Abstract
In this paper, we apply the empirical likelihood method to heteroscedastic partially linear errors-in-variables model. For the cases of known and unknown error variances, the two different empirical log-likelihood ratios for the parameter of interest are constructed. If the error variances are known, the empirical log-likelihood ratio is proved to be asymptotic chi-square distribution under the assumption that the errors are given by a sequence of stationary α-mixing random variables. Furthermore, if the error variances are unknown, we show that the proposed statistic is asymptotically standard chi-square distribution when the errors are independent. Simulations are carried out to assess the performance of the proposed method.
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Fan, GL., Liang, HY. & Wang, JF. Empirical likelihood for heteroscedastic partially linear errors-in-variables model with α-mixing errors. Stat Papers 54, 85–112 (2013). https://doi.org/10.1007/s00362-011-0412-3
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DOI: https://doi.org/10.1007/s00362-011-0412-3
Keywords
- Empirical likelihood
- Partially linear errors-in-variables model
- Heteroscedastic
- α-Mixing
- Confidence region