptotic normality and strong consistency of LS estimators in the EV regression model with NA errors

In this article, the asymptotic normality and strong consistency of the least square estimators for the unknown parameters in the simple linear errors in variables model are established under the assumptions that the errors are stationary negatively associated sequences.

Asymptotic Normality for the Partially Linear EV Models with Longitudinal Data

In this article, we consider a partially linear EV regression model under longitudinal data. By using a weighted kernel method and modified least-squared method, the estimators of unknown parameter, the unknown function are constructed and the asymptotic normality of the estimators are derived. Simulation studies are conducted to illustrate the finite-sample performance of the proposed method.