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Dragi Anevski

Publications and source records attributed to Dragi Anevski.

9 recordsLinked to original sources
arXiv2026

Order restricted estimation of the parameter functions in an additive hazard model

In this paper we propose estimators of the parameter functions in an Aalen additive hasard regression model. The estimators are the individual and componentwise $l^2$ projections of the naive estimators resulting from the ordinary least squares estimator in the Aalen additive hazard model on the space of monotone functions. We provide pointwise limit distribution results for the resulting estimators, that exhibit $n^{-1/3}$ rate of convergence and the Chernoff distribution as the limit distribution.

math.ST↗
arXiv2026

Estimating the distribution of marks of a homogeneous marked Poisson process

In this paper we propose an estimator of the distribution of events of different kinds in a homogeneous Poisson process. We give an explicit solution for the maximum likelihood estimator of the distribution and derive its strong consistency and asymptotic normality. We also provide an order restricted estimator of the distribution and derive its consistency and asymptotic distribution. The inference problem gives rise to a Sylvester-Ramanujan system of equations. We discuss application of the estimator to the detection of neutrons in a novel detector developed at the European Spallation Source in Lund, Sweden.

stat.ME↗
arXiv2018

A stochastic process approach to multilayer neutron detectors

The sparsity of the isotope Helium-3, ongoing since 2009, has initiated a new generation of neutron detectors. One particularly promising development line for detectors is the multilayer gaseous detector. In this paper, a stochastic process approach is used to determine the neutron's energy from the additional data afforded by the multilayer nature of these novel detectors. The data from a multi-layer detector consists of counts of the number of absorbed neutrons along the sequence of the detector's layers, in which the neutron absorption probability is unknown. We study the Maximum Likelihood estimator for the intensity and absorption probability, show its consistency and asymptotic normality, as the experiment time (or the number of incoming neutrons) goes to infinity. We combine these results with known results on the relation between the absorption probability and the wavelength to derive an estimator of the wavelength and to show consistency and asymptotic normality for the estimator.

math.ST↗
arXiv2018

The asymptotic distribution of the isotonic regression estimator over a general countable pre-ordered set

We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution of the isotonized estimator is given by the concatenation of the separate isotonic regressions of the certain subvectors of an unrestrecred estimator's asymptotic distribution. Also, we show that the isotonization preserves the rate of convergence of the underlying estimator. We apply these results to the problems of estimation of a bimonotone regression function and estimation of a bimonotone probability mass function.

math.ST↗
arXiv2016

Functional central limit theorems for the Nelson-Aalen and Kaplan-Meier estimators for dependent stationary data

We derive process limit distribution results for the Nelson-Aalen estimator of a hasard function and for the Kaplan-Meier estimator of a distribution function, under different dependence assumptions. The data are assumed to be right censored observations of a stationary time series. We treat weakly dependent as well as long range dependent data, and allow for qualitative differences in the dependence for the censoring times versus the time of interest

math.ST↗
arXiv2016

Estimating a probability mass function with unknown labels

In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We prove strong consistency and derive the rates of convergence, for an extended model version of the estimator. We also study a sieved estimator for which similar consistency results are derived. Numerical computation of the sieved estimator is of great interest for practical problems, such as forensic DNA analysis, and we present a computational algorithm based on the stochastic approximation of the expectation maximisation algorithm. As an interesting byproduct of the numerical analyses we introduce an algorithm for bounded isotonic regression for which we also prove convergence.

math.ST↗
arXiv2011

Monotone spectral density estimation

We propose two estimators of a monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive pointwise limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.

math.ST↗
arXiv2007

Limit properties of the monotone rearrangement for density and regression function estimation

The monotone rearrrangement algorithm was introduced by Hardy, Littlewood and Pólya as a sorting device for functions. Assuming that $x$ is a monotone function and that an estimate $x_n$ of $x$ is given, consider the monotone rearrangement $\hat{x}_n$ of $x_n$. This new estimator is shown to be uniformly consistent. Under suitable assumptions, pointwise limit distribution results for $\hat{x}_n$ are obtained. The framework is general and allows for weakly dependent and long range dependent stationary data. Applications in monotone density and regression function estimation are detailed.

math.ST↗