Nonparametric smoothing using state space techniques

Patrick E. Brown*, Piet De Jong

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


The authors examine the equivalence between penalized least squares and state space smoothing using random vectors with infinite variance. They show that despite infinite variance, many time series techniques for estimation, significance testing, and diagnostics can be used. The Kalman filter can be used to fit penalized least squares models, computing the smoothed quantities and related values. Infinite variance is equivalent to differencing to stationarity, and to adding explanatory variables. The authors examine constructs called "smoothations" which they show to be fundamental in smoothing. Applications illustrate concepts and methods.

Original languageEnglish
Pages (from-to)37-50
Number of pages14
JournalCanadian Journal of Statistics
Issue number1
Publication statusPublished - Mar 2001
Externally publishedYes


  • Diffuse random vectors
  • Favoured model
  • Kalman filter smoother
  • Locally best invariant tests
  • Penalized least squares
  • Reinsch algorithm
  • Smoothations
  • Spline smoothing


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