%0 Journal Article
%T Wavelet Density Estimation and Statistical Evidences Role for a GARCH Model in the Weighted Distribution
%A Mohammad Abbaszadeh
%A Mahdi Emadi
%J Applied Mathematics
%P 410-416
%@ 2152-7393
%D 2013
%I Scientific Research Publishing
%R 10.4236/am.2013.42061
%X <p class=\"MsoNormal\">
	<span lang=\"EN-US\">We consider </span><i><span lang=\"EN-US\">n</span></i><span lang=\"EN-US\"> observations from the GARCH-type model: </span><i><span lang=\"EN-US\">Z</span></i><span lang=\"EN-US\"> = <i>UY</i></span><span lang=\"EN-US\">, where </span><i><span lang=\"EN-US\">U</span></i><span lang=\"EN-US\"> and </span><i><span lang=\"EN-US\">Y</span></i><span lang=\"EN-US\"> are independent random variables. We aim to estimate density function </span><i><span lang=\"EN-US\">Y</span></i><span lang=\"EN-US\"> where </span><i><span lang=\"EN-US\">Y</span></i><span lang=\"EN-US\"> have a weighted distribution. We determine a sharp upper bound of the associated mean integrated square error. We also make use of the measure of expected true evidence, so as to determine when model leads to a crisis and causes data to be lost.</span> 
</p>
%K Density Estimation
%K GARCH Model
%K Weighted Distribution
%K Wavelets
%K Statistical Evidences
%K Strongly Mixing
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=28420