论文标题
估计订购分布家族的似然比
Estimation of a Likelihood Ratio Ordered Family of Distributions
论文作者
论文摘要
考虑双变量观察$（x_1，y_1），\ ldots，（x_n，y_n）\ in \ mathbb {r} \ times \ times \ mathbb {r {r} $，带有条件条件分布$ q_x $ $ y $ $ y $。目的是估算这些分布的唯一假设，即$ q_x $相对于可能性比顺序，$ x $等距为$ x $。如果观测值相同分布，则相关目标是估算关节分布$ \ MATHCAL {l}（x，y）$，唯一假设在某种意义上它完全是订单二的完全积极的。开发了一种算法，该算法通过经验可能性估算了未知家族$（q_x）_x $。根据估计和模拟和真实数据的预测性能，评估了可能性比顺序对平时随机顺序施加的更强正则化的好处。
Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption that $Q_x$ is isotonic in $x$ with respect to likelihood ratio order. If the observations are identically distributed, a related goal is to estimate the joint distribution $\mathcal{L}(X,Y)$ under the sole assumption that it is totally positive of order two in a certain sense. An algorithm is developed which estimates the unknown family of distributions $(Q_x)_x$ via empirical likelihood. The benefit of the stronger regularization imposed by likelihood ratio order over the usual stochastic order is evaluated in terms of estimation and predictive performances on simulated as well as real data.
