Least Squares Method With Equality Constraints and Polynomial Approximation of Lorenz Curve

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18450%2F19%3A50015901" target="_blank" >RIV/62690094:18450/19:50015901 - isvavai.cz</a>

Výsledek na webu

<a href="https://mme2019.ef.jcu.cz/files/conference_proceedings.pdf" target="_blank" >https://mme2019.ef.jcu.cz/files/conference_proceedings.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Least Squares Method With Equality Constraints and Polynomial Approximation of Lorenz Curve

Popis výsledku v původním jazyce

The least squares method is frequently and successfully used in the solution of various different econometric problems. No restrictions on data sets are usually considered. The only widely known problem with a constraint is the one where a linear model heading through the origin is solved. Nevertheless, we can encounter approximation problems having more data restrictions. For instance, the Lorenz curve which is a curve heading through two given points. In this case, it is useful to apply a least squares method subject to constraints. In this paper, two possible solutions of problems with natural data restrictions are examined. First, it is showed that the constrained problem with two boundary values can be transformed into the classical least squares problem and a special form of the normal equation is derived. A more general problem is then introduced and the Lagrange multiplier method is used to develop a different form of the normal equation. Finally, a polynomial approximation of the Lorenz curve applied to the Czech Republic income data is introduced.

Název v anglickém jazyce

Least Squares Method With Equality Constraints and Polynomial Approximation of Lorenz Curve

Popis výsledku anglicky

The least squares method is frequently and successfully used in the solution of various different econometric problems. No restrictions on data sets are usually considered. The only widely known problem with a constraint is the one where a linear model heading through the origin is solved. Nevertheless, we can encounter approximation problems having more data restrictions. For instance, the Lorenz curve which is a curve heading through two given points. In this case, it is useful to apply a least squares method subject to constraints. In this paper, two possible solutions of problems with natural data restrictions are examined. First, it is showed that the constrained problem with two boundary values can be transformed into the classical least squares problem and a special form of the normal equation is derived. A more general problem is then introduced and the Lagrange multiplier method is used to develop a different form of the normal equation. Finally, a polynomial approximation of the Lorenz curve applied to the Czech Republic income data is introduced.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

50202 - Applied Economics, Econometrics

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Conference Proceedings, 37th International Conference on Mathematical Methods in Economics 2019

ISBN

978-80-7394-760-6

ISSN

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e-ISSN

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Počet stran výsledku

6

Strana od-do

332-337

Název nakladatele

Jihočeská univerzita

Místo vydání

České Budějovice

Místo konání akce

České Budějovice

Datum konání akce

11. 9. 2019

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000507570400055