Wyniki wyszukiwania - Biblioteka Nauki

1

Applications of robust statistics in the portfolio theory

100%

Kaszuba B.

Mathematical Economics

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2012

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nr 8 (15)

63-82

EN

The appropriate selection of portfolio components and determining their weights have a significant influence on the later performance of the investor. The classical method of calculating the weights of individual components in mean variance portfolios is based on sample mean and sample covariance matrix, which are optimal when the data come from multivariate normal distribution. In practice, the distribution of stock returns is not a normal distribution and frequently (albeit to a small extent) is contaminated by outliers; therefore, theoretically, a better approach to determine optimal weights in a portfolio would be to apply robust estimation methods. The main contribution of this paper is to present the possibilities of applying robust statistics methods in the Markowitz portfolio theory. This article contains an overview of the most important robust estimators applied in the portfolio theory. All the methods have been grouped according to the method of determining the outliers and to the accepted disorder models. Moreover, it presents the relevant achievements to date and the results of empirical research in this field. It also shows the potential problems resulting from the practical application of the robust estimation in the rolling horizon.

2

Robust estimation in interlaboratory measurements with small number of measurements

88%

Volodarsky E. T. , Warsza Z. L.

Measurement Automation Monitoring

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2015

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tom Vol. 61, No. 4

104--110

EN

In this paper two robust methods of assessing the value and the uncertainty of the measurand from the samples of small number of experimental data are presented and compared. Those methods can be used when some measurements results contain outliers, i.e. when the values of certain measurement results significantly differ from the others. They allow to set a credible statistical parameters of the measurements with the use of all experimental data. The following considerations are illustrated by the numerical examples of multi-laboratory measurement data key comparison. Compared are the results obtained by a classical method with rejection of outliers with two robust methods: a rescaled median absolute deviation MADS and an iterative two-criteria method. The paper also presents the advantages of the robust iterative statistical method in estimating the accuracy of the tested laboratory measurement results during its accreditation on the sample of four elements with outlier. A comparison with the estimates obtained by the standard procedure for evaluating performance accuracy is also provided.

3

Finding Shortest Triangular Path and its Family inside a Digital Object

88%

Sarkar A. , Biswas A. , Dutt M. , Mondal S.

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2018

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tom Vol. 159, nr 3

297--325

EN

This article presents a combinatorial algorithm to find a shortest triangular path (STP) between two points inside a digital object imposed on triangular grid that runs in O(n/g log n/g) time, where n is the number of pixels on the contour of the object and g is the grid size. Initially, the inner triangular cover which maximally inscribes the object is constructed to ensure that the path lies within the object. An appropriate bounding parallelogram is considered with those two points in diagonally opposite corners and then one of the semi-perimeters of the parallelogram is traversed. Certain combinatorial rules are formulated based on the properties of triangular grid and are applied during the traversal whenever required to shorten the triangular path. A shortest triangular path between any two points may not be unique. Another combinatorial algorithm is presented, which finds the family of shortest triangular path (FSTP) (i.e., the region containing all possible shortest triangular paths) between two given points inside a digital object and runs in O(n/g log n/g) time. Experimental results are presented to verify the correctness, robustness, and efficacy of the algorithms. STP and FSTP can be useful for shape analysis of digital objects and determining shape signatures.

4

Robust Algorithm S to assess the precision of interlaboratory measurements

88%

Volodarsky E. T. , Warsza Z. L. , Kosheva L. , Idźkowski A.

Measurement Automation Monitoring

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2015

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tom Vol. 61, No. 4

111--114

EN

The application of robust statistical methods to assess the precision (uncertainty) of the results of interlaboratory comparison tests is presented. The case, when these results may include outliers is considered. An usual rejection of such data reduces the reliability of evaluation, especially for small samples. The robust methods take into consideration all samples data including outliers. The use of the robust method Algorithm S is provided for estimating the precision of some measuring method tested in comparative studies in the group of accredited laboratories. Result obtained for simulated example is very close to the case with rejection outliers, but more reliable.

5

The statistical models for interpreting the results of parcels area verification in integrated administration and control system IACS

75%

Wolski B. , Toś C.

Structure and Environment

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2018

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tom Vol. 10, no. 1

53--65

EN

A key element of the system IACS is the verification of the parcel area covered by direct subsidies. Control measurements are made by FOTO method, and in a small part by the direct inspection. Statistical methods are used in estimating the significance of differences. The results of such analysis are correct only when the empirical distributions are consistent with the theoretical ones. The problem of distribution adequacy is presented in the paper on the examples of three objects. The hypotheses about the possibility of using the commonly used distributions, and the appropriateness of the modification of the density curves were verified. By questioning the effectiveness of current methods of analysis, the authors point to the advantages of robust statistics. The cognitive effect of the analysis is to indicate the Laplace distribution as a statistical model of the analyzed differences. Research is concluded by proposal of post-control report that sums up relevant properties of the survey results.

PL

Kluczowym elementem programu IACS (Integrated Administration and Control System) jest weryfikacja powierzchni działek objętych dopłatami bezpośrednimi. Pomiary kontrolne wykonywane są metodą FOTO, a w niewielkiej części w ramach inspekcji terenowej. W ocenie istotności różnic zastosowanie znajdują metody statystyczne. Wyniki takich analiz są poprawne pod warunkiem zgodności rozkładów empirycznych z teoretycznymi. Problem adekwatności rozkładów zaprezentowano w artykule na przykładzie trzech obiektów. Zweryfikowano hipotezę o możliwości wykorzystania powszechnie stosowanych rozkładów oraz zbadano zasadność modyfikacji krzywych gęstości. Poddając w wątpliwość efektywność stosowanych obecnie metod analizy, Autorzy wskazują na zalety metod statystyki odpornościowej. Poznawczym efektem analizy jest wskazanie rozkładu Laplace’a jako statystycznego modelu analizowanych różnic. Konkluzję badań stanowi propozycja raportu pokontrolnego zawierającego istotne właściwości wyników pomiaru.

6

Stochastic multivariable self-tuning tracker for non-gaussian systems

75%

Filipovic V.

International Journal of Applied Mathematics and Computer Science

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2005

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tom 15

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nr 3

351-357

EN

This paper considers the properties of a minimum variance self-tuning tracker for MIMO systems described by ARMAX models. It is assumed that the stochastic noise has a non-Gaussian distribution. Such an assumption introduces into a recursive algorithm a nonlinear transformation of the prediction error. The system under consideration is minimum phase with different dimensions for input and output vectors. In the paper the concept of Kronecker's product is used, which allows us to represent unknown parameters in the form of vectors. For parameter estimation a stochastic approximation algorithm is employed. Using the concept of the stochastic Lyapunov function, global stability and optimality of the feedback system are established.

7

Zastosowanie statystyki odpornościowej na przykładzie badań międzylaboratoryjnych

63%

Volodarsky E. T. , Warsza Z. L.

Przegląd Elektrotechniczny

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2013

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tom R. 89, nr 11

260-267

PL

Przedstawiono dwie tzw. odporne metody statystyczne: o przeskalowanym odchyleniu medianowym MAD i iteracyjną Hubera. Sa one stosowanie do oceny niepewności próbek pomiarowych o małej liczbie danych z wartościami odstającymi (ang. outliers). Uwzględnia się w nich wszystkie dane, ale outliery traktuje się inaczej jako mniej wiarygodne. Porównano dla kilku przykładów z badań międzylaboratoryjnych wyniki obliczone wg procedury standardowej oraz oboma metodami odpornymi. Stwierdzono, że metodą Hubera można szacować dokładność pomiarów przy walidacji metody pomiarowej w porównaniu kluczowym i przy okresowej kontroli biegłości laboratorium, gdy dostępna jest jedynie mała próbka z outlierem.

EN

Two robust methods of assessing the uncertainty of samples of experimental data with outliers are presented, i.e.: a rescaled median absolute deviation MADS method and an iterative Huber method. They allow to set a credible accuracy parameters of the measurements with the use of all experimental data, but outliers as less reliable, differently are treated. For small size samples with outliers results obtained by a classical method with rejection of outliers and by above robust methods are compared. It is shown that Huber method can be successfully used in estimation of the accuracy in inter-laboratory measurements, such as key comparisons of the tested method and in proficiency testing in the control or accreditation of the laboratory if such small size sample is only available.

8

Stochastic multivariable self-tuning tracker for non-Gaussian systems

63%

Filipovic V.

International Journal of Applied Mathematics and Computer Science

|

2005

|

tom Vol. 15, no 3

351-357

EN

This paper considers the properties of a minimum variance self-tuning tracker for MIMO systems described by ARMAX models. It is assumed that the stochastic noise has a non-Gaussian distribution. Such an assumption introduces into a recursive algorithm a nonlinear transformation of the prediction error. The system under consideration is minimum phase with different dimensions for input and output vectors. In the paper the concept of Kronecker’s product is used, which allows us to represent unknown parameters in the form of vectors. For parameter estimation a stochastic approximation algorithm is employed. Using the concept of the stochastic Lyapunov function, global stability and optimality of the feedback system are established.

9

Highly robust statistical methods in medical image analysis

63%

Kalina J.

Biocybernetics and Biomedical Engineering

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2012

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tom Vol. 32, no. 2

3-16

EN

Standard multivariate statistical methods in medical applications are too sensitive to the assumption of multivariate normality and the presence of outliers in the data. This paper is devoted to robust statistical methods. In the context of medical image analysis they allow to solve the tasks of face detection and face recognition in a database of images. The results of the robust approaches in image analysis turn out to outperform those obtained with standard methods. Robust methods also have desirable properties appealing for practical applications, including dimension reduction and clear interpretability.

10

Zastosowanie estymacji odpornej w badaniach biegłości laboratorium przy niewielkiej liczbie pomiarów

51%

Volodarsky E. T. , Warsza Z. L. , Koshevaya L. A. , Palianychko D.

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tom R. 59, nr 6

554--557

PL

W pracy przedstawiono zalety odpornej iteracyjnej metody szacowania wskaźników dokładności pomiarów dla oceny biegłości laboratoriów badawczych do celów akredytacji i okresowej kontroli, w szczególności przy braku próbek wzorcowych i przy niewielkiej liczbie elementów próbki oraz występowaniu danej odstającej. Dotyczy to w szczególności laboratoriów, które muszą przeprowadzać badania niszczące lub o wysokich kosztach pomiarów. Porównano na przykładach liczbowych oceny dokładności otrzymane proponowaną iteracyjną metodą odporną i według procedur standardowych.

EN

Advantages of robust iterative statistical method for estimating the accuracy of performance of testing laboratories during their accreditation in the absence of reference materials and with small sample sizes and outliers are presented in the paper. These situation is observed in the laboratory performing the test with the destruction of the samples or in the case of very expensive testing. A comparison with the estimates obtained by the standard procedure for evaluating performance accuracy is also provided.