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1

Kernel conditional quantile estimator under left truncation for functional regressors

Helal N., Said E. O.

Opuscula Mathematica

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2016

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Vol. 36, no. 1

25--48

EN

Let Y be a random real response which is subject to left-truncation by another random variable T. In this paper, we study the kernel conditional quantile estimation when the covariable X takes values in an infinite-dimensional space. A kernel conditional quantile estimator is given under some regularity conditions, among which in the small-ball probability, its strong uniform almost sure convergence rate is established. Some special cases have been studied to show how our work extends some results given in the literature. Simulations are drawn to lend further support to our theoretical results and assess the behavior of the estimator for finite samples with different rates of truncation and sizes.

2

Automatyzacja pracy sieci średniego napięcia a poziom ich niezawodności

Kornatka M

Przegląd Elektrotechniczny

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2014

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R. 90, nr 8

109-112

PL

W artykule, na podstawie danych pochodzących od operatorów systemów dystrybucyjnych, przedstawiono analizę stopnia automatyzacji pracy sieci średniego napięcia i poziomu ich niezawodności. Stosując estymatory jądrowe, wyznaczono rozkłady gęstości prawdopodobieństwa występowania wartości wskaźników SAIDI przerw nieplanowanych oraz liczby łączników sterowanych radiowo. Przedstawiono analizę wpływu poziomu stopnia automatyzacji sieci średniego napięcia na wartości wskaźnika SAIDI przerw nieplanowanych.

EN

The paper presents the analysis of degree of automation of the medium voltage networks operation and their level of reliability, based on the data of distribution system operators. The empirical probability density functions of the unplanned interruptions SAIDI indices and the number of radio-controlled switches have been determined with use of kernel estimators. The analysis of the impact of the automation degree level the MV networks on the SAIDI index unplanned interruptions has been presented.

3

Non-parametric methods of estimation of type A uncertainty of the environmental noise hazard indices

Batko W., Stępień B.

Archives of Acoustics

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2009

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Vol. 34, No. 3

295-303

EN

A control of environmental noise hazards requires estimation of uncertainty of noise indices LDEN, LN. Assessment of the type A standard uncertainty in measurement results - expressed as the standard deviation of the mean, calculated the most often at the assumption of a normal distribution - is significant for the process. Such assumption - in relation to the noise measurement results - is of a relatively low likelihood. Thus, there is a need of looking for non-standard procedures of the standard deviation estimation of the mean of results, without any information of belonging to a certain class of distribution. The aim of the hereby paper is an indication of the possibility of using non-parametric estimators of a density function in the calculation process of the type A standard uncertainty of environmental noise hazard indices. An attention was directed towards kernel estimators. The origin of their application, advantages and the method of constructing was described on the basis of a continuous monitoring of a traffic noise recorded on one of the main arteries of Kraków in 2004 and 2005. Usefulness of three forms of estimators, it means: kernel, unbiased and of maximum likelihood, was analysed.