Uniformly asymptotic normality of estimation of the drift function for diffusion processes

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference Pub Date : 2025-02-21 DOI:10.1016/j.jspi.2025.106274

Shanchao Yang , Qi Lan , Xueyan Xu , Zhu Liang

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引用次数: 0

Abstract

The diffusion process is widely used in finance, and many scholars pay close attention to the statistical estimation of diffusion processes. Some literature has discussed the non parametric kernel estimation of drift and diffusion functions, and proved the consistency and asymptotic normality of the estimators, but the convergence rate of asymptotic normality has not been discussed yet. In this paper, we derive the convergence rate of uniformly asymptotic normality of the drift function estimator by using the method of large and small blocks for stationary and

ρ

-mixing diffusion process. In the case of optimal bandwidth, the rate of uniformly asymptotic normality reaches

n^{- 2 / 15}

. In order to prove the results, we put forward some inequalities for mixing processes with variable sampling interval, which play a key role in the study of limit theory.

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来源期刊

Journal of Statistical Planning and Inference 数学-统计学与概率论

CiteScore

2.10

自引率

11.10%

发文量

审稿时长

3-6 weeks

期刊介绍： The Journal of Statistical Planning and Inference offers itself as a multifaceted and all-inclusive bridge between classical aspects of statistics and probability, and the emerging interdisciplinary aspects that have a potential of revolutionizing the subject. While we maintain our traditional strength in statistical inference, design, classical probability, and large sample methods, we also have a far more inclusive and broadened scope to keep up with the new problems that confront us as statisticians, mathematicians, and scientists. We publish high quality articles in all branches of statistics, probability, discrete mathematics, machine learning, and bioinformatics. We also especially welcome well written and up to date review articles on fundamental themes of statistics, probability, machine learning, and general biostatistics. Thoughtful letters to the editors, interesting problems in need of a solution, and short notes carrying an element of elegance or beauty are equally welcome.