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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
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PROFILE-KERNEL LIKELIHOOD INFERENCE WITH DIVERGING NUMBER OF PARAMETERS.

Clifford Lam1, Jiangqing Fan

  • 1Princeton University.

Annals of Statistics
|January 29, 2009
PubMed
Summary

This study introduces profile likelihood estimation for generalized varying coefficient models with many predictors. The new accelerated algorithm offers efficient and stable estimates, saving computational time.

Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Generalized varying coefficient partially linear models are increasingly used in scientific research.
  • Estimating these models becomes challenging as the number of predictors grows with sample size.
  • Existing methods may lack theoretical guarantees or computational efficiency in high-dimensional settings.

Purpose of the Study:

  • To develop and analyze profile likelihood estimation and inference for generalized varying coefficient partially linear models with a growing number of predictors.
  • To propose a novel and computationally efficient algorithm for estimating these models.
  • To demonstrate the theoretical properties and practical performance of the proposed methods.

Main Methods:

  • Theoretical analysis of the existence and asymptotic normality of the profile likelihood estimator.

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  • Development and investigation of the accelerated profile-kernel algorithm for parameter estimation.
  • Wilk's phenomenon demonstration for profile likelihood ratio inference.
  • Simulation studies to compare the proposed method with existing fully iterative approaches.

    • Main Results:

    • Established the existence and asymptotic normality of the profile likelihood estimator under regularity conditions.
    • The accelerated profile-kernel algorithm provides estimates as efficient as fully iterative methods.
    • The proposed algorithm significantly reduces computational time and improves estimate stability for moderate sample sizes.
    • Successful application of the algorithm to a real-world dataset.

    Conclusions:

    • The profile likelihood approach offers a robust theoretical framework for high-dimensional varying coefficient models.
    • The accelerated profile-kernel algorithm is a computationally efficient and stable alternative for practical applications.
    • This work provides valuable tools for statistical modeling in contemporary scientific endeavors.