Least Absolute Relative Error Estimation

Least Absolute Relative Error Estimation.

Multiplicative regression model or accelerated failure time model, which becomes linear regression model after logarithmic transformation, is useful in analyzing data with positive responses, such as stock prices or life times, that are particularly common in economic/financial or biomedical studies. Least squares or least absolute deviation are among the most widely used criterions in statisti...

Local Least Absolute Relative Error Estimating Approach for Partially Linear Multiplicative Model

The partially linear multiplicative regression model is considered. This model, which becomes a partially linear regression model after taking logarithmic transformation, is useful in analyzing data with positive responses. Chen et al. (2010) mentioned that in many applications the size of relative error, rather than that of error itself, is the central concern of practitioners. We extend the c...

Regression Model Estimation Using Least Absolute Deviations , Least Squares Deviations and Minimax Absolute Deviations Criteria

Regression models and their statistical analyses is the most important tool used by scientists in data analyses especially for modeling the relationship among random variables and making predictions with higher accuracy. A fundamental problem in the theory of errors, which has drawn attention of leading mathematicians and scientists since past few centuries, was that of fitting functions. For t...

Least Absolute Value vs. Least Squares Estimation and Inference Procedures in Regression Models with Asymmetric Error Distributions

Least Absolute Deviations Estimation for the Accelerated Failure Time Model

The accelerated failure time (AFT) model assumes a linear relationship between the event time and the covariates. We propose a robust weighted least-absolute-deviations (LAD) method for estimation in the AFT model with right-censored data. This method uses the Kaplan-Meier weights in the LAD objective function to account for censoring. We show that the proposed estimator is root-n consistent an...