In this paper, with optimal normalized constants,
the asymptotic expansions of the distribution and density of the
normalized maxima from generalized Maxwell distribution are derived.
For the distributional expansion, it shows that the convergence rate
of the normalized maxima to the Gumbel extreme value distribution is
proportional to $1/\log n.$ For the density expansion, on the one
hand, the main result is applied to establish the convergence rate
of the density of extreme to its limit. On the other hand, the main
result is applied to obtain the asymptotic expansion of the moment
In this paper, the higher-order asymptotic
expansion of the moment of extreme from generalized Maxwell
distribution is gained, by which one establishes the rate of
convergence of the moment of the normalized partial
maximum to the moment of the associate Gumbel extreme value distribution.
A common problem in multi-environment trials arises when some genotype-by-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.
A common problem in climate data is missing information. Recently, four methods have been developed which are based in the singular value decomposition of a matrix (SVD). The aim of this paper is to evaluate these new developments making a comparison by means of a simulation study based on two complete matrices of real data. One corresponds to the historical precipitation of Piracicaba / SP - Brazil and the other matrix corresponds to multivariate meteorological characteristics in the same city from year 1997 to 2012. In the study, values were deleted randomly at different percentages with subsequent imputation, comparing the methodologies by three criteria: the normalized root mean squared error, the similarity statistic of Procrustes and the Spearman correlation coefficient. It was concluded that the SVD should be used only when multivariate matrices are analyzed and when matrices of precipitation are used, the monthly mean overcome the performance of other methods based on the SVD.