Empirical likelihood for nonparametric regression models with spatial autoregressive errors
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Online ISSN 2005-2863 Print ISSN 1226-3192
RESEARCH ARTICLE
Empirical likelihood for nonparametric regression models with spatial autoregressive errors Yinghua Li1,2 · Yongsong Qin2 · Yuan Li1 Received: 6 December 2019 / Accepted: 22 September 2020 © Korean Statistical Society 2020
Abstract In this paper, we propose to use the empirical likelihood (EL) method to construct confidence regions for nonparametric regression models with spatial autoregressive errors. It is shown that the EL statistics for the related parameters asymptotically have chi-squared distributions, which are used to construct confidence regions for the parameters. Results from simulation study and real data analysis are also presented. Keywords Nonparametric regression · Spatial autoregressive error · Empirical likelihood · Confidence region AMS Subject Classification Primary 62G05 · secondary 62E20
1 Introduction We firstly outline the introduction of the empirical likelihood (EL) method and its applications in dealing with some types of dependent data (other than spatial data). The EL method as a nonparametric method is an important approach in constructing confidence intervals, introduced by Owen (1988, 1990, 1991, 2001), which can be robust under various distributional assumptions but may still have good properties analogous to the parametric likelihood method. This method has only been used to deal with independent observations for a considerable time after it was introduced. To deal with dependent data, Kitamura (1997) first proposed the blockwise EL (BEL) method to construct confidence intervals for parameters with mixing samples. Chen and Wong (2009) developed BEL method to obtain confidence * Yongsong Qin [email protected] 1
School of Economics and Statistics, Guangzhou University, Guangzhou 510006, Guangdong, China
2
School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, Guangxi, China
13
Vol.:(0123456789)
Journal of the Korean Statistical Society
intervals for quantiles with mixing samples. For time series, Mykland (1995) made the connection between the dual likelihood and the EL and applied the EL approach to models with martingale structures. Chuang and Chan (2002) introduced the EL method to the autoregressive (AR) models where the disturbances form a martingale difference sequence. Chan and Ling (2006) developed the EL for regular generalized autoregressive conditional heteroskedasticity (GARCH) models. In this part, we summarize the progress of the generalized method of moments (GMM), quasi maximum likelihood (QML) method and nonparametric method (other than EL method) used in parametric/nonparametric spatial models. Spatial data arise in a variety of fields, including econometrics, epidemiology, environmental science, image analysis, oceanography and many others. Many spatial econometric models were inspired by questions arising in regional science and economic geography, where the units of observations are geographically determined and the structure of the dependence among these units
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