Abstract
This paper is concerned with a partial linear regression model with serially correlated random errors which are unobservable and modeled by a moving-average process of infinite order. We study a class of estimators for the linear regression coefficients as well as the function characterizing the non-linear part of the model, constructed based on general kernel smoothing and least squares methods. The law of iterated logarithm and strong convergence rates of these estimator are derived by truncating the moving-average error process, a procedure widely applied in the analysis of time series. Our results can be used to establish uniform strong convergence rate of the estimators of autocovariance and autocorrelation functions of the error process.
Original language | English |
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Pages (from-to) | 2251-2273 |
Number of pages | 23 |
Journal | Communications in Statistics - Theory and Methods |
Volume | 31 |
Issue number | 12 |
Publication status | Published - 2002 |
Externally published | Yes |
Keywords
- Linear time series errors
- Nonparametric kernel smoothing
- Partial linear regression model
- Semiparametric least squares estimator
- Strong convergence rates