On the Possibilistic Approach to Linear Regression with Rounded or Interval-Censored Data

Abstract

Consider a linear regression model where some or all of the observations of the dependent variable have been either rounded or interval-censored and only the resulting interval is available. Given a linear estimator β of the vector of regression parameters, we consider its possibilistic generalization for the model with rounded/censored data, which is called the OLS-set in the special case β = Ordinary Least Squares. We derive a geometric characterization of the set: we show that it is a zonotope in the parameter space. We show that even for models with a small number of regression parameters and a small number of observations, the combinatorial complexity of the polyhedron can be high. We therefore derive simple bounds on the OLS-set. These bounds allow to quantify the worst-case impact of rounding/censoring on the estimator β . This approach is illustrated by an example. We also observe that the method can be used for quantification of the rounding/censoring effect in advance, before the experiment is made, and hence can provide information on the choice of measurement precision when the experiment is being planned.

Neural network model for imprecise regression with interval dependent variables

“…The sharp collection region (SCR) is one of three types of socalled "identification regions" that are discussed by Schollmeyer and Augustin in [21], which are sets of all parameters compatible with the interval data and model. This collection region was already introduced and analysed e.g., in [56,57,20] (cf., also [58]).…”

“…Over several decades various regression methods have been developed such as methods for linear regression models where the dependent variable has been either rounded or interval-censored [20,21], methods for models that have intervalvalued covariates and a precise dependent variable [22], interval-based algorithms for the data-fitting problem where measurement errors are supposed to be bounded and known [23,24], some probabilistic [25] and likelihood-based [26] methods, nonparametric methods [27,28], and others [29,30].…”

Algebraic Frameworks for Measurement in the Natural Sciences

“…In many applications, continuum models can be viewed as category-theoretic inverse limits of directed sequences of discrete models. 34 A concrete analysis of rounded data may be found in [1].…”

“…In technical terms, measurement procedures are captured by various (embedding) homomorphisms from given empirical order structures to selected numerical order structures. 1 This kind of measurement-theoretic representation is shown in Figure 1 below, in which the homomorphism Q between an empirical relational structure O, and a numerical relational structure R, < is also known under the uninspired name "scale of measurement".…”

Prediction of Fouling in Condenser Based on Fuzzy Stage Identification and Chebyshev Neural Network

“…Empirical model [1]- [2], probability model [3]- [4] are traditional fouling prediction model, empirical model, only considering an empirical coefficient parameter which isn't related to the time, to measure the impact of the fouling, can not satisfy the actual needs, not to mention determining the cleaning schedule for the equipments [5], probability model is suitable for simple heat exchanger, concerning to complicated heat exchanger such as condenser, the prediction accuracy will be greatly affected by time-varying parameters and big disturbance in the operating process of the condenser [6].…”