Consistency and central limit results for the maximum likelihood estimator in the Admixture Model

Area of Science:

• Population genetics
• Statistical genetics
• Bioinformatics

Background:

• The Admixture Model describes individual genetic makeup based on ancestral populations and allele frequencies.
• Previous research established foundational work on estimators in this model.

Purpose of the Study:

• To investigate the consistency and central limit theorems for maximum likelihood estimators (MLEs) of ancestry and allele frequencies within the Admixture Model.
• To extend existing theoretical results and address boundary cases in the parameter space.

Main Methods:

• Mathematical proofs for consistency of MLEs when estimating both allele frequencies and ancestries.
• Derivation of central limit theorems for estimating ancestry and allele frequencies for finite individuals and markers.
• Application of developed theory to real-world genetic data.

Main Results:

• Demonstrated consistency of MLEs for allele frequencies and ancestries in the Admixture Model.
• Established central limit theorems for finite samples, including boundary parameter space cases.
• Quantified the uncertainty of MLEs using data from the 1000 Genomes Project.

Conclusions:

• The study provides rigorous theoretical guarantees for MLEs in the Admixture Model.
• The findings enhance the reliability of inferring population structure and allele frequencies.
• The developed methods offer a robust framework for analyzing large-scale genomic datasets.