Statistical Inference for Regression Models with Covariate Measurement Error and Auxiliary Information

Area of Science:

• Statistics
• Econometrics
• Marketing Science

Background:

• Regression models are crucial for analyzing relationships between variables.
• Measurement errors in covariates can lead to biased and inconsistent statistical inference.
• Existing methods for handling measurement errors in regression have limitations, including undersmoothing requirements and restrictions on covariate observability.

Purpose of the Study:

• To develop a novel statistical inference method for regression models with covariates measured with errors.
• To address limitations of previous estimation techniques, such as undersmoothing and restrictions on observable covariates.
• To propose and evaluate a jackknife estimation procedure for improved bias and covariance matrix estimation.

Main Methods:

• Utilizing estimating equations for regression coefficient estimation in the presence of measurement errors.
• Developing a jackknife estimation technique by systematically omitting estimating equations.
• Establishing large sample properties of the proposed estimators.
• Conducting simulation studies to compare performance against existing methods.

Main Results:

• The proposed estimating equations method overcomes drawbacks of prior approaches.
• The jackknife estimator is asymptotically equivalent to the estimating equations estimator.
• Simulations indicate that the jackknife estimator exhibits reduced bias in small to moderate sample sizes.
• The jackknife method provides a consistent and heteroscedasticity-robust estimator for the asymptotic covariance matrix.

Conclusions:

• The novel estimating equations and jackknife methods offer improved statistical inference for regression with measurement errors.
• The jackknife approach enhances bias reduction and provides robust covariance estimation.
• The methods are validated through application to a marketing science dataset, demonstrating practical utility.