标题： 基于部分极大值的定位和尺度参数的线性估计 显示英文标题

标题： Linear Estimation of Location and Scale Parameters Using Partial Maxima

摘要： 考虑一个独立同分布的样本 X^*_1,X^*_2,...,X^*_n 来自位置尺度族，并假设唯一可获得的观测值是由部分极大值（或极小值）序列 X^*_{1:1},X^*_{2:2},...,X^*_{n:n}组成，其中 X^*_{j:j}=max{X1*,...,Xj*}。这种截断出现在多种情况下，包括田径比赛中的最佳表现。在部分极大值的情况下，BLUEs（最佳线性无偏估计量）的形式与基于顺序统计量（充分样本）的著名Lloyd（1952，使用顺序统计量对位置和尺度参数进行最小二乘估计，Biometrika，第39卷，第88-95页）的BLUEs形式非常相似，但与经典情况不同，它们的一致性不再明显。本文主要关注尺度参数，表明部分极大值BLUE的方差对于一大类分布来说至多是 O(1/log n) 的阶。 显示英文摘要

摘要： Consider an i.i.d. sample X^*_1,X^*_2,...,X^*_n from a location-scale family, and assume that the only available observations consist of the partial maxima (or minima)sequence, X^*_{1:1},X^*_{2:2},...,X^*_{n:n}, where X^*_{j:j}=max{X^*_1,...,X^*_j}. This kind of truncation appears in several circumstances, including best performances in athletics events. In the case of partial maxima, the form of the BLUEs (best linear unbiased estimators) is quite similar to the form of the well-known Lloyd's (1952, Least-squares estimation of location and scale parameters using order statistics, Biometrika, vol. 39, pp. 88-95) BLUEs, based on (the sufficient sample of) order statistics, but, in contrast to the classical case, their consistency is no longer obvious. The present paper is mainly concerned with the scale parameter, showing that the variance of the partial maxima BLUE is at most of order O(1/log n), for a wide class of distributions.