Two-layer EM algorithm for ALD mixture regression models: A new solution to composite quantile regression

The STIRPAT Analysis on Carbon Emission in Chinese Cities: An Asymmetric Laplace Distribution Mixture Model

“…For more details of the proposed ALDs mixture model and its implementation algorithm, please refer to the work of Wang and Xiang [12].…”

“…Here we briefly describe the ALDs mixture model proposed in Wang and Xiang [12], then apply it to perform the STIRPAT analysis on carbon emission via 76 cities in China during 2002-2012. An asymmetric Laplace distribution (ALD) proposed by Koenker and Machado [26] is a generalization of Laplace distribution (LD).…”

“…See Yu and Zhang [27] for a summary of its properties and extensions. Using the unifying bridge existing between the CQR estimation and the ALD, Wang and Xiang [12] proposed the ALDs mixture model, which could be formulated as:…”

“…Here we adopt the two-layer EM algorithm proposed in Wang and Xiang [12] to obtain the estimators for these unknown parameters. For more details of the proposed ALDs mixture model and its implementation algorithm, please refer to the work of Wang and Xiang [12].…”

“…The CQR estimation not only requires no specific distribution assumption for the error term, but also provides a more efficient estimator. Then in 2017, an improved CQR estimation named as ALDs mixture model is introduced [12]. It assumes that the error term follows a finite mixture of asymmetric Laplace distributions (ALDs), and then develops two-layer EM (Expectation-Maximum) algorithm to obtain the estimators, which shows higher performance.…”