Aleksey Polunchenko

Aleksey Polunchenko
Binghamton University | SUNY Binghamton · Department of Mathematical Sciences

Ph.D.

About

41
Publications
5,725
Reads
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796
Citations
Citations since 2016
22 Research Items
552 Citations
2016201720182019202020212022020406080100
2016201720182019202020212022020406080100
2016201720182019202020212022020406080100
2016201720182019202020212022020406080100
Additional affiliations
August 2009 - August 2012
University of Southern California
Position
  • Research Associate
Education
August 2008 - May 2009
University of Southern California
Field of study
  • Mathematical Finance
August 2004 - August 2009
University of Southern California
Field of study
  • Applied Mathematics
September 2002 - June 2004
Moscow Institute of Physics and Technology
Field of study
  • Applied Physics and Mathematics

Publications

Publications (41)
Article
Full-text available
Change-of-measure is a powerful technique used across statistics, probability and analysis. Particularly known as Wald's likelihood ratio identity, the technique enabled the proof of a number of exact and asymptotic optimality results pertaining to the problem of quickest change-point detection. Within the latter problem's context we apply the tech...
Article
Full-text available
We address the sequential change-point detection problem for the Gaussian model where baseline distribution is Gaussian with variance \sigma^2 and mean \mu such that \sigma^2=a\mu, where a>0 is a known constant; the change is in \mu from one known value to another. First, we carry out a comparative performance analysis of four detection procedures:...
Article
Full-text available
We provide an overview of the state-of-the-art in the area of sequential change-point detection assuming discrete time and known pre- and post-change distributions. The overview spans over all major formulations of the underlying optimization problem, namely, Bayesian, generalized Bayesian, and minimax. We pay particular attention to the latest adv...
Article
Full-text available
Several variations of the Shiryaev-Roberts detection procedure in the context of the simple changepoint problem are considered: starting the procedure at $R_0=0$ (the original Shiryaev-Roberts procedure), at $R_0=r$ for fixed $r>0$, and at $R_0$ that has a quasi-stationary distribution. Comparisons of operating characteristics are made. The differe...
Article
Full-text available
In 1985, for detecting a change in distribution, Pollak introduced a specific minimax performance metric and a randomized version of the Shiryaev-Roberts procedure where the zero initial condition is replaced by a random variable sampled from the quasi-stationary distribution of the Shiryaev-Roberts statistic. Pollak proved that this procedure is t...
Preprint
Full-text available
The topic of interest is the evaluation of the integral I(α;β)≔∫α+∞W1,β2(x)dxx2withα∈(0,∞)andβ∈ℂsuch thatW1,β(α)=0,where Wa,b(z) denotes the Whittaker W function. The question is brought about by a certain Sturm–Liouville problem: the (discrete) spectrum of the respective Sturm–Liouville operator is captured by β=βk, k∈N, and I(α;β) gives the (posi...
Preprint
Full-text available
For the classical Shiryaev--Roberts martingale diffusion considered on the interval $[0,A]$, where $A>0$ is a given absorbing boundary, it is shown that the rate of convergence of the diffusion's quasi-stationary cumulative distribution function (cdf), $Q_{A}(x)$, to its stationary cdf, $H(x)$, as $A\to+\infty$, is no worse than $O(\log(A)/A)$, uni...
Article
We consider the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval [0,A] with absorption at a fixed A > 0. We derive analytically a closed-form formula for the distribution’s fractional moment of an arbitrary given order s∈R; the formula is consistent with that previously found by Polunchenko and Pepelyshev...
Preprint
Full-text available
We consider the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval $[0, A]$ with absorption at a fixed $A > 0$. We derive analytically a closed-form formula for the distribution's fractional moment of an arbitrary given order $s\in\mathbb{R}$; the formula is consistent with that previously found by Polunche...
Preprint
We consider the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval $[0,A]$ with absorption at a fixed $A>0$. We derive analytically a closed-form formula for the distribution's fractional moment of an {\em arbitrary} given order $s\in\mathbb{R}$; the formula is consistent with that previously found by Polun...
Article
Full-text available
We obtain a closed-form formula for the quasi-stationary distribution of the classical Shiryaev martingale diffusion considered on the positive half-line [A, +∞) withA>0 fixed; the state space’s left endpoint is assumed to be the killing boundary. The formula is obtained analytically as the solution of the appropriate singular Sturm–Liouville probl...
Article
Full-text available
We derive analytic closed-form moment and Laplace transform formulae for the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval [0, A] with absorption at a given A > 0.
Article
Full-text available
We obtain a closed-form formula for the quasi-stationary distribution of the classical Shiryaev martingale diffusion considered on the positive half-line $[A,+\infty)$ with $A>0$ fixed; the state space's left endpoint is assumed to be the killing boundary. The formula is obtained analytically as the solution of the appropriate singular Sturm-Liouvi...
Chapter
Full-text available
We offer a numerical study of the effect of headstarting on the performance of a Shiryaev-Roberts (SR) chart set up to control the mean of a normal process. The study is a natural extension of that previously carried out by Lucas and Crosier for the CUSUM scheme in their seminal 1982 paper published in Technometrics. The Fast Initial Response (FIR)...
Preprint
We derive analytic closed-form moment and Laplace transform formulae for the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval $[0,A]$ with absorption at a given $A>0$.
Chapter
We offer a numerical study of the effect of headstarting on the performance of a Shiryaev–Roberts (SR) chart set up to control the mean of a normal process. The study is a natural extension of that previously carried out by Lucas and Crosier (Technometrics 24(3):199–205, 1982. https://doi.org/10.2307/1268679) for the CUSUM scheme. The Fast Initial...
Article
For the classical continuous-time quickest change-point detection problem it is shown that the randomized Shiryaev–Roberts–Pollak procedure is asymptotically nearly minimax-optimal (in the sense of Pollak [Ann. Statist., 13 (1985), pp. 206–227]) in the class of randomized procedures with vanishingly small false alarm risk. The proof is explicit in...
Article
Full-text available
For the classical continuous-time quickest change-point detection problem it is shown that the randomized Shiryaev-Roberts-Pollak procedure is asymptotically nearly minimax-optimal (in the sense of Pollak 1985) in the class of randomized procedures with vanishingly small false alarm risk. The proof is explicit in that all of the relevant performanc...
Article
Full-text available
We consider the first exit time of a Shiryaev-Roberts diffusion with constant positive drift from the interval $[0,A]$ where $A>0$. We show that the moment generating function (Laplace transform) of a suitably standardized version of the first exit time converges to that of the unit-mean exponential distribution as $A\to+\infty$. The proof is expli...
Article
Full-text available
We consider the problem of quickest change-point detection where the observations form a first-order autoregressive (AR) process driven by temporally independent standard Gaussian noise. Subject to possible change are both the drift of the AR(1) process ($\mu$) as well as its correlation coefficient ($\lambda$), both known. The change is abrupt and...
Article
Full-text available
The gist of the quickest change-point detection problem is to detect the presence of a change in the statistical behavior of a series of sequentially made observations, and do so in an optimal detection-speed-vs.-"false-positive"-risk manner. When optimality is understood either in the generalized Bayesian sense or as defined in Shiryaev's multi-cy...
Article
Full-text available
We consider the diffusion generated by the equation with fixed, and where μ≠0 is given, and is standard Brownian motion. We assume that is stopped at with A>0 preset, and obtain a closed-from formula for the quasi-stationary distribution of , i.e., the limit , x∈[0,A]. Further, we also prove QA(x) to be unimodal for any A>0, and obtain its entire...
Article
Full-text available
We consider the problem of efficient financial surveillance aimed at "on-the-go" detection of structural breaks (anomalies) in "live"-monitored financial time series. With the problem approached statistically, viz. as that of multi-cyclic sequential (quickest) change-point detection, we propose a semi-parametric multi-cyclic change-point detection...
Article
Full-text available
We consider the quickest change-point detection problem where the aim is to detect the onset of a pre-specified drift in "live"-monitored standard Brownian motion; the change-point is assumed unknown (nonrandom). The topic of interest is the distribution of the Generalized Shryaev-Roberts (GSR) detection statistic set up to "sense" the presence of...
Conference Paper
Full-text available
We offer a numerical study of the effect of headstarting on the performance of a Shiryaev–Roberts (SR) chart set up to control the mean of a normal process. The study is a natural extension of that previously carried out by Lucas & Crosier (1982) for the CUSUM scheme in their seminal 1982 paper published in Technometrics. The Fast Initial Response...
Article
Full-text available
We establish a simple connection between certain in-control characteristics of the CUSUM Run Length and their out-of-control counterparts. The connection is in the form of paired integral (renewal) equations. The derivation exploits Wald's likelihood ratio identity and the well-known fact that the CUSUM chart is equivalent to repetitive application...
Article
Full-text available
We consider the quickest change-point detection problem where the aim is to detect the onset of a pre-specified drift in "live"-monitored standard Brownian motion; the change-point is assumed unknown (nonrandom). The object of interest is the distribution of the stopping time associated with the Generalized Shryaev-Roberts (GSR) detection procedure...
Conference Paper
Full-text available
We derive analytically an exact closed-form formula for the standard minimax Average Run Length (ARL) to false alarm delivered by the Generalized Shiryaev-Roberts (GSR) change-point detection procedure devised to detect a shift in the baseline mean of a sequence of independent exponentially distributed observations. Specifically, the formula is fou...
Article
Full-text available
We consider the issue of optimal design of the Exponentially Weighted Moving Average (EWMA) chart by properly selecting the smoothing factor and the initial value (headstart) of the decision statistic. The particular problem addressed is that of quickest detection of an abrupt change in the parameter of a discrete-time exponential model. Both pre-...
Conference Paper
Full-text available
We consider the basic quickest change-point detection problem with optimality understood in Pollak's minimax sense. The topic of interest is optimal design of the emerging Generalized Shiryaev-Roberts (GSR) detection procedure. To optimize the GSR procedure, we exploit the fact that the GSR procedure provides a lower bound on Pollak's minimax Supre...
Article
Full-text available
We propose a numerical method to evaluate the performance of the emerging Generalized Shiryaev--Roberts (GSR) change-point detection procedure in a "minimax-ish" multi-cyclic setup where the procedure of choice is applied repetitively (cyclically) and the change is assumed to take place at an unknown time moment in a distant-future stationary regim...
Conference Paper
Full-text available
We provide a bird's eye view onto the area of sequential change-point detection. We focus on the discrete-time case with known pre- and post-change data distributions and offer a summary of the forefront asymptotic results established in each of the four major formulations of the underlying optimization problem: Bayesian, generalized Bayesian, mini...
Article
Full-text available
We consider the problem of efficient on-line anomaly detection in computer network traffic. The problem is approached statistically, as that of sequential (quickest) changepoint detection. A multi-cyclic setting of quickest change detection is a natural fit for this problem. We propose a novel score-based multi-cyclic detection algorithm. The algor...
Article
Full-text available
We address a simple changepoint detection problem where observations are i.i.d. before and after the change with known pre-and post-change distributions. For this setting, the CUSUM test is known to be optimal in the minimax setting for Lorden's essential supremum metric, whereas the Shiryaev-Roberts procedure is optimal for detecting a change that...
Article
Full-text available
In 1985, for detecting a change in distribution Pollak introduced a minimax criterion and a randomized Shiryaev-Roberts procedure that starts off a random variable sampled from the quasi-stationary distribution of the Shiryaev-Roberts statistic. Pollak proved that this procedure is asymp-totically almost optimal as the mean time to false alarm beco...
Article
Full-text available
The CUSUM procedure is known to be optimal for detecting a change in distribution under a minimax scenario, whereas the Shiryaev-Roberts procedure is optimal for detecting a change that occurs at a distant time horizon. As a simpler alternative to the conventional Monte Carlo approach, we propose a numerical method for the systematic comparison of...
Article
Full-text available
For the most popular sequential change detection rules such as CUSUM, EWMA, and the Shiryaev-Roberts test, we develop integral equations and a concise numerical method to compute a number of performance metrics, including average detection delay and average time to false alarm. We pay special attention to the Shiryaev-Roberts procedure and evaluate...
Article
Full-text available
We study asymptotic properties (as A → ∞) of the first exit time from the interval [0, A] of a non-negative Harris-recurrent Markov process. It is shown that under certain fairly general conditions the limiting distribution of the suit-ably normalized first exit time is exponential E(1) and that the moment generating function converges to that of E...
Conference Paper
Full-text available
The problem of decentralized changepoint detection in a distributed multisensor setting with binary quantization (BQ) is addressed. Attention is drawn to the case of composite post-change hypotheses when the post-change parameter is unknown. A multichart CUSUM detection procedure with binary quantization, called the M-BQ-CUSUM test, is proposed. Th...
Article
Full-text available
We develop new procedures for change detection in distributed multi-sensor sys- tems and provide an analytical framework to predict their performance in terms of the tradeoff between detection delay and frequency of false alarms. The configuration where the sensors communicate to a common fusion center is considered. The change in the statistics of...

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