Abstract

This work presents several methods for feature detection in density estimation of univariate data. Two versions of the original Significant Zero Crossings for Derivatives (SiZer) method and two other SiZer approaches for signal detection with Euler and Hadwiger characteristics are explored. The latter are based on approximating level-crossing probabilities by expected number of upcrossings. In addition, a method for two-sample density comparison is proposed, based on the discussed SiZer methodologies. Estimating a single best bandwidth parameter value is difficult. Therefore, all signal detection and comparison approaches utilize the concept of scale-space and color maps, allowing consideration of curve smoothing at multiple bandwidth levels simultaneously. Finally, the proposed methodologies do not compete and are therefore not compared. Instead, they complement each other and combining the observations from all of them together allows for better statistical inference of the data set.