Jussi Klemelä

Jussi Klemelä
University of Oulu
Department of Mathematical Sciences
P.O. Box 3000
90014 University of Oulu, Finland

Email: jussi.klemela at oulu.fi
Phone: +358-8-553 1754
Fax: +358-8-553 1730
Office: Pentti Kaiteran katu 1, M207

Nonparametric function estimation

Teaching

Ekonometrian tilastolliset perusteet 805339A

Opetan Ekonometrian kurssi keväällä 2010. Kurssi alkaa Tiistaina 23.02.2010 kello 12.15. Kurssin laajuus on 6 opintopistettä. Opiskelijoilta edellytetään tilastotieteen peruskurssi tai vastaavat tiedot.

kurssiesite

Rahoituksen tilastotiede/Statistical finance

Huom. Tenttiin ei ole pakko ilmoittautua etukäteen (eikä se ole mahdollista WebOodissa).

Tentti laitoksen yleistentissä Maanantaina 14.12.2009 klo 14-18 luentosalissa L1. Toinen tentti Maanantaina 8.2.2010 laitoksen yleistentissä.

Information

Book

The homepage of the book contains preview, blog, software, the figures, and advice to their reproduction.

Preprints

• J. Klemelä and E. Mammen. Empirical risk minimization in inverse problems: Extended technical version, 2009. (PDF)


• S. Hoderlein, J. Klemelä, and E. Mammen. Analyzing the random coefficient model nonparametrically, 2008. (PDF)


• J. Klemelä Density estimation with stagewise optimization of the empirical risk, 2005. (compressed PostScript, PDF)


• J. Klemelä. Density estimation with locally identically distributed data and with locally stationary data, 2005. (PostScript, PDF)


• J. Klemelä. Complexity penalized support estimation, 2002. (gzipped PostScript, PDF, Abstract and software)


• J. Klemelä. Multivariate histograms with data-dependent partitions, 2001. (PDF)


• J. Klemelä. Optimal recovery and statistical estimation in Lp Sobolev classes, 2003. (PostScript, PDF, Homepage of the article)


• J. Horowitz, J. Klemelä and E. Mammen. Optimal estimation in additive regression. 2002.


• J. Klemelä and A. B. Tsybakov. Exact constants for pointwise adaptive estimation under the Riesz transform, 2001. (PostScript, PDF)


• J. Klemelä. Adaptive estimation of the location of the mode of a multivariate density, 2000. (gzipped PostScript)


• J. Klemelä. Sharp adaptive estimation of quadratic functionals. Prépublication 529, Laboratoire de Probabilités et Modèles Aléatoires, Universités de Paris 6 et Paris 7, 1999. (PostScript, PDF, Abstract and software)


• J. Klemelä and A. B. Tsybakov. Sharp adaptive estimation of linear functionals. Prépublication 540, Laboratoire de Probabilités et Modèles Aléatoires, Universités de Paris 6 et Paris 7, 1999. (PostScript, PDF)

• J. Klemelä. Analysis of the shapes of unimodal densities with nonparametric density estimation, 2008. (PDF)


• J. Klemelä. Level set trees and the analysis of shapes, 2008. (PDF)


• J. Klemelä. Prototypes of visualization tools, 2006. (PDF)


• J. Klemelä. Visualization of the spread of multivariate distributions, 2005. (gzipped PostScript, PDF)


• J. Klemelä. Visualization of scales of multivariate density estimates, 2005. (PDF)


• J. Klemelä. Visualization of multivariate data with tail trees, 2005. (PDF)


• J. Klemelä. Visualization of multivariate density estimates with shape trees, 2004. (gzipped PostScript , PDF)


• J Klemelä. Algorithms for manipulation of level sets of nonparametric density estimates, 2003. (gzipped PostScript, PDF, Homepage of the article)


• J. Klemelä. Visualization of multivariate density estimates with level set trees, 2000. (gzipped PostScript, PDF, Homepage of the article , Software )

• J. Klemelä. Lower bounds for the asymptotic minimax risk with spherical data, 2000. (PostScript)


• J. Klemelä. Asymptotic minimax risk in the uniform norm for the white noise model on the sphere. Discussion Paper 21, Sonderforschungbereich 373, Humboldt Universität, Berlin, 1998. (PostScript)


• J. Klemelä. Estimation of densities and derivatives of densities at a point with spherical data. Technical report, 1997. Partly published in Journal of Multivariate Analysis, 73:18-40,2000. (PostScript)


• J. Klemelä. Integrated risk of the kernel estimator with spherical data. Technical report, 1997. Partly published in Journal of Multivariate Analysis, 73:18-40,2000. (PostScript)


• J. Klemelä. Estimation of densities and functionals of densities with spherical data. A 16, Rolf Nevanlinna Institute, 1997

Software

• R-package "denpro" for the visualization of multivariate density estimates.


• R-package "delt" for the estimation of multivariate densities with adaptive histograms.


• R-package "finatool" for portfolio selection and pricing and hedging of options. The package will be written during spring 2009.

Selected publications

• S. Hoderlein, J. Klemelä, and E. Mammen. (2010). Analyzing the Random Coefficient Model Nonparametrically. Econometric Theory.


• J. Klemelä. (2008). Density estimation with locally identically distributed data and with locally stationary data. J. Time Series Anal. 29: 125-141.


• J. Klemelä. (2007). Visualization of multivariate data with tail trees. Information Visualization 6: 109-122.


• J. Klemelä. (2007). Density estimation with stagewise optimization of the empirical risk. Machine Learn. 67: 169-195.


• J. Klemelä. (2006). Sharp adaptive estimation of quadratic functionals. Probab. Theory Relat. Fields. 134(4): 539-564.


• J. Klemelä. (2004). Visualization of multivariate density estimates with level set trees. J. Comput. Graph. Statist. 13(3): 599-620.


• J. Klemelä and A. B. Tsybakov. (2001). Sharp adaptive estimation of linear functionals. Ann. Statist. 29: 1567-1600.

Animations

• Animations on density estimation
  • Growing of a level set tree tree
  • Growing of a shape tree
  • Growing of a tail tree
  • Slices of a function
  • CART visualization vs. level set tree visualization
• Animations on statistical finance
  • Scatter matrices
  • Scatter matrices; copula transformed data
  • Scatter matrices; original data
  • Hedging
  • Hedging with Gaussian asset prices
  • Hedging with Student asset prices
  • Hedging of an ATM option with Gaussian and Student asset prices
  • Profit distributions
  • Profit distributions of call options
  • Profit distributions of strangles
  • Profit distributions of condors
    • Movie I
    • Movie II

Talks

• Analysis of dependency with density estimation (PDF)
• Level set trees and the analysis of shapes (PDF)
• Likelihood subsetting of financial data (PDF)
• Empirical risk minimization in inverse problems (PDF)
• Density estimation with stagewise optimization of the empirical risk (PDF)
• Visualization of multivariate functions, sets, and data (PDF)
• Visualization of multivariate density estimates with shape trees (PDF)
• Visualization of multivariate density estimates (PDF)

Lectures on nonparametric function estimation

In nonparametric function estimation one approximates and interpolates functions when only noisy data is available. Functions to be estimated include probability density functions, regression functions, spectral density functions, and intensity functions. The lectures will concentrate on the estimation and visualization of multivariate density functions, but the techniques apply also to other kinds of functions. The estimation techniques include the use of anisotropic kernel estimators, minimization estimators, multivariate adaptive histograms, wavelet estimators, best basis selection, and stagewise minimization.

• Lecture I, 1.10.2007 (PDF)
• Lecture II, 15.10.2007 (PDF)
• Lecture III, 29.10.2007 (PDF)
• Lecture IV, 12.11.2007 (PDF)
• Lecture V, 26.11.2007 (PDF)
• Lecture VI, 10.12.2007 (PDF)

Nonparametric function estimation with applications in finance

Material:

• Lecture I, 20.01.2009 (PDF) Johdanto regressiofunktion estimointiin ja portfolion valintaan.
• Lecture II, 27.01.2009 (PDF) Ydinestimointi.
• Lecture III, 03.02.2009 (PDF) Lähimmän naapurin estimointi, yhden indeksin malli.
• Lecture IV, 10.02.2009 (PDF) Yhden indeksin malli, parametriton portfolion valinta (utiliteettifunktiot)
• Lecture V, 17.02.2009 (PDF) Parametriton portfolion valinta, riskin mittaaminen.
• Lecture VI, 24.02.2009 (PDF) Ehdollisen varianssin, kvantiilin, shortfallin, tiheysfunktion ja kertymäfunktion estimointi.
• Lecture VII, 03.03.2009 (PDF) Adaptiiviset regressogrammat.
• ei luentoa, 10.03.2009
• Lecture VIII, 17.03.2009 (PDF) Osittain lineaariset mallit.
• Lecture IX, 24.03.2009 (PDF) Additiiviset mallit ja vaiheittainen estimointi.
• Lecture X, 31.03.2009 (PDF) Datan muunnokset. Lokaalisti lineaarinen estimaattori.
• Lecture XI, 07.04.2009 (PDF) Regressiomenetelmän valinta, silotusparametrin valinta, portfolion valintamenetelmän valinta
• ei luentoa, 14.04.2009
• Lecture XII, 21.04.2009 Kertaus

The course concentrates on nonparametric estimation of regression and classification functions. Regression and classification functions can be used to predict future observations when noisy historical data is available. Nonparametric techniques can be used when a large amount of observations is available and one is not willing to assume strict parametric form for the estimated functions. The course covers methods to select portfolios and to evaluate option contracts making realistic assumptions of the market behaviour. The covered methods include:

• Linear methods, generalized linear models
• Local averaging: kernel and nearest neigborhood regression
• Empirical risk minimization
• Single index models
• Partially linear methods
• Support vector machines
• Aggregation
• Tree based methods

The R-package "finatool" implements the methods that are covered in the lecture series.

Relevant literature includes:

• Härdle, W., Mueller, M., Sperlich, S., and Werwatz, A. (2004). Nonparametric and Semiparametric Models. Springer.
• Franke, J., Härdle, W., and Hafner, C. M. (2008). Statistics of Financial Markets. Springer.
• Bouchaud, J.-P. and Potters, M. (2003). Theory of Financial Risks and Derivative Pricing, Cambridge Univ. Press, 2nd ed.
• The homepage of log-optimal portfolios
• Variable Selection for Portfolio Choice. Ait-Sahalia, Y. and Brandt, M. Journal of Finance, 2001, 56, 1297-1351.
• Funktioiden estimointi, Lasse Holmström.