get_tau: Get a Specific tau_{i}.

In CovEsts: Nonparametric Estimators for Covariance Functions

Get a Specific \tau_{i}.

Description

A helper function that transforms the knots from generate_knots into the following form: For i = -p , -p + 1, \dots , -2, -1 , m + 2, m + 3, \dots , m + p , m + p + 1, it is equal to \tau_{i} = i / (m + 1), and for i = 0, \dots , m + 1, it is \tau_{i} = \kappa_{i}. See Choi, Li & Wang (2013) page 615 for details. This is a helper function of get_taus.

Usage

get_tau(i, p, m, kVec)

Arguments

i	The knot index (-p through m + p + 1).
p	The order of the splines.
m	The number of nonboundary knots.
kVec	Knot vector - see generate_knots.

Value

The numerical value of \tau_{i}.

References

Choi, I., Li, B. & Wang, X. (2013). Nonparametric Estimation of Spatial and Space-Time Covariance Function. JABES 18, 611-630. https://doi.org/10.1007/s13253-013-0152-z

Examples

kVec <- generate_knots(2)
get_tau(1, 3, 2, kVec)

CovEsts documentation built on Sept. 10, 2025, 10:39 a.m.