Simple linear regression with interval censored dependent and independent variables.

Area of Science:

• Statistics
• Biometry
• Data Analysis

Background:

• Linear regression models are widely used but often assume precise measurements.
• Interval censoring, where data falls within a range rather than a specific point, is common in real-world applications.
• Existing methods may not adequately handle situations with both dependent and independent variables being interval-censored.

Purpose of the Study:

• To develop a simple linear regression model capable of handling interval-censored dependent and independent variables.
• To derive maximum likelihood estimators for the model parameters.
• To compare the performance of these new estimators against those from ordinary linear regression models and to develop prediction intervals.

Main Methods:

• The study focuses on a simple linear regression framework.
• Maximum likelihood estimation (MLE) is employed to estimate model parameters.
• Performance comparison is conducted against standard ordinary linear regression estimators.
• Prediction intervals for the response variable are developed.

Main Results:

• Maximum likelihood estimators for parameters in interval-censored linear regression were obtained.
• The performance of these estimators was evaluated and compared to ordinary linear regression.
• Prediction intervals for the response variable were successfully developed.

Conclusions:

• The proposed linear regression model effectively accommodates interval-censored data for both variables.
• Maximum likelihood estimators show competitive or superior performance compared to traditional methods.
• The model and prediction intervals are applicable to real-world scenarios, such as audiometric studies for threshold prediction.