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|Title||Kernel Estimation of the Conditional Mode for Mixing Data|
|Title in Arabic||تقدير النواة للمنوال المشروط للبيانات الممزوجة|
We are interested in the area of nonparametric prediction, therefore, we study the relationship between a current observation and previous observations, where the conditional density function plays an important role. In this thesis, we study the kernel estimation of the conditional probability density function, and the conditional mode function. We start our study by considering the mode of a sample of identically independent distributed (i.i.d.) data. Then, we state some sufficient conditions under which the kernel estimator of the conditional mode is asymptotically normally distributed. In addition, we generalize it for the case of α-mixing processes by considering additional conditions on the α-mixing process to obtain the same asymptotic behavior in the i.i.d. case. Finally, we use the conditional mode estimation in some applications, using local and international real data and simulated data. the proposal estimator in three studies for simulation and real data proved it is good and efficiency estimator by MSE error and correlation coefficient.
|Publisher||الجامعة الإسلامية - غزة|
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