Related papers: Optimal estimation of the rough Hurst parameter in…
Understanding signal behavior across scales is vital in areas such as natural phenomena analysis and financial modeling. A key property is self-similarity, quantified by the Hurst exponent (H), which reveals long-term dependencies.…
This paper presents $whittlehurst$, a Python package implementing Whittle's likelihood method for estimating the Hurst exponent in fractional Brownian motion (fBm). While the theoretical foundations of Whittle's estimator are…
The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown…
In this short note, we show how to use concentration inequalities in order to build exact confidence intervals for the Hurst parameter associated with a one-dimensional fractional Brownian motion
Hurst exponent is an important feature summarizing the noisy high-frequency data when the inherent scaling pattern cannot be described by standard statistical models. In this paper, we study the robust estimation of Hurst exponent based on…
This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…
In this paper, we propose a modified Newton-Raphson algorithm to estimate the frequency parameter in the fundamental frequency model in presence of an additive stationary error. The proposed estimator is super efficient in nature in the…
The characteristic feature of semi-selfsimilar process is the invariance of its finite dimensional distributions by certain dilation for specific scaling factor. Estimating the scale parameter $\lambda$ and the Hurst index of such processes…
In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-dependent PDEs. The latter arise from the functional It\^o formula…
Optimal estimation of a coin's bias using noisy data is surprisingly different from the same problem with noiseless data. We study this problem using entropy risk to quantify estimators' accuracy. We generalize the "add Beta" estimators…
Many quantum algorithms contain an important subroutine, the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory.…
Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…
We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on $(0,\infty)$. For the maximum likelihood (ML) estimator and…
We propose a new algorithm to generate a fractional Brownian motion, with a given Hurst parameter, 1/2<H<1 using the correlated Bernoulli random variables with parameter p; having a certain density. This density is constructed using the…
We derive the strong consistency of the least squares estimator for the drift coefficient of a fractional stochastic differential system. The drift coeffcient is one-sided dissipative Lipschitz and the driving noise is additive and…
When measurements from dynamical systems are noisy, it is useful to have estimation algorithms that have low sensitivity to measurement noises and outliers. In the first set of results described in this paper we obtain optimal estimators…
Since the middle of the 90's, multifractional processes have been introduced for overcoming some limitations of the classical Fractional Brownian Motion model. In their context, the Hurst parameter becomes a Holder continuous function H(?)…
The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of…
Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…
We study the Hardy-H\'enon parabolic equations on $\mathbb{R}^{N}$ ($N=2, 3$) under the effect of an additive fractional Brownian noise with Hurst parameter $H>\max\left(1/2, N/4\right).$ We show local existence and uniqueness of a mid…