bvhar (version 2.1.2)

relspne: Evaluate the Estimation Based on Relative Spectral Norm Error

Description

This function computes relative estimation error given estimated model and true coefficient.

Usage

relspne(x, y, ...)
# S3 method for bvharsp
relspne(x, y, ...)

Value

Spectral norm value

Arguments

x

Estimated model.

y

Coefficient matrix to be compared.

...

not used

Details

Let $\Vert \cdot {\Vert }_2$ be the spectral norm of a matrix, let $\hat{\mathrm{\Phi }}$ be the estimates, and let $\mathrm{\Phi }$ be the true coefficients matrix. Then the function computes relative estimation error by $$\frac{\Vert \hat{\mathrm{\Phi }}-\mathrm{\Phi }{\Vert }_2}{\Vert \mathrm{\Phi }{\Vert }_2}$$

References

Ghosh, S., Khare, K., & Michailidis, G. (2018). High-Dimensional Posterior Consistency in Bayesian Vector Autoregressive Models. Journal of the American Statistical Association, 114(526).