arXiv subjects

Stergios B. Fotopoulos

Publications and source records attributed to Stergios B. Fotopoulos.

5 recordsLinked to original sources

arXiv2026

High Dimensional Change Point Models for Two-Directional Data

We develop methodology for recovery of change points for data observed on more than one temporal index where changes may occur simultaneous in both indices, where the spatial component may be high dimensional. The work is motivated by climate monitoring problems where long series of data are available, e.g., daily observations (index 1) over several years (index 2). Such data may be evolving over the annual time scale, along with dynamic seasonal changes in the shorter time scale. We model this as a high dimensional mean process observed on a two dimensional grid with change points. Asymptotic estimation and inference results are developed under a single change point setup, including rates of convergence of the proposed method as well the resulting limiting distributions. The method is extended to the case of multiple changes. Theoretical results are supported numerically with monte-carlo simulations. We implement our work on a large scale climate data for the Pacific Northwest region of the United States.

stat.ME↗

arXiv2020

Inference on the change point in high dimensional time series models via plug in least squares

We study a plug in least squares estimator for the change point parameter where change is in the mean of a high dimensional random vector under subgaussian or subexponential distributions. We obtain sufficient conditions under which this estimator possesses sufficient adaptivity against plug in estimates of mean parameters in order to yield an optimal rate of convergence $O_p(ξ^{-2})$ in the integer scale. This rate is preserved while allowing high dimensionality as well as a potentially diminishing jump size $ξ,$ provided $s\log (p\vee T)=o(\surd(Tl_T))$ or $s\log^{3/2}(p\vee T)=o(\surd(Tl_T))$ in the subgaussian and subexponential cases, respectively. Here $s,p,T$ and $l_T$ represent a sparsity parameter, model dimension, sampling period and the separation of the change point from its parametric boundary. Moreover, since the rate of convergence is free of $s,p$ and logarithmic terms of $T,$ it allows the existence of limiting distributions. These distributions are then derived as the {\it argmax} of a two sided negative drift Brownian motion or a two sided negative drift random walk under vanishing and non-vanishing jump size regimes, respectively. Thereby allowing inference of the change point parameter in the high dimensional setting. Feasible algorithms for implementation of the proposed methodology are provided. Theoretical results are supported with monte-carlo simulations.

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arXiv2019

An efficient two step algorithm for high dimensional change point regression models without grid search

We propose a two step algorithm based on $\ell_1/\ell_0$ regularization for the detection and estimation of parameters of a high dimensional change point regression model and provide the corresponding rates of convergence for the change point as well as the regression parameter estimates. Importantly, the computational cost of our estimator is only $2\cdotp$Lasso$(n,p)$, where Lasso$(n,p)$ represents the computational burden of one Lasso optimization in a model of size $(n,p)$. In comparison, existing grid search based approaches to this problem require a computational cost of at least $n\cdot {\rm Lasso}(n,p)$ optimizations. Additionally, the proposed method is shown to be able to consistently detect the case of `no change', i.e., where no finite change point exists in the model. We work under a subgaussian random design where the underlying assumptions in our study are milder than those currently assumed in the high dimensional change point regression literature. We allow the true change point parameter $τ_0$ to possibly move to the boundaries of its parametric space, and the jump size $\|β_0-γ_0\|_2$ to possibly diverge as $n$ increases. We then characterize the corresponding effects on the rates of convergence of the change point and regression estimates. In particular, we show that, while an increasing jump size may have a beneficial effect on the change point estimate, however the optimal rate of regression parameter estimates are preserved only upto a certain rate of the increasing jump size. This behavior in the rate of regression parameter estimates is unique to high dimensional change point regression models only. Simulations are performed to empirically evaluate performance of the proposed estimators. The methodology is applied to community level socio-economic data of the U.S., collected from the 1990 U.S. census and other sources.

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arXiv2016

Change-point analysis in frequency domain for chronological data

The purpose of this study is to provide a new methodology of how one can consistently estimate a change-point in time series data. In contrast with previous studies, the suggested methodology employs only the empirical spectral density and its first moment. This is accomplished when both the means and variances before and after the unidentified time point are unknown. Then, the well-known Gauss-Newton algorithm is applied to estimate and provide asymptotic results for the parameters involved. Simulations carried out under different distributions, sizes and unknown time points confirm the validity and accuracy of the methodology. The real-world example considered in the paper illustrates the robustness of the methodology in the presence of even extreme outliers.

stat.ME↗

arXiv2010

Exact asymptotic distribution of change-point mle for change in the mean of Gaussian sequences

We derive exact computable expressions for the asymptotic distribution of the change-point mle when a change in the mean occurred at an unknown point of a sequence of time-ordered independent Gaussian random variables. The derivation, which assumes that nuisance parameters such as the amount of change and variance are known, is based on ladder heights of Gaussian random walks hitting the half-line. We then show that the exact distribution easily extends to the distribution of the change-point mle when a change occurs in the mean vector of a multivariate Gaussian process. We perform simulations to examine the accuracy of the derived distribution when nuisance parameters have to be estimated as well as robustness of the derived distribution to deviations from Gaussianity. Through simulations, we also compare it with the well-known conditional distribution of the mle, which may be interpreted as a Bayesian solution to the change-point problem. Finally, we apply the derived methodology to monthly averages of water discharges of the Nacetinsky creek, Germany.

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