Interval-valued data regression using nonparametric additive models

Abstract Interval-valued data are observed as ranges instead of single values and frequently appear with advanced technologies in current data collection processes. Regression analysis of interval-valued data has been studied in the literature, but mostly focused on parametric linear regression models. In this paper, we study interval-valued data regression based on nonparametric additive models. By employing one of the current methods based on linear regression, we propose a nonparametric additive approach to properly analyze interval-valued data with a possibly nonlinear pattern. We demonstrate the proposed approach using a simulation study and a real data example, and also compare its performance with those of existing methods.

[1]  Jan de Leeuw,et al.  Non-linear canonical correlation , 1983 .

[2]  T. Barnett.  Variations in Near-Global Sea Level Pressure , 1985 .

[3]  J. Horowitz.  Nonparametric Additive Models , 2012 .

[4]  J. Loh,et al.  Density estimation for grouped data with application to line transect sampling , 2010, 1011.2037.

[5]  Enno Mammen,et al.  Smooth backfitting in generalized additive models , 2008, 0803.1922.

[6]  Mathew W. McLean,et al.  Journal of Computational and Graphical Statistics Functional Generalized Additive Models Functional Generalized Additive Models Accepted Manuscript Accepted Manuscript , 2022 .

[7]  Lynne Billard,et al.  Dependencies and Variation Components of Symbolic Interval-Valued Data , 2007 .

[8]  W. Härdle,et al.  Estimation of additive regression models with known links , 1996 .

[9]  A. Hense,et al.  Internal variability in a 1000-yr control simulation with the coupled climate model ECHO-G — I. Near-surface temperature, precipitation and mean sea level pressure , 2005 .

[10]  Francisco de A. T. de Carvalho,et al.  Univariate and Multivariate Linear Regression Methods to Predict Interval-Valued Features , 2004, Australian Conference on Artificial Intelligence.

[11]  Edwin Diday,et al.  Capacities, Credibilities in Analysis of Probabilistic Objects by Histograms and Lattices , 1998 .

[12]  Hiroe Tsubaki,et al.  A bivariate generalized linear model with an application to meteorological data analysis , 2005 .

[13]  S. Wood.  Modelling and smoothing parameter estimation with multiple quadratic penalties , 2000 .

[14]  P. Bertrand,et al.  Descriptive Statistics for Symbolic Data , 2000 .

[15]  Francisco de A. T. de Carvalho,et al.  Centre and Range method for fitting a linear regression model to symbolic interval data , 2008, Comput. Stat. Data Anal..

[16]  Arnab Maity,et al.  Nonparametric additive regression for repeatedly measured data , 2009 .

[17]  Chen-Chia Chuang,et al.  Constructing the linear regression models for the symbolic interval-values data using PSO algorithm , 2011, Proceedings 2011 International Conference on System Science and Engineering.

[18]  E. Mammen,et al.  ORACLE-EFFICIENT NONPARAMETRIC ESTIMATION OF AN ADDITIVE MODEL WITH AN UNKNOWN LINK FUNCTION , 2010, Econometric Theory.

[19]  R. Tibshirani,et al.  Generalized additive models for medical research , 1986, Statistical methods in medical research.

[20]  Edwin Diday,et al.  Symbolic Data Analysis: Conceptual Statistics and Data Mining (Wiley Series in Computational Statistics) , 2007 .

[21]  Russ E. Davis,et al.  Predictability of Sea Surface Temperature and Sea Level Pressure Anomalies over the North Pacific Ocean , 1976 .

[22]  John E. Kutzbach,et al.  Empirical Eigenvectors of Sea-Level Pressure, Surface Temperature and Precipitation Complexes over North America , 1967 .

[23]  Yongho Jeon,et al.  A resampling approach for interval‐valued data regression , 2012, Stat. Anal. Data Min..

[24]  Ana Colubi,et al.  Linear Regression Analysis for Interval-valued Data Based on Set Arithmetic: A Review , 2013 .

[25]  Francisco de A. T. de Carvalho,et al.  Bivariate Generalized Linear Model for Interval-Valued Variables , 2009, 2009 International Joint Conference on Neural Networks.

[26]  Edward J. Tarbuck,et al.  The Atmosphere: An Introduction to Meteorology , 2015 .

[27]  R. Tibshirani,et al.  Linear Smoothers and Additive Models , 1989 .

[28]  J. Friedman,et al.  Estimating Optimal Transformations for Multiple Regression and Correlation. , 1985 .

[29]  S. Wood.  Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models , 2011 .

[30]  S. Wood.  Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models , 2004 .

[31]  Francis W. Zwiers,et al.  Detection of human influence on sea-level pressure , 2003, Nature.

[32]  Francisco de A. T. de Carvalho,et al.  Constrained linear regression models for symbolic interval-valued variables , 2010, Comput. Stat. Data Anal..

[33]  Edwin Diday,et al.  Probabilist, possibilist and belief objects for knowledge analysis , 1995, Ann. Oper. Res..

[34]  C. J. Stone,et al.  Additive Regression and Other Nonparametric Models , 1985 .

[35]  J. Friedman,et al.  Projection Pursuit Regression , 1981 .

[36]  Subhashis Ghosal,et al.  Fast Bayesian model assessment for nonparametric additive regression , 2014, Comput. Stat. Data Anal..

[37]  Fang Yao,et al.  Robust Estimation for Generalized Additive Models , 2014 .

[38]  Wolfgang Karl Härdle,et al.  Derivative Estimation and Testing in Generalized Additive Models , 2003 .

[39]  Gil González-Rodríguez,et al.  Estimation of a flexible simple linear model for interval data based on set arithmetic , 2011, Comput. Stat. Data Anal..

[40]  L. Billard,et al.  Regression Analysis for Interval-Valued Data , 2000 .

[41]  S. Wood.  Generalized Additive Models: An Introduction with R , 2006 .

[42]  G. Cordeiro,et al.  Bivariate symbolic regression models for interval-valued variables , 2011 .