The phrase "a double shrinkage" is correct and usable in written English.
It can be used in contexts discussing reductions or decreases in size, quantity, or intensity, particularly in fields like textiles, economics, or psychology.
Example: "The fabric experienced a double shrinkage after the first wash and again after drying, leading to a significant size reduction."
Alternatives: "twofold shrinkage" or "dual shrinkage".
We obtained such estimators by considering a Steinian double shrinkage method, which leads to covariance matrix estimators that are non-singular, well-conditioned, expressed in a recursive way and thus computable on data streams.
Such covariance matrices are estimated via an optimal double shrinkage method, which provides positive definite estimates even in presence of a few data points, or of data having components with small variance.
We thus use an optimal double shrinkage estimator of the covariance matrix, which provides always positive definite matrices, that are then inverted to compute the Mahalanobis distance.
Actually some of such variables have a very small variance; anyway our optimal double shrinkage estimator of the covariance matrices of the clusters guarantees positive definite estimates also in this situation, stabilizing thus the local Mahalanobis distances that we use in our procedure.
Our optimal double shrinkage estimators are thus necessary to overcome this instability, and as a byproduct, they can take into account the deviation of the kurtosis from the Gaussian case.
end{aligned}Differently from the BFR algorithm, here we estimate the covariance matrices of the clusters with the optimal double shrinkage estimators described in the previous section.
Second, using EBV as the response variable results in double shrinkage of the genomic breeding values, particularly when the reliabilities of the EBV are low.
In our study less information was available for the reference animals compared to Guo et al. [ 3], which implies that the expected double shrinkage was increased when using EBV as the response variable.
