Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Implements Lagrangian multiplier smoothing splines for flexible nonparametric regression and function estimation. Provides tools for fitting, prediction, and inference using a constrained optimization approach to enforce smoothness. Supports generalized linear models, Weibull accelerated failure time (AFT) models, Cox proportional hazards models, quadratic programming constraints, and customizable working-correlation structures, with options for parallel fitting. The core spline construction builds on Ezhov et al. (2018) . Quadratic-programming and SQP details follow Goldfarb & Idnani (1983) and Nocedal & Wright (2006) . For smoothing spline and penalized spline background, see Wahba (1990) and Wood (2017) . For variance-component and correlation-parameter estimation, see Searle et al. (2006) . The default multivariate partitioning step uses k-means clustering as in MacQueen (1967).

Introduction

This R package implements Lagrangian multiplier smoothing splines, which reformulate smoothing splines through constrained optimization. This approach provides direct access to predictor-response relationships through interpretable coefficients, unlike other formulations that require post-fitting algebraic manipulation.

Additionally, this package allows for fitting survival models, GLMs, MMRMs, and many other models sunder arbitrary linear equality and inequality constraints upon coefficients.

I have ensured that asymptotic confidence interval coverage remains at the nominal 95% level for all models contained in this package, including for survival models and models with marginal correlation structures.

I will not be continuing to pursue publication for this idea, due to personal life, work, and difficulty in finding an appropriate journal. For those interested, an unpublished manuscript with reproducible code appears in the "Article" folder, which justifies and explains the proposed method.