Efficient Robust Estimation for Linear Models with Missing Response at Random | JoVE Visualize

Area of Science:

Statistics
Econometrics
Data Science

Background:

Mean regression methods for linear models with missing data fail with infinite error variance.
Likelihood function specification for imputation is challenging, especially with skewed data.
Existing methods struggle with robustness and efficiency in the presence of outliers or heavy-tailed errors.

Purpose of the Study:

To develop novel composite quantile regression and weighted quantile average procedures for parameter estimation in linear regression models with missing responses at random.
To enhance robustness and efficiency, particularly for heavy-tailed errors or outliers.
To simultaneously select significant variables and estimate parameters using adaptive penalization.

Main Methods:

Developed composite quantile regression and weighted quantile average estimation procedures.
Imputed both missing and observed responses using estimated conditional quantiles.
Utilized parametrically estimated propensity scores to weight check functions for parameter estimation.
Proposed adaptive penalization for variable selection and parameter estimation.
Investigated asymptotic properties and developed an efficient algorithm for implementation.
Introduced an IC-type statistic for selecting penalty parameters.

Main Results:

The proposed composite quantile regression and weighted quantile average methods provide robust and efficient coefficient estimation.
The methods are resistant to heavy-tailed errors and outliers in the response variable.
Adaptive penalization effectively performs simultaneous variable selection and parameter estimation.
Asymptotic properties of the estimators are theoretically established.
An efficient algorithm facilitates practical implementation.

Conclusions:

The novel quantile-based estimation procedures offer a robust and efficient alternative to mean regression for linear models with missing data.
The methods are particularly advantageous for skewed data and datasets with heavy-tailed error distributions.
The proposed adaptive penalization and model selection criteria enhance the practical utility of the techniques.