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Empirical likelihood for linear regression models with missing responses. (English) Zbl 1163.62031

Summary: To make inference on \(\beta\) \((\in R^p)\) in a linear regression model \(Y_i=x_i^\prime \beta +\epsilon _i\) with missing responses, Q. Wang and J. N. K. Rao [Empirical likelihood for linear regression models under imputation for missing responses. Can. J. Stat. 29, No. 4, 597–608 (2001; Zbl 0994.62060)] constructed an empirical likelihood (EL) statistic based on the ‘complete’ data set after linear regression imputation which is asymptotically a sum of weighted \(\chi_1^2\) variables with unknown weights. We use a new method to produce a ‘complete’ data set for \(Y\). Based on this data set, we construct an EL statistic on \(\beta \), and show that the EL statistic has the limiting distribution of \(\chi_p^2\) which is used to construct confidence regions for \(\beta \) without adjustment. Results of a simulation study on the finite sample performance of EL-based confidence regions for \(\beta \) are reported.

MSC:

62G08 Nonparametric regression and quantile regression
62E20 Asymptotic distribution theory in statistics
62J05 Linear regression; mixed models
62G15 Nonparametric tolerance and confidence regions
62G05 Nonparametric estimation

Citations:

Zbl 0994.62060
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References:

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