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This article is devoted to the problem of detection of forest and nonforest 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 nonparametric 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 each other and with those from standard machine learning using satellite data.

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∈(0,1) and the stability index α∈(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 (Ann. Probab. 45 (2017) 4477–4528). 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., Funding Agencies:Project "Ambit fields: probabilistic properties and statistical inference" - Villum Fonden Danmarks GrundforskningsfondÖrebro University Project "Models for macro and financial economics after the financial crisis" - Jan Wallander and Tom Hedelius Foundation P18-0201

Linear fractional stable motion is a type of a stochastic integral driven by symmetric alpha-stable Levy motion. The integral could be considered as a non-Gaussian analogue of the fractional Brownian motion. The present paper discusses R package rlfsm created for numerical procedures with the linear fractional stable motion. It is a set of tools for simulation of these processes as well as performing statistical inference and simulation studies on them. We introduce: tools that we developed to work with that type of motions as well as methods and ideas underlying them. Also we perform numerical experiments to show finite-sample behavior of certain estimators of the integral, and give an idea of how to envelope workflow related to the linear fractional stable motion in S4 classes and methods. Supplementary materials, including codes for numerical experiments, are available online. rlfsm could be found on CRAN and gitlab.