# Multiscale clustering of nonparametric regression curves

## TL;DR

This paper introduces a bandwidth-free multiscale clustering method for nonparametric regression time series, capable of identifying group structures without smoothing parameters, with proven statistical properties and demonstrated through simulations and real data.

## Contribution

It proposes a novel multiscale clustering approach that estimates group structures in nonparametric regression time series without bandwidth tuning, applicable to dependent data.

## Key findings

- Method successfully identifies group structures in simulated data.
- Theoretical analysis confirms estimator consistency under dependence.
- Real-data application demonstrates practical utility.

## Abstract

In a wide range of modern applications, we observe a large number of time series rather than only a single one. It is often natural to suppose that there is some group structure in the observed time series. When each time series is modelled by a nonparametric regression equation, one may in particular assume that the observed time series can be partitioned into a small number of groups whose members share the same nonparametric regression function. We develop a bandwidth-free clustering method to estimate the unknown group structure from the data. More precisely speaking, we construct multiscale estimators of the unknown groups and their unknown number which are free of classical bandwidth or smoothing parameters. In the theoretical part of the paper, we analyze the statistical properties of our estimators. Our theoretical results are derived under general conditions which allow the data to be dependent both in time series direction and across different time series. The technical analysis of the paper is complemented by a simulation study and a real-data application.