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The estimation of the corruption perception index

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Baszczyńska A., Pekasiewicz D., Uniwersytet Łódzki; Wydział Ekonomiczno-Socjologiczny; Instytut Statystyki i Demografii
Acta Universitatis Lodziensis. Folia Oeconomica
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2011
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vol. 255
PL
W pracy przedstawiono wyniki nieparametrycznej analizy wskaźnika percepcji korupcji. Na analizę tę składa się metoda jądrowa estymacji funkcji gęstości oraz wybrane metody estymacji przedziałowej wartości średniej wskaźnika percepcji korupcji. Do rozważanych metod estymacji wartości średniej należą: jedna z metod bootstrapowych oraz metody wykorzystujące dodatkowe informacje o zmiennej takie jak asymetria rozkładu, ograniczoność zbioru wartości zmiennej. Przeprowadzona analiza dotyczy estymacji wskaźnika percepcji korupcji w 2008 roku różnymi metodami, w oparciu o próby proste różnej liczebności. Porównanie uzyskanych wyników estymacji pozwoliło sformułować wnioski dotyczące dokładności oszacowań, a tym samym efektywności rozpatrywanych metod.
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Application of Kernel Estimation in Analysis of Labour Productivity of the Largest Polish Firms in 2004-2008

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Batóg B., Batóg J., Mojsiewicz M.
Folia Oeconomica Stetinensia
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2009
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vol. 8
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issue 1
126-139
EN
The parametric methods of statistical and econometric analysis are not always useful in examination of labour productivity of economic entities. In previous works the Authors found that the labour productivity is characterized by the lack of stable regularities in the range of structure and interdependency. In that case it is possible to apply non-parametric methods. In the paper the Authors tried to model the distributions of the labour productivity in time by means of kernel estimation using classical approaches (Epanechnikov, Rosenblatt) and the new proposition called kernel B. It seems that proposed approach is a useful merger of the statistical modeling theory and economic practice which allows to analyze the changes in the labour productivity - the essential factor for long-term economic growth and the welfare of society. The empirical results show that the labour productivity in the largest Polish companies had increased in 2004-2008 but the growths had not the same dynamics in different economic sectors.
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Konwergencja bezrobocia w Polsce w latach 1999-2006

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Tyrowicz J., Wójcik P.
Gospodarka Narodowa. The Polish Journal of Economics
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2007
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vol. 219
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issue 10
1-20
EN
The article discusses the convergence of unemployment rates at the county level in Poland in 1999-2006, on the basis of available statistical data. The authors examine both β- and δ-convergence; the former involves the relationship between the growth of the unemployment rate and its initial level, and the latter is based on an analysis of the dispersion of the rates and their changes over time. The authors use methods that enable them to examine changes in the distribution of the analyzed variables. These methods include transition matrices and a nonparametric kernel estimation method. Transition matrices make it possible to determine the likelihood of a county’s unemployment rate increasing, decreasing or remaining constant, while classifying the rates into several brackets. Kernel estimation, in turn, makes it possible to analyze the full conditional function of the density of the distribution of the unemployment rate at the county level and its changes over time. These methods were borrowed from research into regional convergence for income. They make it possible to detect the occurrence of polarization, or the so-called club convergence. The analysis of unemployment rates at the county level in 1999-2006 reveals a far-reaching stability of the regional distribution of unemployment rates-in terms of both monthly and yearly changes. Over the past seven years, no δ-convergence has occurred. The researchers have only detected slightly growing similarities between labor markets in counties with the highest relative unemployment rates. The analysis of β-convergence reveals a far-reaching divergence of unemployment levels in individual counties in Poland. This trend is less pronounced in counties with the lowest relative unemployment rates, while being markedly stronger on labor markets heavily affected by joblessness. Overall, the study places a question mark over the effectiveness of cohesion policies carried out in Poland through various channels since 1999.
4
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ON THE RESAMPLING METHOD IN SAMPLE MEDIAN ESTIMATION

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Kończak G.
Acta Universitatis Lodziensis. Folia Oeconomica
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2014
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vol. 3
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issue 302
EN
Bootstrap is one of the resampling statistical methods. This method was proposed by B. Efron. The main idea of bootstrap is to treat the original sample of values as a stand-in for the population and to resample with replacement from it repeatedly. Bootstrap allows estimation of the sampling distribution of almost any statistics using only very simple methods. This paper presents a modification of a resampling procedure based on bootstrap sampling. The proposal leads to sampling from population with density function f(x), where f(x) is estimated based on the kernel estimation. The properties of the method were analyzed in the median estimation in Monte Carlo study.The proposal could be useful for the parameters estimation in the case of a small sample. This method could be used in quality control procedures such as control charts or in the acceptance sampling.
5
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Proposal of New Cluster Analysis Algorithm

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Korzeniewski J., University of Łódź C. o. S. M.
Acta Universitatis Lodziensis. Folia Oeconomica
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2006
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vol. 196
EN
One of well-known groups of cluster analysis methods is the group of methods based on density estimation. In the paper we propose a new method of defining dusters which consists of two steps. In the first step we find local maxima of the joint distribution thus establishing clusters centres. In the second step we assign observations to one of existing clusters centres. The number of clusters is assumed to be known. In both steps we use similar technique based on the kernel density estimator with the Epanechnikov kernel. The performance of the method is analyzed in an example of application to the Gordon (1999) data. In the analysis the Rousseeuw indices are used to assess clusters cohesion as well as and some comparisons with other methods of defining clusters are presented. The results look promising.
PL
Jedną z dobrze znanych grup metod analizy skupień są metody oparte na szacowaniu gęstości. W artykule zaproponowana jest nowa metoda wyszukiwania skupień, która składa się z dwóch kroków. W pierwszym kroku znajdujemy maksima lokalne rozkładu łącznego, które przyjmujemy jako centra skupień. W drugim kroku każda obserwacja przyłączana jest do jednego z centrów. Zakładamy z góry liczbę skupień. W obydwu krokach używamy tej samej techniki opartej na estymatorze jądrowym funkcji gęstości z jądrem Epanecznikowa. Działanie metody jest przeanalizowane na przykładzie danych Gordona (1999). W analizie wykorzystano indeksy Rousseeuwa spoistości skupień, jak również przedstawiono porównanie z innymi metodami analizowania skupień. Wyniki wyglądają obiecująco.
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BIAVERAGE AND MULIMODALITY IN INVESTIGATING DISTRIBUTION OF ELECTRICITY PRICES

88%
Baszczyńska A., Pekasiewicz D.
Acta Universitatis Lodziensis. Folia Oeconomica
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2014
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vol. 3
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issue 302
EN
In the paper chosen statistical methods concerning analysis of random variable distributions are presented. Investigating modality of distribution is one of the most interesting and important stages in random variable analysis. Among others, the following methods can be used: kernel density estimation, the Hartigan test of unimodality and the biavarage. The example showing application of these methods from the one-day-ahead market of electricity is presented.
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