Breadcrumb
Nonparametric Regression
Given noisy data observed at certain intervals, the aim is to approximate the data by a function without restricting ourselves to functions from a small family like linear or polynomial models. Smoothness or simplicity assumptions are made instead.
Real-world applications
Practical applications of nonparametric regression include image decompression and signal cleaning, and general problems of dealing with missing data.
Many methods have been suggested and studied, the most popular ones are kernel estimators, spline smoothing, local polynomial regression and wavelet thresholding.
Local extreme values play an important role in many applications of nonparametric statistics because their positions have often meaningful interpretations. So recent methods based on minimising total variation, like the taut string method, try to fit the data with a function that contains local extreme values only at positions where indicated by the data.
Ongoing projects
- "Smoothing under monotonicity and convexity constraints" by Arne Kovac.
- "Bivariate density estimation and BV regularisation" by Arne Kovac, Andreas Obereder and Otmar Scherzer.
Recent publications
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Modelling and forecasting financial log-returns as locally stationary wavelet processes (2005)
Piotr Fryzlewicz
Journal of Applied Statistics, vol: 32, Pages: 503 - 528
URL provided by the author -
Haar-Fisz estimation of evolutionary wavelet spectra (2006)
Piotr Fryzlewicz, Guy Nason
Journal of the Royal Statistical Society Series B, vol: 68, Pages: 611 - 634
URL provided by the author