TY - JOUR

T1 - Regression models using the LINEX loss to predict lower bounds for the number of points for approximating planar contour shapes

AU - Jayasinghe, J. M.Thilini

AU - Ellingson, Leif

AU - Prematilake, Chalani

N1 - Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2022

Y1 - 2022

N2 - Researchers in statistical shape analysis often analyze outlines of objects. Even though these contours are infinite-dimensional in theory, they must be discretized in practice. When discretizing, it is important to reduce the number of sampling points considerably to reduce computational costs, but to not use too few points so as to result in too much approximation error. Unfortunately, determining the minimum number of points needed to achieve sufficiently approximate the contours is computationally expensive. In this paper, we fit regression models to predict these lower bounds using characteristics of the contours that are computationally cheap as predictor variables. However, least squares regression is inadequate for this task because it treats overestimation and underestimation equally, but underestimation of lower bounds is far more serious. Instead, to fit the models, we use the LINEX loss function, which allows us to penalize underestimation at an exponential rate while penalizing overestimation only linearly. We present a novel approach to select the shape parameter of the loss function and tools for analyzing how well the model fits the data. Through validation methods, we show that the LINEX models work well for reducing the underestimation for the lower bounds.

AB - Researchers in statistical shape analysis often analyze outlines of objects. Even though these contours are infinite-dimensional in theory, they must be discretized in practice. When discretizing, it is important to reduce the number of sampling points considerably to reduce computational costs, but to not use too few points so as to result in too much approximation error. Unfortunately, determining the minimum number of points needed to achieve sufficiently approximate the contours is computationally expensive. In this paper, we fit regression models to predict these lower bounds using characteristics of the contours that are computationally cheap as predictor variables. However, least squares regression is inadequate for this task because it treats overestimation and underestimation equally, but underestimation of lower bounds is far more serious. Instead, to fit the models, we use the LINEX loss function, which allows us to penalize underestimation at an exponential rate while penalizing overestimation only linearly. We present a novel approach to select the shape parameter of the loss function and tools for analyzing how well the model fits the data. Through validation methods, we show that the LINEX models work well for reducing the underestimation for the lower bounds.

KW - LINEX loss function

KW - Linear regression

KW - lower bound prediction

KW - planar contours

KW - shape analysis

UR - http://www.scopus.com/inward/record.url?scp=85116852635&partnerID=8YFLogxK

U2 - 10.1080/02664763.2021.1986685

DO - 10.1080/02664763.2021.1986685

M3 - Article

AN - SCOPUS:85116852635

VL - 49

SP - 4294

EP - 4313

JO - Journal of Applied Statistics

JF - Journal of Applied Statistics

SN - 0266-4763

IS - 16

ER -