risk_stein: Stein Risk function from Pang et al. (2009).
In sparsediscrim: Sparse and Regularized Discriminant Analysis

Description Usage Arguments Value References

This function finds the value for α \in [0,1] that empirically minimizes the average risk under a Stein loss function, which is given on page 1023 of Pang et al. (2009).

1	risk_stein(N, K, var_feature, num_alphas = 101, t = -1)

`N`	the sample size.
`K`	the number of classes.
`var_feature`	a vector of the sample variances for each dimension.
`num_alphas`	The number of values used to find the optimal amount of shrinkage.
`t`	a constant specified by the user that indicates the exponent to use with the variance estimator. By default, t = -1 as in Pang et al. See the paper for more details.

list with

alpha: the alpha that minimizes the average risk under a Stein loss function. If the minimum is not unique, we randomly select an alpha from the minimizers.
risk: the minimum average risk attained.

Pang, H., Tong, T., & Zhao, H. (2009). "Shrinkage-based Diagonal Discriminant Analysis and Its Applications in High-Dimensional Data," Biometrics, 65, 4, 1021-1029. https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1541-0420.2009.01200.x

sparsediscrim documentation built on July 1, 2021, 9:07 a.m.