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DIRECTIONALLY DIFFERENTIABLE ECONOMETRIC MODELS
Published online by Cambridge University Press: 22 August 2017
Abstract
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The current article examines the limit distribution of the quasi-maximum likelihood estimator obtained from a directionally differentiable quasi-likelihood function and represents its limit distribution as a functional of a Gaussian stochastic process indexed by direction. In this way, the standard analysis that assumes a differentiable quasi-likelihood function is treated as a special case of our analysis. We also examine and redefine the standard quasi-likelihood ratio, Wald, and Lagrange multiplier test statistics so that their null limit behaviors are regular under our model framework.
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Footnotes
The co-editor, Yoon-Jae Whang, and two anonymous referees provided very helpful comments for which we are most grateful. The second author (Halbert White) passed away while the submission version was written. He formed the outline of the article and also provided an exemplary guide for writing a quality research paper. The authors benefited from discussions with Yoichi Arai, Seung Chan Ahn, In Choi, Horag Choi, Robert Davies, Graham Elliott, Chirok Han, John Hillas, Jung Hur, Hide Ichimura, Isao Ishida, Yongho Jeon, Estate Khmaladze, Chang-Jin Kim, Chang Sik Kim, Tae-Hwan Kim, Naoto Kunitomo, Hon Ho Kwok, Taesuk Lee, Bruce Lehmann, Mark Machina, Jaesun Noh, Kosuke Oya, Taeyoung Park, Peter Phillips, Erwann Sbai, Juwon Seo, Donggyu Sul, Denis Tkachenko, Albert K.C. Tsui, Hung-Jen Wang, Yoshihiro Yajima, Byung Sam Yoo, Ping Yu, and other seminar participants at Sogang University, the University of Auckland, the University of Hong Kong, the University of Tokyo, Osaka University, the Econometrics Study Group of the Korean Econometric Society, VUW, Yonsei University, and other conference participants at NZESG (Auckland, 2013). Cho acknowledges support from the Yonsei University Future-leading Research Initiative of 2017 (2017-22-0090).
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