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https://doi.org/10.1007/s10549-021-06243-2

has been cited by the following article:

• 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.