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bvhar (version 2.2.2)

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 \(\lVert \cdot \rVert_2\) be the spectral norm of a matrix, let \(\hat{\Phi}\) be the estimates, and let \(\Phi\) be the true coefficients matrix. Then the function computes relative estimation error by $$\frac{\lVert \hat{\Phi} - \Phi \rVert_2}{\lVert \Phi \rVert_2}$$

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).