Least Median Of Squares Estimation In Power Systems

Static state estimators currently in use in power systems are prone to masking by multiple bad data. This is mainly because the power system regression model contains many leverage points; typically they have a cluster pattern. As reported recently in the statistical literature, only high breakdown point estimators are robust enough to cope with gross errors corrupting such a model. This paper deals with one such estimator, the least median of squares estimator, developed by Rousseeuw in 1984. The robustness of this method is assessed while applying it to power systems. Resampling methods are developed, and simulation results for IEEE test systems discussed. © 1991 IEEE.

ROBREG: Stata module providing robust regression estimators

robreg provides a number of robust estimators for linear regression models. Among them are the high breakdown-point and high efficiency MM-estimator, the Huber and bisquare M-estimator, and the S-estimator, each supporting classic or robust standard errors. Furthermore, basic versions of the LMS/LQS (least median of squares) and LTS (least trimmed squares) estimators are provided. Note that the moremata package, also available from SSC, is required.

Stochastic Optimization in Robust Statistic

2000 Mathematics Subject Classification: 62J05, 62G35

Scheme of squares: Part I. Systems formalism for potentiostatic studies

The so-called “Scheme of Squares”, displaying an interconnectivity of heterogeneous electron transfer and homogeneous (e.g., proton transfer) reactions, is analysed. Explicit expressions for the various partial currents under potentiostatic conditions are given. The formalism is applicable to several electrode geometries and models (e.g., semi-infinite linear diffusion, rotating disk electrodes, spherical or cylindrical systems) and the analysis is exact. The steady-state (t→∞) expressions for the current are directly given in terms of constant matrices whereas the transients are obtained as Laplace transforms that need to be inverted by approximation of numerical methods. The methodology employs a systems approach which replaces a system of partial differential equations (governing the concentrations of the several electroactive species) by an equivalent set of difference equations obeyed by the various partial currents.

Scheme of squares: Part II. Systems formalism for sinusoidal perturbations

We extend here the formalism developed in Part I (for the potentiostatic response) to the admittance analysis of the scheme of squares. The results are applicable, as before, to several configurations of the electrode such as the rotating disk or the planar. All that one has to do is “to plug in” the appropriate matrices relating the interfacial concentrations to the fluxes.

Identification of prospective locations for generation expansion with least augmentation of network

With ever increasing demand for electric energy, additional generation and associated transmission facilities has to be planned and executed. In order to augment existing transmission facilities, proper planning and selective decisions are to be made whereas keeping in mind the interests of several parties who are directly or indirectly involved. Common trend is to plan optimal generation expansion over the planning period in order to meet the projected demand with minimum cost capacity addition along with a pre-specified reliability margin. Generation expansion at certain locations need new transmission network which involves serious problems such as getting right of way, environmental clearance etc. In this study, an approach to the citing of additional generation facilities in a given system with minimum or no expansion in the transmission facility is attempted using the network connectivity and the concept of electrical distance for projected load demand. The proposed approach is suitable for large interconnected systems with multiple utilities. Sample illustration on real life system is presented in order to show how this approach improves the overall performance on the operation of the system with specified performance parameters.

Towards identification of Wiener systems with the least amount of a priori information on the nonlinearity

In this paper, we investigate what constitutes the least amount of a priori information on the nonlinearity so that the FIR linear part is identifiable in the non-Gaussian input case. Three types of a priori information are considered including quadrant information, point information and locally monotonous information. In all three cases, identifiability has been established and corresponding identification algorithms are developed with their convergence proofs.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

A.S.T.M. manual on presentation of data : including Supplement A ... Supplement B ... Tables of squares and square roots /

Manual "originally issued in 1933; two supplements covering additonal material ... issued separately in 1935 ... combining this material in one volume and amplifying certain sections of the text"--Fore. to second printing, March, 1937.

Buchanan's tables of squares : containing the square of every foot, inch, and sixteenth of an inch between one sixteenth of an inch and fifty feet : for engineers and calculators /

Mode of access: Internet.

Barlow's tables of squares, cubes, square roots, cube roots, reciprocals of all integer numbers up to 10,000.

Mode of access: Internet.

High breakdown bundle adjustment

Identifying the parameters of a model such that it best fits an observed set of data points is fundamental to the majority of problems in computer vision. This task is particularly demanding when portions of the data has been corrupted by gross outliers, measurements that are not explained by the assumed distributions. In this paper we present a novel method that uses the Least Quantile of Squares (LQS) estimator, a well known but computationally demanding high-breakdown estimator with several appealing theoretical properties. The proposed method is a meta-algorithm, based on the well established principles of proximal splitting, that allows for the use of LQS estimators while still retaining computational efficiency. Implementing the method is straight-forward as the majority of the resulting sub-problems can be solved using existing standard bundle-adjustment packages. Preliminary experiments on synthetic and real image data demonstrate the impressive practical performance of our method as compared to existing robust estimators used in computer vision.