Georgy Shevlyakov

Robustness in data analysis : criteria and methods

General remarks Huber minimax approach Hampel approach optimization criteria in data analysis - a probability-free approach introductory remarks translation and scale equivariant contrast functions orthogonal equivariant contrast functions monotonically equivariant contrast functions minimal sensitivity to small perturbations in the data affine equivariate contrast functions robust mimimax estimation of location introductory remarks robust estimation of location in models with bounded variances robust estimation of location in models with bounded subranges robust estimators of multivariate location least informative lattice distributions robust estimation of scale introductory remarks measures of scale defined by functionals M-, L-, and R-estimators of scale Huber minimax estimator of scale final remarks robust regression and autoregression introductory remarks the minimax variance regression robust autoregression robust identification in dynamic models final remarks robustness of L1-norm estimators introductory remarks stability of L1-approximations robustness of the L1-regression final remarks robust estimation of correlation introductory remarks analysis - Monte Carlo experiment analysis - asymptotic characteristics synthesis minimax variance correlation two-stage estimators - rejection of outliers plus classics computation and data analysis technologies introductory remarks on computation adaptive robust procedures smoothing quantile functions by the Bernstein polynomials robust bivariate boxplots applications on robust elimination in the statistical theory of reliability robust detection of signals based on optimisation criteria statistical analysis of sudden cardiac death risk factors.

Priority queueing with finite buffer size and randomized push-out mechanism

The non-preemptive priority queueing with a flnite bufier is considered. We introduce a randomized push-out bufier management mechanism which allows to control very e‐ciently the loss probability of priority packets. The packet loss probabilities for priority and non-priority tra‐c are calculated using the generating function approach. In the particular case of the standard non-randomized push-out scheme we obtain explicit analytic expressions. The theoretical results are illustrated by numerical examples. The randomized push-out scheme is compared with the threshold based push-out scheme. It turns out that the former is much easier to tune than the latter. The proposed scheme can be applied to the Difierentiated Services of the Internet.

On Robust estimation of a correlation coefficient

Robust estimation of the correlation coefficient of a bivariate normal distribution is considered in the case of a contamination scheme. A number of conventional robust estimates are studied, and some new estimates are proposed. Their properties are examined on finite samples and in asymptotics with the use of Monte-Carlo and the influence functions techniques correspondingly. It is shown that one of the proposed estimates called a median correlation coefficient has high robustness properties.

Minimax variance estimation of a correlation coefficient for ε-contaminated bivariate normal distributions

A minimax variance (in the Huber sense) estimator of a correlation coefficient for [var epsilon]-contaminated bivariate normal distributions is given by the trimmed correlation coefficient. Consistency and asymptotic normality of this estimator are established, and the explicit expression for its asymptotic variance is obtained. The limiting cases of this estimator are the sample correlation coefficient with [var epsilon]=0 and the median correlation coefficient as [var epsilon]-->1. In [var epsilon]-contaminated normal models, the proposed trimmed correlation coefficient is superior in efficiency than the sample correlation coefficient.

Fast highly efficient and robust one-step M-estimators of scale based on Qn

A parametric family of M-estimators of scale based on the Rousseeuw–Croux Qn-estimator is proposed; estimator’s bias and efficiency are studied. A low-complexity one-step M-estimator is obtained allowing a considerably faster computation with greater than 80% efficiency and the highest possible 50% breakdown point. Analytical and Monte Carlo modeling results confirm the effectiveness of the proposed approach.

Asymptotically minimax bias estimation of the correlation coefficient for bivariate independent component distributions

For bivariate independent component distributions, the asymptotic bias of the correlation coefficient estimators based on principal component variances is derived. This result allows to design an asymptotically minimax bias (in the Huber sense) estimator of the correlation coefficient, namely, the trimmed correlation coefficient, for contaminated bivariate normal distributions. The limit cases of this estimator are the sample, median and MAD correlation coefficients, the last two simultaneously being the most B- and V-robust estimators. In contaminated normal models, the proposed estimators dominate both in bias and in efficiency over the sample correlation coefficient on small and large samples.

Power system state estimation with fusion method

A distributed power system consisting of multiple subsystems with individual state estimators needs to be globallymonitored using a system-wide state estimation function. To solve this problem, researchers have used several methods which can be categorized into three approaches: integrated state estimation, parallel state estimation and distributed state estimation. In literature, these methods are often separately applied and their temporary failures or states of poor quality can degrade the global state estimation.We propose a fusion method being able to combine different state estimation solutions in order to obtain a more reliable and accurate system-wide state estimation

Fusion of Decisions Modeled as Weak Signals in Wireless Sensor Networks

Distributed detection has newly received research interest due to the success of the emerging wireless sensor network (WSN) technology. To deal with the problem of distributed detection for the WSN having the energy constraint, the fusion of decisions modeled as weak signals is studied. By using the weak signal model and additive non-Gaussian noise channels in the canonical parallel fusion scheme, we propose an asymptotic fusion rule applicable for wide classes of noise probability density functions (pdfs). In the particular case of a known pdf, an optimal detection rule is given. Both asymptotic analysis and Monte Carlo simulation are used to examine the performance of the proposed detection fusion rule.

A New Measure of Outlier Detection Performance

Traditionally, the performance of statistical tests for outlier detection is evaluated by their power and false alarm rate. It requires ensuring the upper bound for false alarm rate while measuring the detection power, which proves to be a difficult task. In this paper we introduce a new measure of outlier detection performance H m as the harmonic mean of the power and unit minus false alarm rate. The H m maximizes the detection power by minimizing the false alarm rate and enables an easier way for evaluation and parameters tuning of an outlier detection algorithm.

On Robust Estimation of a Correlation Coefficient and Correlation Matrix

Various robust estimators of a correlation coefficient of the bivariate normal distribution are considered under a contamination scheme. Conventional and new robust estimators are studied in finite samples by Monte Carlo and in asymptotics by the influence functions technique. It is shown that the following proposed estimators: the one called a median correlation coefficient and the other, two-stage algorithm based on the preliminary rejection of outliers, with consequent application of the sample correlation coefficient to the rest of the data, have high robustness properties. These most advantageous approaches are used to construct robust estimators of a correlation matrix, and the two-stage algorithm with the rejection of outliers in every two dimensional cut of a multivariate space manifests high robustness.