Asymptotic distributions for estimated expected functionals of general random elements

Yasutaka Shimizu

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arXiv · 2005.02532

Asymptotic distributions for estimated expected functionals of general random elements

Yasutaka Shimizu

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Abstract

We consider an estimation problem of expected functionals of a general random element that values in a metric space. If the functional forms an explicit function of some unknown parameters, we can estimate it by plugging-in a suitable estimator in to the function, and we can find the asymptotic distribution. However, if the functional is implicit in the parameters, it causes a problem of specifying asymptotic distribution. This paper gives a general condition to specify the asymptotic distribution even if the functional is implicit in the parameters, and further investigates it in detail when the random elements are semimartingales.

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Yasutaka Shimizu. 2020-05-05. Asymptotic distributions for estimated expected functionals of general random elements. https://arxiv.org/abs/2005.02532

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