Intra and Outer Bootstrap Methods in Deming Regression Analysis

Abstract

Deming regression is a type of regression method that fits a regression line when the measurements of both the explanatory variable and the response variable are assumed to be subject to normally distributed errors. Recall that in ordinary least squares regression, the explanatory variable is assumed to be measured without error. Bootstrapping is a type of resampling where large numbers of smaller samples of the same size are repeatedly drawn, with replacement, from a single original sample. In this study, two different bootstrap methods are introduced as intra and outer bootstrap. It is proposed to use the introduced bootstrap methods together with Deming regression. This study provides an investigation of outer bootstrap Deming methods in cases where outliers are high, and intra bootstrap Deming methods in cases where the central spread is high. In the application part, the proposed methods on 7 different data sets previously used in the literature were used. It was seen that the intra bootstrap method results had less mean square error value than the classical Deming regression results in all datasets except one. According to the results obtained from the study, it was seen that the estimation values made with the intra bootstrap method gave more successful results than the classical bootstrap and outer bootstrap. Intra bootstrapping method will be a guide for researchers who will work with Deming regression and data with few observations.