Estimate A and r parameters for Fourier envelope

Estimates parameters A and r that bound the Fourier transform decay. Uses linear programming by default, with automatic fallback to grid search.

Usage

get_est_Ar(Y = 1, X, xi_interval, r_stepsize = 150, method = "auto")

Arguments

Y

Numeric vector (default 1 for density estimation)

X

Numeric vector of sample data

xi_interval

List with xi_lb and xi_ub

r_stepsize

Grid resolution for fallback method (default 150). Only used when method="grid". Ignored for LP method.

method

Character: "lp" (default), "grid", or "auto"

Value

Named numeric vector with est_A and est_r

Details

The LP-based method (default) is typically 1-5x faster than grid search, with speedup depending on sample size and Fourier transform computation cost. The grid search method is preserved for validation and as fallback if LP solver is unavailable.

The function finds the minimal-area envelope line in log-log space by minimizing the integral subject to envelope constraints on the Fourier transform decay.