Estimating confidence regions over bounded domains

  • Authors:
  • Bruno Eklund

  • Affiliations:
  • Department of Economic Statistics, Stockholm School of Economics, SE-113 83 Stockholm, Sweden

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2005

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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. 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, is proposed. 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.