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 -