Conformal Normal Curvature Local Influence Diagnostics

Computes conformal normal curvature (CNC) local influence diagnostics from a fitted EVBS regression model. The CNC approach of Poon and Poon (1999) produces a scale-invariant influence measure bounded in \([0,1]\); the aggregate contribution statistic of Zhu and Lee (2001) attributes curvature to individual observations and is compared against interpretable reference thresholds.

Usage

cnc_diagnostics(fit)

Arguments

fit

A fitted model object returned by evbsreg.fit. The function uses the influence matrix fit$B.

Value

A list with components:

eigenvalues

Numeric vector: the raw eigenvalues of \(B\).

eigenvalues_norm

Numeric vector: the absolute normalized eigenvalues \(|\lambda_i^*|\).

eigenvectors

Matrix: the eigenvectors of \(B\) (columns).

thresholds

Numeric vector of length 7: the reference thresholds \(q/\sqrt{n}\) for \(q = 1, \ldots, 7\).

Bj

Matrix of dimension \(8 \times n\): rows 1–7 hold the aggregate contributions \(B_j(q)\) for \(q=1,\ldots,7\); row 8 holds the global aggregate over all eigenvectors.

bq

Numeric vector of length 8: the reference values \(b(q)\) for flagging influential observations at each level.

n

Integer: the sample size.

Details

The function performs the symmetric eigendecomposition of the influence matrix \(B\), normalizes the eigenvalues to unit norm, and for each threshold \(q = 1, \ldots, 7\) identifies the \(q\)-influential eigenvectors (those whose normalized eigenvalue exceeds \(q/\sqrt{n}\)). The aggregate contribution of observation \(j\) at level \(q\), \(B_j(q)\), is the sum of the normalized eigenvalues weighted by the squared eigenvector coordinates of observation \(j\).

References

Poon, W.-Y. and Poon, Y. S. (1999). Conformal normal curvature and assessment of local influence. Journal of the Royal Statistical Society, Series B, 61, 51–61.

Zhu, H. and Lee, S. (2001). Local influence for incomplete-data models. Journal of the Royal Statistical Society, Series B, 63, 111–126.

Ospina, R., Lima, J. I. C., Barros, M., and Macedo, A. M. S. (2026). Local influence diagnostics for the extreme-value Birnbaum-Saunders regression model. Submitted.

See also

evbsreg.fit, plot_cnc.

Examples

data(itajai)
X <- cbind(1, itajai$pressure)
fit <- evbsreg.fit(X, itajai$wind)
diag <- cnc_diagnostics(fit)

## Top normalized eigenvalues
head(diag$eigenvalues_norm, 4)
#> [1] 0.6967768 0.4951145 0.4454736 0.2663023

## Observations flagged at q = 7
which(diag$Bj[7, ] > diag$bq[7])
#> [1]  27  43  44  47  82  87 108 110 120