arXiv subjects

Dmitry Otryakhin

Publications and source records attributed to Dmitry Otryakhin.

3 recordsLinked to original sources

arXiv2022

Automatic deforestation detectors based on frequentist statistics and their extensions for other spatial objects

This paper is devoted to the problem of detection of forest and non-forest areas on Earth images. We propose two statistical methods to tackle this problem: one based on multiple hypothesis testing with parametric distribution families, another one -- on non-parametric tests. The parametric approach is novel in the literature and relevant to a larger class of problems -- detection of natural objects, as well as anomaly detection. We develop mathematical background for each of the two methods, build self-sufficient detection algorithms using them and discuss practical aspects of their implementation. We also compare our algorithms with those from standard machine learning using satellite data.

cs.CV↗

arXiv2022

Estimation of sub-Gaussian random vectors using the method of moments

The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We present a method based on application of the method of moments to the empirical characteristic function. Further, we show almost sure convergence of our estimators, discover their limiting distribution and demonstrate their finite-sample performance.

math.ST↗

arXiv2018

Estimation of the linear fractional stable motion

In this paper we investigate the parametric inference for the linear fractional stable motion in high and low frequency setting. The symmetric linear fractional stable motion is a three-parameter family, which constitutes a natural non-Gaussian analogue of the scaled fractional Brownian motion. It is fully characterised by the scaling parameter $σ>0$, the self-similarity parameter $H \in (0,1)$ and the stability index $α\in (0,2)$ of the driving stable motion. The parametric estimation of the model is inspired by the limit theory for stationary increments Lévy moving average processes that has been recently studied in \cite{BLP}. More specifically, we combine (negative) power variation statistics and empirical characteristic functions to obtain consistent estimates of $(σ, α, H)$. We present the law of large numbers and some fully feasible weak limit theorems.

stat.ME↗