Semi-parametric Order-based Generalized Multivariate Regression

TL;DR

This paper introduces a semi-parametric, order-based multivariate regression method that is invariant to the response transformation, with proven consistency and competitive performance demonstrated through simulations and real data comparisons.

Contribution

The paper presents a novel semi-parametric algorithm for multivariate regression based on response ordering, with theoretical guarantees and practical performance evaluation.

Findings

Algorithm is a consistent estimator of the true coefficients.

Squared estimation error decreases at a rate of o(1/√n).

Performs well compared to traditional methods on synthetic and real data.

Abstract

In this paper, we consider a generalized multivariate regression problem where the responses are monotonic functions of linear transformations of predictors. We propose a semi-parametric algorithm based on the ordering of the responses which is invariant to the functional form of the transformation function. We prove that our algorithm, which maximizes the rank correlation of responses and linear transformations of predictors, is a consistent estimator of the true coefficient matrix. We also identify the rate of convergence and show that the squared estimation error decays with a rate of $o(1/\sqrt{n})$. We then propose a greedy algorithm to maximize the highly non-smooth objective function of our model and examine its performance through extensive simulations. Finally, we compare our algorithm with traditional multivariate regression algorithms over synthetic and real data.