Chapter 5 Conclusion
The simulations based on the basic functions did not show considerable difference between estimators. However, first generation wavelet estimator had a higher MSE and MAE compared to other estimators in the basic function case. In case of signals with uniform grids and different signal-to-noise-ratio, second generation wavelet estimators had much smaller MSE and MAE than other estimator except for a small number of cases where nonparametric estimators has smaller MSE or MAE.
The results show that for the uniform grid cases and for all tested signal-to-noise-ratio, first generation wavelet had a much larger MSE and MAE compared to second generation method. Changing the grid to the left-skewed and right-skewed did not have any noticeable effect on the MSE and MAE of the second generation wavelet and kernel smoothing, but results an increase in the MSE and MAE of first generation and spline.
In conclusion, the results showed second generation wavelet estimator is a suitable and powerful tool for analyzing the datasets with irregular grid. In would be interesting to study this estimators in the case with more than one independent variable and comparing the results with other estimators and applying methods to time series data which are correlated.