Module peer 

Structured-penalty scalar-on-function regression via PEER.

PEER (Partially Empirical Eigenvectors for Regression) estimates the coefficient function β(t) via penalized normal equations (W_c'W_c + λQ)β = W_c'y_c, where W_c is the centered, integration- weighted design matrix and Q is a penalty chosen from three families.

Penalty families

• PeerPenalty::Ridge — identity penalty (uniform shrinkage).
• PeerPenalty::Difference — second-difference roughness (D’D, order 2).
• PeerPenalty::Decree — caller-supplied structured penalty matrix.

Quick start

use fdars_core::matrix::FdMatrix;
use fdars_core::peer::{peer, PeerConfig, PeerPenalty, LambdaChoice};
use fdars_core::helpers::simpsons_weights;

// Tiny synthetic dataset: n=10 observations, m=5 evaluation points.
let (n, m) = (10_usize, 5_usize);
let argvals: Vec<f64> = (0..m).map(|i| i as f64 / (m - 1) as f64).collect();
let mut data = FdMatrix::zeros(n, m);
let mut y = vec![0.0_f64; n];
let true_beta: Vec<f64> = argvals.iter()
    .map(|&t| (std::f64::consts::PI * t).sin()).collect();
let w = simpsons_weights(&argvals);
for i in 0..n {
    for j in 0..m {
        let xi = ((i * m + j) as f64 * 0.3).sin();
        data[(i, j)] = xi;
        y[i] += xi * true_beta[j] * w[j];
    }
}
// Fit PEER with Ridge penalty and a fixed λ.
let config = PeerConfig {
    penalty: PeerPenalty::Ridge,
    lambda: LambdaChoice::Fixed(1e-3),
};
let fit = peer(&data, &y, &argvals, &config).unwrap();
assert_eq!(fit.beta.len(), m);
assert!(fit.fitted_values.iter().all(|v| v.is_finite()));
// Predict on training data — must reproduce fitted_values (self-consistency).
let preds = fit.predict(&data, &argvals).unwrap();
for (p, f) in preds.iter().zip(&fit.fitted_values) {
    assert!((p - f).abs() < 1e-9);
}

Structs

LpeerResult

Result of the lpeer longitudinal PEER estimator.

PeerConfig

Configuration for the peer estimator.

PeerResult

Result of the peer estimator.

Enums

LambdaChoice

How to choose the smoothing parameter λ for the PEER estimator.

LambdaMethod

Records which λ-selection path actually ran.

PeerPenalty

Penalty family for the PEER estimator.

Functions

lpeer

Fit the longitudinal PEER scalar-on-function regression model with subject random effects.

peer

Fit the PEER scalar-on-function regression model.