Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Convergence and rates for fixed-interval multiple-track smoothing using k-means type optimization

Tools
- Tools
+ Tools

Thorpe, Matthew and Johansen, Adam M. (2016) Convergence and rates for fixed-interval multiple-track smoothing using k-means type optimization. Electronic Journal of Statistics, 10 (2). pp. 3693-3722. doi:10.1214/16-EJS1209

[img]
Preview
PDF (Creative Commons 2.5 )
WRAP-convergence-rates-fixed-type-Johansen-2016.pdf - Published Version - Requires a PDF viewer.

Download (371Kb) | Preview
[img] PDF
WRAP_rate_of_convergence_in_splines_with_da_v4.pdf - Accepted Version
Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer.

Download (407Kb)
Official URL: http://doi.org/10.1214/16-EJS1209

Request Changes to record.

Abstract

We address the task of estimating multiple trajectories from unlabeled data. This problem arises in many settings, one could think of the construction of maps of transport networks from passive observation of travellers, or the reconstruction of the behaviour of uncooperative vehicles from external observations, for example. There are two coupled problems. The first is a data association problem: how to map data points onto individual trajectories. The second is, given a solution to the data association problem, to estimate those trajectories. We construct estimators as a solution to a regularized variational problem (to which approximate solutions can be obtained via the simple, efficient and widespread k-means method) and show that, as the number of data points, n, increases, these estimators exhibit stable behaviour. More precisely, we show that they converge in an appropriate Sobolev space in probability and with rate n −1/2.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Asymptotic efficiencies (Statistics), Sobolev spaces
Journal or Publication Title: Electronic Journal of Statistics
Publisher: Institute of Mathematical Statistics
ISSN: 1935-7524
Official Date: 3 December 2016
Dates:
DateEvent
3 December 2016Available
25 October 2016Accepted
Volume: 10
Number: 2
Page Range: pp. 3693-3722
DOI: 10.1214/16-EJS1209
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Engineering and Physical Sciences Research Council (EPSRC), Selex ES Ltd

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item
twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us