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(ii) Except for neglecting the variations of the missing values around the imputed values and for an unusual order of iterations - iteratively re-estimating individual principal components - KG's method is similar to the regularized EM algorithm exploiting spatial and stationary temporal covari- ability described in Schneider (2001). (A principal compo- nent technique similar to that of KG and Beckers and Rixen (2003) but with the more usual order of iterations - itera- tively re-estimating covariance matrices and all relevant prin- cipal components - was presented by Everson and Sirovich (1995).) KG's principal component technique for imputing missing values corresponds to an orthogonal or truncated to- tal least squares (auto-)regression ( Fierro et al., 1997) and can be used in a regularized EM algorithm as discussed in Schneider (2001). As KG's method, a regularized EM algo- rithm with truncated total least squares regression uses lead- ing principal components based on the entire dataset, includ- ing all records and variables with missing and available val- ues. An innovation in KG's method is to make the time lag up to which temporal covariability is exploited an adaptive parameter. (iii) As a result of the similarity of KG's method and a regularized EM algorithm exploiting spatio-temporal covari- ability with truncated total least squares regressions, several of KG's claims of how their method differs from regularized EM algorithms are incorrect. For example, KG's contrast- ing of their method as being "non-parametric" as opposed to the "parametric" regularized EM algorithm is incorrect. The EM algorithm for Gaussian data yields maximum likelihood estimates of mean values, covariance matrices, and missing values, with their attendant optimality properties, but it and its regularized variants can also be justified under weaker as- sumptions (as least squares methods or regularized variants). KG's method is just as parametric as the regularized EM al- gorithm.

nonlinear processes in geophysics

Comment on &amp;quot;Spatio-temporal filling of missing points in geophysical data sets&amp;quot; by D. Kondrashov and M. Ghil, Nonlin. Processes Geophys., 13, 151–159, 2006