A mutual information estimator with exponentially decaying bias

Area of Science:

• Statistics
• Bioinformatics
• Information Theory

Background:

• Estimating mutual information is crucial for understanding relationships in data.
• Existing methods like maximum likelihood estimation can be unreliable, inflating Type I errors.
• A need exists for robust estimators, especially for discrete variables.

Purpose of the Study:

• To propose a novel nonparametric estimator for mutual information.
• To evaluate the statistical properties of the proposed estimator, including bias and efficiency.
• To demonstrate the estimator's utility in analyzing gene expression data.

Main Methods:

• Developed a nonparametric estimation technique for mutual information.
• Analyzed the estimator's asymptotic normality and efficiency.
• Investigated the bias behavior, showing exponential decay with sample size.
• Applied the estimator to assess gene-gene associations using expression levels.

Main Results:

• The proposed estimator exhibits asymptotic normality and efficiency.
• The estimator demonstrates a bias that decreases exponentially with increasing sample size.
• The method provides a viable inferential tool, outperforming maximum likelihood estimation in certain scenarios.
• Simulations confirm the estimator's performance characteristics.

Conclusions:

• The novel nonparametric estimator offers a statistically sound and efficient approach to mutual information estimation.
• Its rapidly decaying bias and asymptotic properties make it suitable for inferential tasks, particularly in bioinformatics.
• The estimator effectively assesses associations between genes based on expression data, providing reliable insights.