A modified intersection of confidence intervals approach in the multivariate data density estimation

Data density estimation provides estimates of the probability function from which a set of data is drawn. It is better to estimate density from the data, hence the variable bandwidth approach. One of the popular approaches in density estimation is the multivariate kernel density estimation (MKDE). It is a nonparametric estimation approach which requires a kernel function and a band-width. This work focuses on a proposed modified intersection of confidence intervals (MICI_H) approach in the multivariate data density estimation. It is based on the intersection of confidence intervals (ICI). It is an attempt to correct the problem of discontinuities and boundary value problem in the density to be constructed. The quality of the estimates obtained of the proposed approach showed some improvements over the existing methods in kernel density estimation. This is seen in the lower asymptotic mean integrated error (AMISE) and a relative rate of convergence in the approach.

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