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Concave likelihood-based regression with finite-support response variables.

K O Ekvall1,2, M Bottai2

  • 1Department of Statistics, University of Florida, Gainesville, Florida, USA.

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Summary
This summary is machine-generated.

We introduce a new regression framework for bounded, discrete data, enhancing statistical modeling for various applications. This approach ensures reliable estimation and convergence for complex datasets in scientific research.

Keywords:
concavefinite supportinterval-censoringmaximum likelihoodpenalizedregressionsurvival analysis

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Regression Analysis

Background:

  • Observed data in practice are often discrete and bounded, necessitating specialized regression models.
  • Existing methods for interval-censored data with log-concave distributions are limited in scope.

Purpose of the Study:

  • To develop a unified framework for likelihood-based regression modeling with finite support response variables.
  • To extend existing models for interval-censored data to a broader class of bounded outcomes.

Main Methods:

  • Proposed a novel regression model accommodating finite support response variables.
  • Established asymptotic normality for maximizers of the concave log-likelihood.
  • Derived convergence rates for L1-regularized estimators under sparsity.
  • Employed an inexact proximal Newton algorithm for parameter estimation.

Main Results:

  • The log-likelihood function is concave, ensuring desirable statistical properties.
  • Asymptotic normality is established for the maximizer as sample size increases.
  • Efficient convergence rates are achieved for regularized estimators with high-dimensional data.
  • The inexact proximal Newton algorithm demonstrates guaranteed convergence.

Conclusions:

  • The proposed unified framework effectively models regression with finite support.
  • The methods are broadly applicable to discrete time survival analysis, survey outcomes, and interval-censored regression.
  • Simulations and data examples confirm the utility and applicability of the developed techniques.