# Consistency of the k-Nearest Neighbor Regressor under Complex Survey Designs

arXiv: https://arxiv.org/abs/2603.17551 · HTML: https://mlsanity.com/paper/2603.17551/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 18 Mar 2026.

## Builds on (most cited first, 3 of 3)

- [Universal consistency and rates of convergence of multiclass prototype algorithms in metric spaces](https://mlsanity.com/paper/2010.00636/) (2020)
- [Building Consistent Regression Trees From Complex Sample Data](https://mlsanity.com/paper/1407.1079/) (2014)
- [Nearest neighbor imputation for general parameter estimation in survey sampling](https://mlsanity.com/paper/1707.00974/) (2017)

## Abstract (arXiv)

We study the consistency of the k-nearest neighbor regressor under complex survey designs. While consistency results for this algorithm are well established for independent and identically distributed data, corresponding results for complex survey data are lacking. We show that the k-nearest neighbor regressor is consistent under regularity conditions on the sampling design and the distribution of the data. We derive lower bounds for the rate of convergence and show that these bounds exhibit the curse of dimensionality, as in the independent and identically distributed setting. Empirical studies based on simulated and real data illustrate our theoretical findings.