What question did this study set out to answer?

The aim is to estimate the drift parameter θ of a fractional Ornstein-Uhlenbeck process driven by a Hermite process.

June 23, 2026Communication in Statistics- Theory and Methods0 citations

Minimum L 1 -norm estimation for fractional Ornstein-Uhlenbeck type process driven by a Hermite process

БРБ. Л. С. Пракаса РаоCR Rao Advanced Institute of Mathematics, Statistics and Computer Science

Key Points

The aim is to estimate the drift parameter θ of a fractional Ornstein-Uhlenbeck process driven by a Hermite process.
Developed a minimum L1-norm estimator for drift parameter θ.
Analyzed asymptotic properties of the estimator as noise approaches zero.
Studied the limiting distribution of the scaled difference between estimated and true parameter.
The minimum L1-norm estimator is shown to be consistent.
The random variable ϵ−1(θϵ∗−θ) converges to a limiting distribution as ϵ→0.

Abstract

We investigate the problem of estimation of the drift parameter θ of the fractional Ornstein-Uhlenbeck process dXt=θXtdt+ϵdZtq, H, X0=x0, 0≤t≤1, where the process Ztq, H, 0≤t≤1 is a Hermite process and ϵ is a small noise. We study the asymptotic properties of the minimum L1-norm estimator θϵ∗=arg⁡minθ∫01|Xt−xt (θ) |dt as ϵ→0. Here xt (θ) =x0exp⁡θt. We prove that the estimator is consistent and that the random variable ϵ−1 (θϵ∗−θ) has a limiting distribution as ϵ→0.

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