The Elliptically Optimal Confidence Interval: A Bivariate Extension of Wilson's Score Method

Battle Count: 57

This paper addresses confidence intervals for differences of binomial proportions, which is a fundamental statistical inference problem. While binomial proportions appear in trading contexts (e.g., win rates, success rates of strategies), the paper is purely theoretical statistics with no connection to financial modeling, time series, portfolio optimization, or market microstructure. The methodology (Wilson score intervals, elliptical regions, coverage analysis) has no direct application to quantitative trading strategies or financial risk management.

The closed-form solution requires evaluating six cases based on thresholds R1 and R2, which depend on sample sizes, observed difference, and confidence level. The bounds themselves involve square roots and rational expressions. The six-case logic is straightforward but requires careful handling of boundary conditions and the special balanced-design conventions. Exact coverage computation requires O(n1*n2) enumeration. The profiled variance representation (Lemma 2) simplifies the conceptual understanding but the practical implementation still requires the case analysis of Table 1. Overall moderate complexity - no iterative optimization needed, but the case logic and edge conditions require careful coding.

All results are derived in closed form with explicit formulas. Exact coverage is computed via deterministic enumeration of the binomial support (O(n1*n2) operations). The paper provides complete proofs in appendices. Code is stated to be available from the author on request but no public repository is linked. The six-case structure and all thresholds are fully specified.