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Generic rank-order delete-one jackknife (prefix/suffix engine)

Source: R/jackknife-rank-full.R
jackknife_rank_full.Rd

Computes all \(n\) leave-one-out estimates for a rank-weighted linear estimator \(\hat\theta_t = \sum_i w_n[r_{it}]\,\phi_i\) at each of \(m\) target points, using an \(O(n \cdot m \cdot q)\) prefix/suffix algorithm.

Usage

jackknife_rank_full(ranks, PHI, wn, wnm1)

Arguments

ranks

Integer matrix (\(n \times m\)); column \(t\) is a permutation of 1:n giving the rank of each observation for target \(t\) (rank 1 = nearest).

PHI

Finite numeric matrix (\(n \times q\)); row \(i\) is the \(q\)-dimensional signal contribution of observation \(i\). For a scalar signal, pass cbind(y).

wn

Finite numeric vector of length \(n\); rank-weight table at full sample size \(n\). Entry wn[r] is the weight assigned to rank \(r\).

wnm1

Finite numeric vector of length \(n-1\); rank-weight table at leave-one-out sample size \(n-1\).

Value

A list with:

theta0

Numeric matrix (\(q \times m\)); baseline estimates at full sample size.

theta_loo

Array with dim = c(n, q, m); element [i, qq, t] is the leave-one-out estimate after deleting observation \(i\) for signal dimension \(qq\) and target \(t\).

info

List with fields n, m, q.

Details

The rank-weight rule is supplied via precomputed tables wn and wnm1 rather than a spec object, so the function is completely agnostic to the weight construction. Callers are responsible for providing consistent tables:

  • wn should be the rank-weight sequence evaluated at sample size \(n\) (i.e. for the full-sample estimator).

  • wnm1 should be the same rule evaluated at sample size \(n-1\) (i.e. for each leave-one-out sub-sample).

When the package was compiled with C++ support, the C++ engine is used. Otherwise the function falls back silently to a pure-R implementation of the same algorithm.

See also

jackknife_fast_rank() for the finite-support L-stat engine; jackknife_slow_rank() for the reference implementation.

Examples

set.seed(1)
n <- 20L; m <- 3L; q <- 2L
ranks <- apply(matrix(runif(n * m), n, m), 2L, rank)
storage.mode(ranks) <- "integer"
PHI <- matrix(rnorm(n * q), n, q)
# toy uniform rank weights
wn   <- rep(1 / n, n)
wnm1 <- rep(1 / (n - 1L), n - 1L)
out <- jackknife_rank_full(ranks, PHI, wn, wnm1)
dim(out$theta_loo)   # c(n, q, m)
#> [1] 20  2  3
dim(out$theta0)      # c(q, m)
#> [1] 2 3