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随机变量依赖关系的非参数度量AI 解读

In 1959 A. Renyi proposed a set of axioms for a measure of dependence for pairs of random variables. In the same year A. Sklar introduced the general notion of a copula. This is a function which links an $n$-dimensional distribution function to its one-dimensional margins and is itself a continuous distribution function on the unit $n$-cube, with uniform margins. We show that the copula of a pair of random variables $X, Y$ is invariant under a.s. strictly increasing…

分位数区间内外置信区间的置信系数界AI 解读

In this article, bounds for the confidence coefficients of outer and inner confidence intervals for quantile intervals are obtained using properties of convex functions. The bounds obtained here are sharper than the bounds given in Krewski (1976) and Reiss and Ruschendorf (1976).

基于密度—分位数函数的最优间距选择AI 解读

In this paper design techniques for continuous parameter time series regression analysis are employed to develop a general approach to optimal spacing selection for the linear estimation of location and scale parameters by sample quantiles from uncensored or censored samples. The spacings derived from this approach are asymptotically optimal in the sense that they result in near optimal asymptotic relative efficiencies for large values of $k$, the number of spacing elements.…

对称分位数平均及相关估计量AI 解读

The average of two complementary order statistics is termed a symmetric quantile average. In addition to having quite good efficiency, robustness and computational properties, exact nonparametric confidence intervals for location can be derived from it. A related type of estimator called a combined quantile average is introduced; it is slightly more difficult to compute than the symmetric quantile average, but can have better efficiency and robustness properties. In fact the…

基于部分删失数据的卷积估计AI 解读

An estimator is proposed for the convolution of distribution functions, based on samples with some right-censored observations. The asymptotic variance of the estimator is calculated, and the method is illustrated with a set of cancer data.

随机删失数据的拟合优度图与检验AI 解读

In this paper, we consider nonparametric procedures for assessing goodness of fit when the data may be subject to random censoring. We introduce two classes of large-sample tests, based, respectively, on the maximum and average weighted difference between the specified survival function and the Kaplan-Meier estimate of the true survival function. The procedures in the first class are inverted to obtain simultaneous confidence bands for the survival and cumulative hazard…

简单回归模型中的 Brown–Mood 型中位数估计量AI 解读

In the context of simple linear regression we investigate a class of estimators for the parameters which contains the Brown-Mood estimators. We derive the asymptotic efficiency properties of the class of slope estimators and find the most efficient slope estimator. This estimator is shown to have efficiency properties analogous to those of other median estimators for slope found in the literature. The equations which define the optimal estimators are median analogues of the…

单样本与双样本秩检验对粗大误差的稳健性AI 解读

The classical nonparametric hypotheses of symmetry and equality of distribution functions are extended to hypotheses of approximate symmetry and approximate equality, by allowing for gross errors, which is indispensable for practical applications. It is shown that for these hypotheses one- and two-sample rank statistics maintain their distribution freeness, which now refers to their stochastically extreme laws. These laws are evaluated asymptotically, also under similarly…

未知均匀分布下的极小极大停止规则AI 解读

An invariance-based method of obtaining the minimax stopping rule when sampling from an unknown uniform distribution is presented and applied to two problems, maximizing the probability of selecting the smallest observation and minimizing the expected quantile of the observation selected. In the first problem, the minimax rules use only the relative ranks of the observations; in the second problem they are shown to achieve asymptotic risk (3 + 2 √2)1/√2/n ≈ 3.4780/n, which…

混合比例的非参数估计AI 解读

SUMMARY Non-parametric estimates of mixing proportions based on kernel-type density estimators are badly suited to several types of data. They suffer from aberrations due to rounding or truncation of the measurements, and their construction involves the crucial choice of the “window size”, or smoothing parameter. In many circumstances estimators based on the empiric distribution function would be more suitable, and in this paper we investigate their properties. The…

经验贝叶斯分布函数渐近最优性的一则注记AI 解读

This paper establishes the asymptotic optimality (in the sense of Robbins) of the empirical Bayes distribution function created from the Bayes rule relative to the Dirichlet process prior with unknown parameter $\alpha(.)$. It will follow that the same result applies to the estimation of the mean of a distribution function.

Cox 回归模型：诱导分位数过程的不变性原理与重复显著性检验AI 解读

For the Cox regression model, the partial likelihood functions involve linear combinations of induced order statistics. Some invariance principles pertaining to such linear combinations of induced order statistics are studied and the theory is incorporated in the formulation of some repeated significance tests (for the hypothesis of no regression) based on these partial likelihoods.

中位生存时间的估计AI 解读

Two methods are proposed for setting confidence intervals for the median survival time. It is shown how these are related to bootstrap methods for censored data, and some numerical comparisons are presented.

模型误设下位置与尺度参数的最小均方距离估计AI 解读

SUMMARY The paper is concerned with estimating location and scale parameters by estimators minimizing a mean squared distance between the empirical distribution function and a conveniently chosen parameterized-distribution function. Within the true parametric family the location estimator has the same asymptotic distribution as that of Hodges & Lehmann. If the underlying distribution is not a member of the assumed parametric family, the questions concerning bias, rather than…

随机删失数据的非参数二元分布估计AI 解读

The estimation of a bivariate distribution function with randomly censored data is considered. It is assumed that the censoring occurs independently of the lifetimes, and that deaths and losses which occur simultaneously can be separated. Two estimators are developed: a reduced-sample estimator and a self-consistent one. It is shown that the latter estimator satisfies a nonparametric likelihood function and is unique up to the final uncensored values in any dimension; it…

随机删失数据的拟合优度图与检验AI 解读

In this paper, we consider nonparametric procedures for assessing goodness of fit when the data may be subject to random censoring. We introduce two classes of large-sample tests, based, respectively, on the maximum and average weighted difference between the specified survival function and the Kaplan-Meier estimate of the true survival function. The procedures in the first class are inverted to obtain simultaneous confidence bands for the survival and cumulative hazard…

用核方法估计分布函数与分位数的札记AI 解读

A distribution function is estimated by integrating a kernel estimator of the density. Quantiles are estimated by inverting the estimate of the distribution function. Second-order properties of both these estimators are studied.

对称分位数平均及相关估计量AI 解读

The average of two complementary order statistics is termed a symmetric quantile average. In addition to having quite good efficiency, robustness and computational properties, exact nonparametric confidence intervals for location can be derived from it. A related type of estimator called a combined quantile average is introduced; it is slightly more difficult to compute than the symmetric quantile average, but can have better efficiency and robustness properties. In fact the…

利用部分删失数据估计分布卷积AI 解读

An estimator is proposed for the convolution of distribution functions, based on samples with some right-censored observations. The asymptotic variance of the estimator is calculated, and the method is illustrated with a set of cancer data.

两个相关 t 随机变量乘积的分布AI 解读

Two forms of the distribution function of the product of two correlated t variates are presented. The distribution function is studied as a function of three parameters.

线性模型中的修剪最小二乘估计AI 解读

We consider two methods of defining a regression analog to a trimmed mean. The first was suggested by Koenker and Bassett and uses their concept of regression quantiles. Its asymptotic behavior is completely analogous to that of a trimmed mean. The second method uses residuals from a preliminary estimator. Its asymptotic behavior depends heavily on the preliminary estimate; it behaves, in general, quite differently than the estimator proposed by Koenker and Bassett, and it…

通过提名抽样估计总体中位数AI 解读

In nomination sampling, the largest values from several independent random samples (nominees) are rank ordered, and an estimate of the population median is formed by interpolating between 2 of these order statistics. The resulting estimate compares favorably to the sample median of a simple random sample from the same population. When historical data sets retain only extreme values, nomination sampling may offer the only practical way to estimate the population median. The…

Johnson 曲线参数的分位数估计量AI 解读

Easy quantile estimators are given for the parameters of Johnson curves. The estimators are at least as good as moment estimators.

正态分布函数的计算AI 解读

A slight modification of a formula of A. J. Strecock provides a simple approximation to the normal distribution function which is accurate to nine decimal places.