KERNEL-SMOOTHED CONDITIONAL QUANTILES OF CORRELATED BIVARIATE DISCRETE DATA.

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Standard quantile regression methods assume continuous covariates, limiting their application with discrete socio-economic data.
• Discrete variables are common in research due to measurement scales and confidentiality needs.
• Existing methods struggle with pairwise correlations between discrete response and covariate variables.

Purpose of the Study:

• To develop a nonparametric estimation algorithm for conditional quantiles with discrete response and covariate variables.
• To address the challenge of pairwise correlations between these discrete variables.
• To enhance computational efficiency for large datasets through data aggregation.

Main Methods:

• Proposed a novel algorithm for nonparametric estimation of conditional quantiles for discrete variables.
• Utilized a binning operation to aggregate data into smaller subsets for computational efficiency.
• Developed two kernel-based binned conditional quantile estimators: one for untransformed and one for rank-transformed discrete response data.

Main Results:

• Established asymptotic properties for both proposed estimators.
• Demonstrated excellent estimation accuracy (bias, MSE, confidence interval coverage) through simulations.
• Showcased significant computational savings compared to direct kernel estimation on large datasets.

Conclusions:

• The proposed method effectively estimates conditional quantiles for discrete, potentially correlated variables.
• Data prebinning offers substantial computational advantages for large-scale analyses.
• The methodology is applicable to real-world health datasets, such as patient data for congestive heart failure.