Kelmansky Diana Mabel, Ricci Lila
Instituto de Cálculo, UBA-CONICET, Buenos Aires, Argentina.
Centro Marplatense de Investigaciones Matemáticas, UNMdP, Mar del Plata, Argentina.
Microarrays (Basel). 2017 Feb 10;6(1):5. doi: 10.3390/microarrays6010005.
The traditional approach with microarray data has been to apply transformations that approximately normalize them, with the drawback of losing the original scale. The alternative stand point taken here is to search for models that fit the data, characterized by the presence of negative values, preserving their scale; one advantage of this strategy is that it facilitates a direct interpretation of the results. A new family of distributions named gpower-normal indexed by p∈R is introduced and it is proven that these variables become normal or truncated normal when a suitable gpower transformation is applied. Expressions are given for moments and quantiles, in terms of the truncated normal density. This new family can be used to model asymmetric data that include non-positive values, as required for microarray analysis. Moreover, it has been proven that the gpower-normal family is a special case of pseudo-dispersion models, inheriting all the good properties of these models, such as asymptotic normality for small variances. A combined maximum likelihood method is proposed to estimate the model parameters, and it is applied to microarray and contamination data. Rcodes are available from the authors upon request.
处理微阵列数据的传统方法是应用近似归一化的变换，但缺点是会失去原始尺度。本文采取的另一种观点是寻找适合数据的模型，其特点是存在负值且保留其尺度；这种策略的一个优点是便于直接解释结果。引入了一个由(p\in R)索引的名为gpower-正态的新分布族，并证明当应用适当的gpower变换时，这些变量会变成正态或截尾正态。根据截尾正态密度给出了矩和分位数的表达式。这个新族可用于对包括非正值在内的不对称数据进行建模，这是微阵列分析所需要的。此外，已证明gpower-正态族是伪离散模型的一个特例，继承了这些模型的所有良好性质，如小方差时的渐近正态性。提出了一种组合最大似然方法来估计模型参数，并将其应用于微阵列和污染数据。如有需要，作者可提供R代码。
