Moments of Linear Discriminant Functions and an Asymptotic Confidence Interval for the Log Odds Ratio
该文推导了包含Anderson线性判别函数和对数优势比最小方差无偏估计的统计量的矩，给出了前四阶精确中心矩和累积量的渐近展开，并基于Peers & Iqbal方法构造了对数优势比的渐近置信区间，模拟显示该区间性质良好。
A general expression is obtained for the moments of a statistic which contains Anderson's linear discriminant function and the minimum variance unbiased estimator of the log odds ratio as special cases. The result is given in terms of certain invariant polynomials of matrix argument, and is used to derive the first four exact central moments, together with asymptotic expansions of the cumulants. This provides an alternative approach to Okamoto's expansion as an Edgeworth series. An asymptotic confidence interval is also obtained for the log odds ratio, using a method of Peers & Iqbal (1985), which allows for the estimation of nuisance parameters. Simulation shows that the interval has quite good properties over a range of parameter values.