Notes on Kernel Based Mode Estimation Using More Efficient Sampling Designs

The mode estimation of a probability density function has become tractable in light of increasing computational power. The mode is one of the measures of the central tendency as well as the most probable value, which is not influenced by the tail of the distribution. Ranked set sampling (RSS) is a structural sampling method which improves the efficiency of parameter estimation in many circumstances and typically leads to a reduction in sample size and hence study cost. In this paper we investigate some of the asymptotic properties of kernel based mode estimation using RSS and compare it to mode estimation from that of simple random sampling (SRS). We demonstrate that kernel based mode estimation using RSS is consistent and asymptotically normal with lower variance than using SRS. Improved performance of the mode estimation using RSS compared to SRS is confirmed through a simulation study. A real data illustration using a Duchenne muscular dystrophy dataset is provided also.