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Empirical likelihood for linear models under \(m\)-dependent errors. (English) Zbl 1064.62080

From the paper: Consider the following linear model: \[ y=x^T\beta+e, \] where \(x\in\mathbb{R}^p\) is a non-random design vector, \(\beta\in\mathbb{R}^p\) is an unknown regression coefficient, \(y\in\mathbb{R}\) is the response, and \(e\in\mathbb{R}\) is an unobservable random error. Let \(x_1, \dots,x_n\) be the design vectors, \(y_1,\dots,y_n\) be the corresponding observations, and \(e_1,\dots,e_n\) be the random errors. We assume that \(e_1,\dots,e_n\) are \(m\)-dependent. Our aim is to construct empirical likelihood confidence regions for \(\beta\). It is shown that the blockwise empirical likelihood is a good way to deal with dependent samples.

MSC:

62J05 Linear regression; mixed models
62G30 Order statistics; empirical distribution functions
62G05 Nonparametric estimation
62G07 Density estimation
62E20 Asymptotic distribution theory in statistics
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References:

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