Study of Nonparametric Estimation Techniques

Abstract

In this chapter, we studied the estimation of the reliability parameter 𝑅 based on maximum penalized likelihood estimation. Furthermore, some of the previous studies on Maximum Penalized Likelihood Estimation (MPLE) approaches were reviewed. Based on the simulation studies, a comparison of the MPLE of the reliability parameter 𝑅 when 𝜇1>𝜇2 and the MLE of the reliability parameter 𝑅 is made. The calculations were worked out based on different sample sizes. From the results in Tables (4.1 – 4.6), we observed that the values of the biases and mean square error of MPLE of 𝑅 and MLE of 𝑅 decreases as the sample size increases, except for few cases. This may be due to fluctuation in data. The biases and mean square error of MPLE of 𝑅 is smaller than biases and mean square error of MLE of 𝑅 for all sizes (n, m) and for ( 𝜇1=0.5, 𝜇2=0,𝜃1=1, 𝜃2=1 and true value of 𝑅=0.696735) and ( 𝜇1=1, 𝜇2=0,𝜃1=0.5, 𝜃2=1 and true value of 𝑅=0.754747), so the MPLE of 𝑅 is better than the MLE of 𝑅. Although relatively few preference, but it will be useful in medical fields that need to be accurate