arXiv subjects

Zehaan Naik

Publications and source records attributed to Zehaan Naik.

2 recordsLinked to original sources

arXiv2026

Least Absolute Deviations Estimation for Sinusoidal Models

We study robust parameter estimation in sinusoidal regression models within a least absolute deviations (LAD) framework. While classical approaches rely predominantly on least-squares formulations, they are known to be sensitive to heavy-tailed noise and outliers. We formulate the estimation problem as direct minimization of the LAD objective and propose a simple, modular coordinate descent algorithm that exploits the partial convexity of the objective: amplitude parameters are updated via weighted median computations, leading to substantial computational improvements over traditional simplex-based optimization methods, while frequency parameters are estimated via a periodogram-inspired grid search with local refinement. We establish strong consistency and asymptotic normality of the proposed estimator under mild regularity conditions. Empirically, we demonstrate the method's effectiveness on both synthetic datasets and real-world time series, including the Mauna Loa atmospheric CO2 data, air passenger data, and UK drivers' deaths data, where robustness to non-Gaussian noise is essential. The proposed approach provides a simple, interpretable, and robust alternative to least-squares-based methods for sinusoidal signal estimation.

stat.ME↗

arXiv2026

Coordinate Descent Algorithm for Least Absolute Deviations Regression

Least Absolute Deviations (LAD) regression provides a robust alternative to ordinary least squares by minimizing the sum of absolute residuals. However, its widespread use has been limited by the computational cost of existing solvers, particularly simplex-based methods in high-dimensional settings. We propose a coordinate descent algorithm for LAD regression that avoids matrix inversion, naturally accommodates the non-differentiability of the objective function, and remains well-defined even when the number of predictors exceeds the number of observations. The key observation is that each coordinate update reduces to a one-dimensional minimization admitting a closed-form solution given by a median or weighted median. The resulting algorithm has per-iteration complexity $O(p\,n \log n)$ and is provably convergent due to the convexity of the LAD objective and the exactness of each coordinate update. Experiments on synthetic and real datasets show that the method matches the accuracy of linear-programming-based LAD solvers while offering improved scalability and stability in high-dimensional regimes, including cases where $p \ge n$. The method is easy to implement, requires no specialized optimization software, and provides a practical tool for robust linear models.

stat.ME↗