Nonlinear Prediction Theory and the Estimation of Proportions in a Finite Population
针对一般非线性模型，发展了有限总体推断的预测方法，推导了总体总量及其方差的估计量，并证明了独立随机变量下的渐近性质。该方法应用于估计具有特定特征的单位总数，实证表明非线性伯努利模型有用但存在困难，并与比率和线性回归估计进行了比较。
Abstract Abstract The prediction approach to finite population inference is developed for a general nonlinear model. An estimator of the finite population total and an estimator of its variance are derived, and the asymptotic properties of both are obtained when the random variables in the model are independent. The theory is applied to the problem of estimating the total number of units that have a specified characteristic. An empirical study is presented, which confirms that a nonlinear Bernoulli model is potentially useful for that problem but also illustrates difficulties that may be encountered. Comparisons with the ratio and linear regression estimators are also included. Key Words: Superpopulation modelNonlinear modelAsymptotic normalityConsistencyBernoulli random variablesLogistic regression