Classification of Non-Parametric Regression Functions in Longitudinal Data Models

Abstract

We investigate a longitudinal data model with non-parametric regression functions that may vary across the observed individuals. In a variety of applications, it is natural to impose a group structure on the regression curves. Specifically, we may suppose that the observed individuals can be grouped into a number of classes whose members all share the same regression function. We develop a statistical procedure to estimate the unknown group structure from the data. Moreover, we derive the asymptotic properties of the procedure and investigate its finite sample performance by means of a simulation study and a real data example.

Multiscale clustering of nonparametric regression curves

“…Indeed, the clusters produced by our multiscale method are fairly similar to those obtained there. Hence, our multiscale approach confirms the results of the bandwidth-dependent algorithm from Vogt and Linton (2017), but without the need to go through the complicated bandwidth-selection procedure from there which may very well perform less accurate in other applications. 9 Extensions and modifications 9.1 Extension to the multivariate case and to other model settings Throughout the paper, we have restricted attention to real-valued regressors X it .…”

“…In what follows, we revisit the application example from Vogt and Linton (2017). The aim of this example is to investigate the effect of trading venue fragmentation on market quality in the European stock market.…”

“…, G K 0 along with their unknown number K 0 from the data sample at hand. As in Vogt and Linton (2017), we drop stocks from the sample for which data points are missing. Moreover, we eliminate stocks i with a very small empirical support S i of the fragmentation data {X it : 1 ≤ t ≤ T }.…”

“…It is also possible to combine them with other distance-based clustering approaches. In particular, they can be employed as distance statistics in the thresholding algorithm of Vogt and Linton (2017). To do so, we replace the L 2 -type distance statistics ∆ ij from Vogt and Linton (2017) by the multiscale statistics d ij and construct the threshold estimators of the unknown groups G 1 , .…”

“…A distance-based clustering algorithm is then applied to the distances ρ ij . This strategy has for example been used in Vogt and Linton (2017).…”