A Universal Kriging Predictor for Probability Density Function Based on Gaussian Mixture Model

With an increase in the demand of infinite‐dimensional data analysis, the research community has focused on the analysis of probability density distributions (PDFs). The modeling of PDF is a critical issue in many applications, for example, inflation rate and income distribution. In spatial analysis, making statistical inferences at unobserved locations is a critical task. Many interpolation methods, such as the Kriging method, are developed to appropriately address this problem. However, if we aim to infer PDFs at unobserved locations, there are very few alternative methods for performing the interpolation of PDFs. To solve this problem, we propose a Kriging interpolation method based on Gaussian mixture models (GMMs) for PDFs. We employ the expectation–maximization (EM) algorithm for estimating the parameters of GMM and utilize a linear solution system to determine the weight coefficients of the Kriging predictor. Furthermore, we conduct a theoretical study of the proposed method and establish the asymptotic normality of parameter estimates. Through extensive simulations, we demonstrate that the proposed method outperforms other existing methods in predicting the PDF at unknown locations. A real‐world data analysis based on household income distribution dataset shows that the proposed method is suitable for spatial prediction of PDFs at unknown locations.