Estimating confidence regions over bounded domains
AbstractEstimating a density function over a bounded domain can be very complicated and resulting in an unsatisfactory or unrealistic density estimate. In many cases a one-to-one transformation can be applied to the considered data set, but there are also situations where such a unique transformation may not exist. This paper proposes a method to estimate confidence regions over bounded domains when a one-to-one transformation either does not exist or its existence is difficult to verify. By taking into account parameter restrictions of a underlying model, a nonlinear grid can be constructed, over which the density function can be estimated. The method is illustrated by applying it to the kurtosis/first-order autocorrelation of squared observations of the GARCH(1,1) model.
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Bibliographic InfoPaper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 548.
Length: 12 pages
Date of creation: 28 Nov 2003
Date of revision:
Publication status: Published in Computational Statistics and Data Analysis, 2005, pages 349-360.
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Kernel estimation; nonlinear grid; GARCH model; highest density region;
Other versions of this item:
- Eklund, Bruno, 2005. "Estimating confidence regions over bounded domains," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 349-360, April.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-12-14 (All new papers)
- NEP-ECM-2003-12-14 (Econometrics)
- NEP-ETS-2003-12-14 (Econometric Time Series)
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