Least absolute deviations estimation for uncertain regression with imprecise observations

Abstract

Traditionally regression analysis answers questions about the relationships among variables based on the assumption that the observation values of variables are precise numbers. It has long been dominated by least squares techniques, mostly due to their elegant theoretical foundation and ease of implementation. However, in many cases, we can only get imprecise observation values and the assumptions upon which the least squares is based may not be valid. So this paper characterizes the imprecise data in terms of uncertain variables and proposes a novel robust approach under the principle of least absolute deviations to estimate the unknown parameters in uncertain regression models. Finally, numerical examples are documented to illustrate our method.

Leave-$p$ -Out Cross-Validation Test for Uncertain Verhulst-Pearl Model With Imprecise Observations

“…We can get the uncertain distributionˆ ofŷ from (15). Take α as the confidence level and we can obtain that…”

“…Furthermore, the Chapman-Richards growth model [14] was studied by using the principle of least squares. Recently, Liu and Yang [15] put forward the least absolute deviations (LAD) estimate, and then Lio and Liu [13] presented the maximum likelihood estimation. Lio and Liu [12] provided the interval estimation for predicting the response variables.…”

Analysis and prediction of confirmed COVID-19 cases in China with uncertain time series

“…In addition, some researchers analysed the other uncertain regression models, such as the uncertain Verhulst-Pearl model by Liu ( 2019b ), the uncertain Gompertz regression model by Hu and Gao ( 2020 ), the uncertain revised regression model by Fang and Hong ( 2020 ), and the uncertain Chapman–Richards growth model by Liu and Jia ( 2020 ). Other scholars have suggested the various estimation approaches, such as the least absolute deviations estimation by Liu and Yang ( 2020b ), the Tukeys biweight estimation by Chen ( 2020 ), and the uncertain maximum likelihood estimation by Lio and Liu ( 2020 ). To test the fitness of estimation in an uncertain regression model, Ye and Liu ( 2020b ) introduced an uncertain hypothesis test.…”

Uncertain growth model for the cumulative number of COVID-19 infections in China

“…Yao and Liu (2018) proposed least squares estimations for unknown parameters in uncertain multiple regression models. Motivated by this, researchers considered other estimations such as least absolute deviations estimations (Liu and Yang 2020a), Tukey's biweight estimations (Chen 2020), and maximum likelihood estimations (Lio and Liu 2020). In addition, Lio and Liu (2018) provided the confidence interval for the response variable.…”