Antieigenvalues and total antieigenvalues of normal operators

We will study antieigenvalues, total antieigenvalues, antieigenvectors, and total antieigenvectors for normal operators. This will generalize the earlier work of the author and Karl Gustafson on normal matrices on finite dimensional spaces. We will also study antieigenvalues and total antieigenvalues of semigroups generated by accretive normal operators.     

Minimax estimation and the least squares method

This paper is devoted to the problem of minimax estimation of parameters in linear regression models with uncertain second order statistics. The solution to the problem is shown to be the least squares estimator corresponding to the least favourable matrix of the second moments. This allows us to construct a new algorithm for minimax estimation closely connected with the least squares method. As an example, we consider the problem of polynomial regression introduced by A. N. Kolmogorov     

On a method of calculation of hypersingular integrals

We propose a method for calculation of one-dimensional and two-dimensional hypersingular integrals, which allows to obtain a solution in the analytic form in a series of cases. Based on this method, we construct an approximate method for calculation of one-dimensional and twodimensional hypersingular integrals having singularities on rather complicated manifolds. We give estimates of errors of suggested algorithms.     

Adjoint-free calculation method for conditional nonlinear optimal perturbations

Adjoint-free calculation method is proposed to compute conditional nonlinear optimal perturbations(CNOP) combined with initial perturbations and model parameter perturbations. The new approach avoids the use of adjoint technique in the optimization process. CNOPs respectively generated by ensemble-based and adjoint-based methods are compared based on a simple theoretical model.     

A truncated estimation method with guaranteed accuracy

This paper presents a truncated estimation method of ratio type functionals by dependent sample of finite size. This method makes it possible to obtain estimators with guaranteed accuracy in the sense of the $L_m$ -norm, $m\ge 2$ . As an illustration, the parametric and non-parametric estimation problems on a time interval of a fixed length are considered. In particular, parameters of linear (autoregressive) and non-linear discrete-time processes are estimated. Moreover, the parameter estimation problem of non-Gaussian Ornstein-Uhlenbeck process by discrete-time observations and the estimation problem of a multivariate logarithmic derivative of a noise density of an autoregressive process with guaranteed accuracy are solved. In addition to non-asymptotic properties, the limit behavior of presented estimators is investigated. It is shown that all the truncated estimators have asymptotic properties of basic estimators. In particular, the asymptotic efficiency in the mean square sense of the truncated estimator of the dynamic parameter of a stable autoregressive process is established.     

A parameter estimation method for model analysis

To solve a class of nonlinear parameter estimation problems, a method combining the regularized structured nonlinear total least norm (RSNTLN) method and parameter separation scheme is suggested. The method guarantees the convergence of parameters and has an advantages in reducing the residual norm over the use of RSNTLN only. Numerical experiments for two models appeared in signal processing show that the suggested method is more effective in obtaining solution and parameter with minimum residual norm.     

Density estimation by the penalized combinatorial method

Let f be an unknown multivariate density belonging to a prespecified parametric class of densities, , where k is unknown, but for all k and each has finite Vapnik-Chervonenkis dimension. Given an i.i.d. sample of size n drawn from f, we show that it is possible to select automatically, and without extra restrictions on f, an estimate with the property that . Our method is inspired by the combinatorial tools developed in Devroye and Lugosi (Combinatorial Methods in Density Estimation, Springer, New York, 2001) and it includes a wide range of density models, such as mixture models or exponential families.     

Stability likelihood of coalitions in a two-stage cartel game: An estimation method

Existing formulations of a cartel game aim at finding stable coalitions, i.e. a coalition is labelled stable or not stable. Uncertainty about the underlying structure and/or parameter values gives rise to sensitivity or uncertainty analysis. In this paper we follow a probabilistic robustness concept: What is the probability a product, design or policy really fulfils the requirements or properties it is expected to. Following this idea, we introduce the concept of stability likelihood: What is the probability a coalition can be labelled as stable. Methods are described based on Monte Carlo Simulation and Directional Simulation to estimate such a probability and we illustrate the performance for several cases.     

A new method of numerical calculation for stagnation point flows

Zusammenfassung Bei der Berechnung von zweidimensionalen inkompressiblen Potentialströmungen um abgerundete und symmetrische Körper erhält man einen Annäherungswert für den Bereich nahe dem Staupunkt, indem man annimmt, dass die Strömungsart dieselbe ist wie die um einen Kreiszylinder.Mit der Eingliederung dieses Verfahrens in Thom's Squaring Verfahren kann man dann die Berechnung leicht mit Hilfe eines elektronischen Computers durchführen. Dieses Verfahren könnte nützlich sein für eine Annäherungsauswertung ohne unangemessene Verfeinerung des Netzes im Strombereich.     

A robust and efficient estimation method for single-index varying-coefficient models

A new estimation procedure based on modal regression is proposed for single-index varying-coefficient models. The proposed method achieves better robustness and efficiency than that of Xue and Pang (2013). We establish the asymptotic normalities of proposed estimators and evaluate the performance of the proposed method by a numerical simulation.     

A method for constructing an optimal estimate calculation algorithm

The problem of searching for an optimal procedure for constructing the best (in a certain sense) algorithm in the family of estimate calculation algorithms is considered. Such a procedure is designed, and upper bounds for its complexity are derived. The case of a two-dimensional feature space is analyzed in detail.     

On the sign method of estimation for nonlinear regression

The present paper contains some results of application of a method of statistical data processing based on the use of the signs of deviations. The basis of this method is the sign technique developed in [1] for the linear regression. Interest in this method is due to the following reasons: for an almost arbitrary (and unknown to the experimenter) law of distribution of the observation errors, one succeeds in constructing distribution-free rules of testing hypotheses and interval estimation. Under very weak constraints on the properties of the initial distribution, these statistical criteria are in some sense optimal [2]. In addition, the sign methods are stable with respect to outliers and other noise. Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 131–142, Perm, 1990.