Search results

1

Grafy a teoria stabilnych alokacji

100%

Kozioł-Kaczorek D., Pietrych Ł.

Econometrics. Ekonometria. Advances in Applied Data Analytics

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2016

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issue 3 (53)

102-114

EN

The paper discusses a model of matching process which was proposed by two American mathematicians: David Gale and Lloyd S. Shapley. The basic concept defined by them was the stable allocation, which can be achieved with so-called deferred acceptance algorithm. The article analyzes the problems discussed by the theory of stable allocations on the basis of graph theory. It has been shown that the issues raised by this theory can be ana-lyzed using bipartite graphs and networks weighted. They also formulated conditions which should be met in purpose to solve a problem of matching. References relate to the labor market, as a discussed issue is applicable in practice, especially in the design of systems of recruitment companies. The aim of the article is to present the problem of bilateral associa-tions with the use of the language of graph theory and an indication of possible applications in the area of search and match of job seekers and employers.

2

Optimal allocation for equal probability two-stage design

75%

Molefe W.

Statistics in Transition new series

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2022

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vol. 23

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issue 4

129-148

EN

This paper develops optimal designs when it is not feasible for every cluster to be represented in a sample as in stratified design, by assuming equal probability two-stage sampling where clusters are small areas. The paper develops allocation methods for two-stage sample surveys where small-area estimates are a priority. We seek efficient allocations where the aim is to minimize the linear combination of the mean squared errors of composite small area estimators and of an estimator of the overall mean. We suggest some alternative allocations with a view to minimizing the same objective. Several alternatives, including the area-only stratified design, are found to perform nearly as well as the optimal allocation but with better practical properties. Designs are evaluated numerically using Switzerland canton data as well as Botswana administrative districts data.

3

Optimal Allocation of the Sample in the Poisson Item Count Technique

45%

Bernardelli M., Kowalczyk B.

Acta Universitatis Lodziensis. Folia Oeconomica

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2018

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vol. 3

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issue 335

35-47

PL

Pośrednie metody ankietowania stanowią podstawowe narzędzie stosowane w przypadku pytań drażliwych. Artykuł nawiązuje do nowej, pośredniej metody zaproponowanej w pracy Tiana i wsp. (2014) i dotyczy optymalnej alokacji próby między grupę badaną i kontrolną. W przypadku gdy alokacji dokonuje się w oparciu o estymatory metodą momentów, rozwiązanie optymalne nie nastręcza trudności i zostało podane w pracy Tiana i wsp. (2014). Jednak to estymacja metodą największej wiarogodności ma lepsze własności, w związku z czym wyznaczenie alokacji optymalnej na jej podstawie jest zadaniem, którego rozwiązanie wydaje się mieć większe znaczenie praktyczne. Zadanie to nie jest trywialne, gdyż w przypadku omawianej metody pośredniej drażliwa zmienna badana ma charakter ukryty i jest zmienną nieobserwowalną. Wzór explicite na wariancję estymatora największej wiarogodności nieznanej frakcji cechy drażliwej nie jest dostępny, a sam estymator wyznaczyć można, używając odpowiednich algorytmów numerycznych. Do określenia optymalnej alokacji próby w oparciu o estymatory NW wykorzystane zostały symulacje Monte Carlo oraz iteracyjny algorytm EM

EN

Indirect methods of questioning are of utmost importance when dealing with sensitive questions. This paper refers to the new indirect method introduced by Tian et al. (2014) and examines the optimal allocation of the sample to control and treatment groups. If determining the optimal allocation is based on the variance formula for the method of moments (difference in means) estimator of the sensitive proportion, the solution is quite straightforward and was given in Tian et al. (2014). However, maximum likelihood (ML) estimation is known from much better properties, therefore determining the optimal allocation based on ML estimators has more practical importance. This problem is nontrivial because in the Poisson item count technique the study sensitive variable is a latent one and is not directly observable. Thus ML estimation is carried out by using the expectation‑maximisation (EM) algorithm and therefore an explicit analytical formula for the variance of the ML estimator of the sensitive proportion is not obtained. To determine the optimal allocation of the sample based on ML estimation, comprehensive Monte Carlo simulations and the EM algorithm have been employed.

Refine search results

1 Acta Universitatis Lodziensis. Folia Oeconomica

1 Econometrics. Ekonometria. Advances in Applied Data Analytics

1 Statistics in Transition new series

1 Bernardelli M.

1 Kowalczyk B.

1 Kozioł-Kaczorek D.

1 Molefe W.

1 Pietrych Ł.

1 2022

1 2018

1 2016

Grafy a teoria stabilnych alokacji

Optimal allocation for equal probability two-stage design

Optimal Allocation of the Sample in the Poisson Item Count Technique