Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/86680 
Year of Publication: 
2008
Series/Report no.: 
Tinbergen Institute Discussion Paper No. 08-114/4
Publisher: 
Tinbergen Institute, Amsterdam and Rotterdam
Abstract: 
We consider the problem of smoothing data on two-dimensional grids with holes or gaps. Such grids are often referred to as difficult regions. Since the data is not observed on these locations, the gap is not part of the domain. We cannot apply standard smoothing methods since they smooth over and across difficult regions. More unfavorable properties of standard smoothers become visible when the data is observed on an irregular grid in a non-rectangular domain. In this paper, we adopt smoothing spline methods within a state space framework to smooth data on one- or two-dimensional grids with difficult regions. We make a distinction between two types of missing observations to handle the irregularity of the grid and to ensure that no smoothing takes place over and across the difficult region. For smoothing on two-dimensional grids, we introduce a two-step spline smoothing method. The proposed solution applies to all smoothing methods that can be represented in a state space framework. We illustrate our methods for three different cases of interest.
Subjects: 
Bivariate smoothing
Geo-statistics
Missing observations
Smoothing spline model
State space methods
JEL: 
C13
C22
C32
Document Type: 
Working Paper

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