Nonparametric density estimation concerning social benefits in Malta

Abstract

Nonparametric density estimation involves obtaining an estimate for the unknown probability density function given a sample of size 𝑛 but without having any prior knowledge on the form of the function. We shall consider the wavelet and kernel density estimation methods to obtain the estimate of the unknown density function. Since this density function is unknown, we shall work in an infinite dimensional space. However, in practice we are not able to work in this space, thus we shall use the method of sieves to approximate our infinite dimensional space with a sequence of finite dimensional spaces. We shall use wavelets as our orthonormal bases which will then be used to obtain the required wavelet density estimator. On the other hand, the kernel density estimator is based on the choice on the smoothing parameter and the kernel function. We shall compare the two nonparmateric methods by applying both techniques to a sample of Maltese individuals who were entitled to receive different types of social benefits.