Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 548: Estimating confidence regions over bounded domains

Bruno Eklund ()
Additional contact information
Bruno Eklund: Dept. of Economic Statistics, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, SE-113 83 Stockholm, Sweden

Abstract: Estimating 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.

Keywords: Kernel estimation; nonlinear grid; GARCH model; highest density region

JEL-codes: C14; C22

12 pages, November 28, 2003

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