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An alternative methodology for imputing missing data in trials with genotype-by-environment interaction: some new aspects

100%

Arciniegas-Alarcón S., García-Peña M., Krzanowski W. J., Santos Dias C. T. d.

Biometrical Letters

2014

tom 51

nr 2

75-88

A common problem in multi-environment trials arises when some genotypeby- environment combinations are missing. In Arciniegas-Alarcón et al. (2010) we outlined a method of data imputation to estimate the missing values, the computational algorithm for which was a mixture of regression and lower-rank approximation of a matrix based on its singular value decomposition (SVD). In the present paper we provide two extensions to this methodology, by including weights chosen by cross-validation and allowing multiple as well as simple imputation. The three methods are assessed and compared in a simulation study, using a complete set of real data in which values are deleted randomly at different rates. The quality of the imputations is evaluated using three measures: the Procrustes statistic, the squared correlation between matrices and the normalised root mean squared error between these estimates and the true observed values. None of the methods makes any distributional or structural assumptions, and all of them can be used for any pattern or mechanism of the missing values.

Probabilities of discrepancy between minima of cross-validation, Vapnik bounds and true risks

84%

Klęsk P.

International Journal of Applied Mathematics and Computer Science

2010

tom 20

nr 3

525-544

Two known approaches to complexity selection are taken under consideration: n-fold cross-validation and structural risk minimization. Obviously, in either approach, a discrepancy between the indicated optimal complexity (indicated as the minimum of a generalization error estimate or a bound) and the genuine minimum of unknown true risks is possible. In the paper, this problem is posed in a novel quantitative way. We state and prove theorems demonstrating how one can calculate pessimistic probabilities of discrepancy between these minima for given for given conditions of an experiment. The probabilities are calculated in terms of all relevant constants: the sample size, the number of cross-validation folds, the capacity of the set of approximating functions and bounds on this set. We report experiments carried out to validate the results.

Ograniczanie wyników

1 Biometrical Letters

1 International Journal of Applied Mathematics and Computer Science

1 Arciniegas-Alarcón S.

1 García-Peña M.

1 Klęsk P.

1 Krzanowski W. J.

1 Santos Dias C. T. d.

1 2014

1 2010

Wyniki wyszukiwania

An alternative methodology for imputing missing data in trials with genotype-by-environment interaction: some new aspects

Probabilities of discrepancy between minima of cross-validation, Vapnik bounds and true risks