On computation of semiparametric maximum likelihood estimators with shape constraints

Area of Science:

• Statistics
• Computational Statistics
• Semiparametric Models

Background:

• Maximum likelihood estimation (MLE) for semiparametric models with shape constraints is well-established.
• Computational aspects of semiparametric MLE, particularly with high missing data, are less explored.
• Existing methods like the expectation-maximization (EM) algorithm can be computationally intensive.

Purpose of the Study:

• To develop a computationally efficient framework for semiparametric MLE.
• To address the computational challenges of existing methods when dealing with high missing data rates.
• To provide a versatile computational tool applicable to various data structures.

Main Methods:

• Proposing an inexact block coordinate ascent (BCA) algorithm for semiparametric MLE.
• Theoretically proving the convergence of the proposed BCA algorithm.
• Demonstrating the applicability of the framework to diverse data types like panel count, interval-censored, and degradation data.

Main Results:

• The proposed inexact block coordinate ascent (BCA) algorithm offers a computationally feasible approach to semiparametric MLE.
• Simulation studies indicate superior performance in terms of accuracy and speed compared to existing algorithms.
• The method is validated using two real-world datasets.

Conclusions:

• The developed computational framework provides an efficient and accurate solution for semiparametric MLE.
• The R package BCA1SG is available on CRAN, facilitating the practical application of this method.
• This work enhances the computational toolkit for analyzing complex data structures in statistics.