TITLE:
An Analysis of Two-Dimensional Image Data Using a Grouping Estimator
AUTHORS:
Kazumitsu Nawata
KEYWORDS:
Two-Dimensional Image Analysis, High-Resolution and Low-Resolution Im-ages, Semiparametric Estimator, Machine Learning, Grouping Estimator
JOURNAL NAME:
Open Journal of Statistics,
Vol.12 No.1,
February
7,
2022
ABSTRACT: Machine learning methods, one type of methods used in artificial
intelligence, are now widely used to analyze two-dimensional (2D) images in
various fields. In these analyses, estimating the boundary between two regions
is basic but important. If the model contains stochastic factors such as random
observation errors, determining the boundary is not easy. When the probability
distributions are mis-specified, ordinal methods such as probit and logit
maximum likelihood estimators (MLE) have large biases. The grouping estimator
is a semiparametric estimator based on the grouping of data that does not
require specific probability distributions. For 2D images, the grouping is
simple. Monte Carlo experiments show that the grouping estimator clearly
improves the probit MLE in many cases. The grouping estimator essentially makes
the resolution density lower, and the present findings imply that methods using
low-resolution image analyses might not be the proper ones in high-density
image analyses. It is necessary to combine and compare the results of high- and
low-resolution image analyses. The grouping estimator may provide theoretical
justifications for such analysis.