Abstract
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.
Highlights
It is well known that the simple errors-in-variables (EV, for short) regression model was proposed by Deaton [1] to correct for the effects of sampling error and is somewhat more practical than the ordinary regression model
For more details about the EV regression model, one can refer to Fuller [2], Fusek and Fuskova [3], Carroll et al [4], Hslao et al [5], and so on
Under the case that the errors are sequences of dependent random variables, Fazekas and Kukush [14] studied the asymptotic properties of an estimator in nonlinear functional EV models with α-mixing error terms; Miao et al [15] studied the strong consistency of LS estimators in the EV
Summary
It is well known that the simple errors-in-variables (EV, for short) regression model was proposed by Deaton [1] to correct for the effects of sampling error and is somewhat more practical than the ordinary regression model. Under the case that the errors are sequences of dependent random variables, Fazekas and Kukush [14] studied the asymptotic properties of an estimator in nonlinear functional EV models with α-mixing error terms; Miao et al [15] studied the strong consistency of LS estimators in the EV regression model with negatively associated (NA, for short) errors; Miao et al. The main purpose of the paper is to investigate the strong consistency of LS estimators in the EV regression model with negatively orthant dependent (NOD, for short) errors, which generalizes and improves the corresponding one of Miao et al [15]. The paper is organized as follows: main results of the paper are presented, including the strong consistency, weak consistency and complete consistency of LS estimators in the EV regression model with NOD errors.
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