Estimation of MSE-RPs and Resampling
Kai‐Tai Fang, Huajun Ye, Yongdao Zhou · 2025
This chapter concerns statistical simulation under the underlying distribution with some unknown parameters. Assume that the type of F ( x , θ) is known but with some unknown parameters θ. By a random sample one can find the estimates of the unknown parameters, denoted by https://www.w3.org/1998/Math/MathML" display="inline"> θ ^ https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003589389/c4fffe8c-66b5-414a-a8ca-034fdce51b49/content/math1_289.tif "/> , then we can generate MSE-RPs of and construction approximation distributions for F ( x , https://www.w3.org/1998/Math/MathML" display="inline"> θ ^ https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003589389/c4fffe8c-66b5-414a-a8ca-034fdce51b49/content/math1_289.tif "/> ). Statistical estimation via resampling from these approximation distributions is considered. A general theory for the consistency of statistical estimation is introduced. In this chapter, we pay more attention to estimating MSE-RPs of univariate distributions. In particular, the estimation of MSE-RPs for the location-scale distributions with unknown parameters is discussed. The moment estimation and maximum likelihood estimation and their bias correction are studied.