WYBRANE WŁASNOŚCI PRZESTRZENNYCH KWANTYLI
Słowa kluczowe:
Analizy wielowymiarowe, przestrzenne kwantyle, estymacja przestrzennych kwantyli.Abstrakt
Warunkowe kwantyle są wykorzystywane w ekonomii, biomedycynie lub w przemyśle. Mamy problemy z wprowadzeniem relacji porządku w obserwacjach wielowymiarowych, co przenosi się również na uogólnienie definicji kwantyli oraz warunkowych kwantyli (regresji kwantylowej) w przestrzeni wielowymiarowej. Omówimy własności przestrzennych kwantyli oraz ich estymatory. Wnioskowanie nieparamertyczne jest wykorzystywane przy opisie kwantylowym. Przedstawimy różne notacje wielowymiarowych kwantyli oraz przestrzennych funkcji kwantylowych w zapisie dla próby badawczej.
Pobrania
Bibliografia
Abdous B., Theodorescu R. (1992), Note on the spatial quantile of a random vector, “Statistics and Probability Letter”, 13, pp. 333-336.
Google Scholar
Barnett V. (1976), The ordering of multivariate data (with comments), “Journal of Royal Statistical Society”, Ser. A, 139, pp. 318-354.
Google Scholar
Chakraborty B. (2001), On affine equivariant multivariate quantiles, T”he Institute of Statistical Mathematics”, 53, pp. 380-403.
Google Scholar
Chaudhuri P. (1992a), Multivariate location estimation using extension of R-estimates through U-statistics type approach, “Annals of Statistics”, 20, pp. 897-916.
Google Scholar
Chaudhuri P. (1992b), Generalized regression quantiles: Forming a useful toolkit for robust linear regression, (in:) Dodge Y. (ed.), L1 Statistical Analysis and Related Methods, Amsterdam: North-Holland, pp. 169-185.
Google Scholar
Chaudhuri P. (1996), On a geometric notation of quantiles for multivariate data, “Journal of the American Statistical Association”, 91, pp. 862-872.
Google Scholar
Chaouch M., Gannoun A., Saracco J. (2008), Conditional Spatial Quantile: Characterization and Nonparametric Estimation, Cahier Du Gretha – 10.
Google Scholar
Dabo-Niang S., Thiam (2010), Robust quantile estimation and prediction for spatial processes, “Statistics and Probability Letters”, 80, pp. 1447-1458.
Google Scholar
Eddy W. F. (1985), Ordering of Multivariate Data, (in:) Billard L. (ed.), Computer Science and Statistics: The Interface, Amesterdam: North-Holland, pp. 25-30.
Google Scholar
Efron B. (1991), Regression percentiles using asymmetric squared error loss, “Statistica Sinica”, 1,
Google Scholar
pp. 93-125.
Google Scholar
Ferguson T. (1967), Mathematical Statistics: A Decision Theory Approach, Academic Press: New York.
Google Scholar
Koenker R., Basset G. (1978), Regression Quantiles, “Econometrica”, 46, pp. 33-50.
Google Scholar
Koenker R., Portnoy S. (1987), L Estimation for linear models, “Journal of the American statistical Association”, 82, pp. 851-857.
Google Scholar
Oja H. (1983), Descriptive Statistics for Multivariate Trimming, “Statistics and Probability Letters”, 1, pp. 327-332.
Google Scholar
Plackett R. L. (1976), Comment on Ordering of multivariate data by V. Barnett, “Journal of the Royal Statistical Society”, Ser. A, 139, pp. 344-346.
Google Scholar
Reiss R. D. (1989), Approximation distributions of order statistics with applications to nonparametric statistics, New York: Springer.
Google Scholar
Serfling R. (1980), Approximation theorem of mathematical statistics, New York: John Wiley.
Google Scholar
Serfling R. (2002), Quantile functions for multivariate analysis: approaches and applications, “Annals of Statistics”, 25, pp. 435-477.
Google Scholar
Trzpiot G. (2008), The Implementation of Quantile Regression Methodology in VaR Estimation, “Studies and Researches of Faculty of Economics and Management University of Szczecin”.
Google Scholar
Trzpiot G. (2009a), Quantile Regression Model versus Factor Model Estimation, “Financial Investments and Insurances”, Vol 60.
Google Scholar
Trzpiot G. (2009b), Application weighted VaR in capital allocation, “Polish Journal of Environmental Studies”, Vol 18, 5B.
Google Scholar
Trzpiot G. (2009c), Estimation methods for quantile regression, “Economics Studies”, 53.
Google Scholar
Trzpiot G. (2010), Quantile Regression Model of Return Rate Relation – Volatility for Some Warsaw Stock Exchange Indexes, “Finances, Financial Markets and Insurances. Capital Market”, Vol 28, pp. 61-76.
Google Scholar
Trzpiot G. (2011a), Bayesian Quantile Regression, „Studia Ekonomiczne”, Zeszyty Naukowe nr 65, pp. 33-44.
Google Scholar
Trzpiot G. (2011b), Some tests for quantile regression models, “Acta Universitatis Lodziensis Folia Economica”, 255, pp. 125-135.
Google Scholar
Trzpiot G. (2012), Spatial quantile regression, “Comparative Economic Research. Central and Eastern Europe”, vol. 15, no 4, pp. 265-279.
Google Scholar
Trzpiot G. (2013), Properties of transformation quantile regression model, “Acta Universitatis Lodziensis Folia Economica”, 285, pp. 125-137.
Google Scholar
Zuo Y., Serfling R. (2000), General notions of statistical depth function, “Annals of Statistics”, 28, pp. 461-482.
Google Scholar
