The College of Administration and Economics at the University of Baghdad discussed , a master’s thesis in field of Statistics by the student (Ayat Hussein Hanoon) and tagged with (Estimation of the robust wavelet regression under the boundary problem with application) , Under supervision of (Assist.Prof Dr. Saad Kadhem Hamza )
The wavelet reduction estimator is an attractive technique for estimating nonparametric regression functions because of its high properties, but it suffers from the problem of parametricity resulting from the wavelet transform and being very sensitive in the case of the presence of outlier values in the dependent variable. The presence of these values leads to the failure of the wavelet transform to reconstruct a good signal in the case of choosing a general threshold for all levels of the wavelet coefficients.
In this thesis, a polynomial model and a local polynomial of degree 2 were used to address the boundary problem in wavelet reduction, in addition to using flexible robust threshold values to address the problem of outliers, as they deal with those coefficients at each level separately, unlike the global threshold values that deal with all levels at the same time. Estimation methods were used that varied in terms of addressing the boundary problem by using polynomial models and local polynomial models (polynomial models, local polynomial models), and using robust threshold values (Oh, Ebays). Robust estimation methods such as (MM, Median filter) were also used through simulation experiments. Three sample sizes and noise ratios (snr=5,10) and outlier ratios of 10% were chosen based on the application aspect. The thesis showed that the best estimation methods are the M4 method (MLPOWE), followed by the M2 method (LPOWE, LPOWO) through the comparison criterion (AMSE), as the research was conducted on real data. Daily, represented by the rates of solar radiation values falling in Iraq, specifically the city of Baghdad, and the relative humidity rates for the period from 3/15/2023 to 11/1/2023, with a sample size of (256), as the research showed the stability of the amount of solar radiation falling for the coming periods and the accuracy of the model used in the estimation.
