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

(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 covariability described in Schneider (2001). (A principal component technique similar to that of KG and Beckers and Rixen (2003) but with the more usual order of iterations ‐ iteratively re-estimating covariance matrices and all relevant principal components ‐ was presented by Everson and Sirovich (1995).) KG’s principal component technique for imputing missing values corresponds to an orthogonal or truncated total 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 algorithm with truncated total least squares regression uses leading principal components based on the entire dataset, including all records and variables with missing and available values. 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 covariability 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 contrasting 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 assumptions (as least squares methods or regularized variants). KG’s method is just as parametric as the regularized EM algorithm.