Quantile regression with nominated samples: An application to a bone mineral density study.

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Quantile regression is crucial for analyzing conditional quantiles, especially in the tails of distributions.
• Traditional methods like simple random sampling (SRS) can be inefficient for tail estimation.
• Nomination sampling designs leverage rank information to improve sample representativeness from distribution tails.

Purpose of the Study:

• To develop and evaluate new methods for quantile regression using maxima or minima nomination sampling.
• To propose novel loss functions that incorporate rank information from nominated samples.
• To provide an alternative approach translating nomination sampling problems to SRS equivalents.

Main Methods:

• Development of new loss functions for quantile regression with nominated samples.
• Formulation of an alternative method to convert nomination sampling problems to SRS problems.
• Comparative numerical studies assessing relative efficiencies against SRS.
• Application to a real-world cohort study on bone mineral density.

Main Results:

• Quantile regression with nomination sampling demonstrates higher relative efficiencies for tail quantiles compared to SRS.
• Methods based on nomination sampling can achieve comparable mean squared errors with substantially smaller sample sizes (up to 1/10th of SRS).
• The approach is effective in analyzing bone mineral density quantiles in a large cohort study.

Conclusions:

• Nomination sampling designs offer a more efficient and cost-effective alternative to SRS for quantile regression, particularly for tail analysis.
• The proposed methods effectively utilize rank information to improve estimation accuracy.
• This approach has significant practical implications for large-scale studies requiring precise tail quantile estimation.