Optimal Convex M-Estimation for Linear Regression via Antitonic Score Matching
Fit a linear regression model via antitonic score matching
Linear regression via antitonic score matching
Coefficients of an asm regression model
Confidence intervals for coefficients in an asm regression model
Generate diagnostic plots for an asm regression model
Predict new responses using an asm regression model.
Short description of a fitted asm regression model
Print summary of the asm regression model
Residuals from an asm regression model
Summary of an asm regression model
Performs linear regression with respect to a data-driven convex loss function that is chosen to minimize the asymptotic covariance of the resulting M-estimator. The convex loss function is estimated in 5 steps: (1) form an initial OLS (ordinary least squares) or LAD (least absolute deviation) estimate of the regression coefficients; (2) use the resulting residuals to obtain a kernel estimator of the error density; (3) estimate the score function of the errors by differentiating the logarithm of the kernel density estimate; (4) compute the L2 projection of the estimated score function onto the set of decreasing functions; (5) take a negative antiderivative of the projected score function estimate. Newton's method (with Hessian modification) is then used to minimize the convex empirical risk function. Further details of the method are given in Feng et al. (2024) <doi:10.48550/arXiv.2403.16688>.