The law of iterated logarithm for the estimations of diffusion-type processes

This paper mainly discusses the asymptotic behaviours on the lasso-type estimators for diffusion-type processes with a small noise. By constructing the objective function on the estimation, in view of convexity argument, it is proved that the estimator for different values of γ satisfies the iterate...

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Veröffentlicht in:	Advances in difference equations 2020-01, Vol.2020 (1), p.1-15, Article 33
Hauptverfasser:	Mao, Mingzhi, Huang, Gang
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Approach of argmins Convergence Convexity Difference and Functional Equations Diffusion-type processes Functional Analysis Mathematics Mathematics and Statistics Objective function Ordinary Differential Equations Partial Differential Equations The law of iterated logarithm
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Beschreibung
Zusammenfassung:	This paper mainly discusses the asymptotic behaviours on the lasso-type estimators for diffusion-type processes with a small noise. By constructing the objective function on the estimation, in view of convexity argument, it is proved that the estimator for different values of γ satisfies the iterated logarithm law. The result also presents the exponential convergence principle for the estimator converging to the true value.
ISSN:	1687-1847 1687-1839 1687-1847
DOI:	10.1186/s13662-020-2506-5