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规则序列采样设计的渐近最优性AI 解读

We study linear estimators for the weighted integral of a stochastic process. The process may only be observed on a finite sampling design. The error is defined in a mean square sense, and the process is assumed to satisfy Sacks-Ylvisaker regularity conditions of order $r \epsilon \mathbb{N}_0$. We show that sampling at the quantiles of a particular density already yields asymptotically optimal estimators. Hereby we extend the results of Sacks and Ylvisaker for regularity $r = 0$…

有限总体分布函数的一种新估计量AI 解读

In this paper we propose a new estimator for the finite population distribution function when there is auxiliary information available about the population. The new estimator has a smaller asymptotic mean squared error than two leading estimators in the literature. In fact, it is in an optimised form in terms of mean squared error. Results are reported for simulation studies on real and artificial populations.

马尔可夫链蒙特卡洛中样本均值的渐近效率AI 解读

SUMMARY In many cases, a univariate time series derived from a time reversible stationary Markov chain has the property that there is a distribution function on [–1, 1] ([0, 1]) such that, for all non-negative integers l, its lth moment is the lth lag autocorrelation of the time series. We discuss some consequences of this property. Effects of the asymptotic efficiency of the sample mean on the efficiency of subsampling a stationary Markov chain are discussed. The…

非参数重要性抽样AI 解读

Importance sampling is a widely used variance reduction simulation technique for the evaluation of high-dimensional integrals. A key step in the implementation of importance sampling is to choose a proper distribution function from which pseudorandom numbers are generated. Parametric sampling distributions, if available at all, are often inadequate for high-dimensional integrals over irregular regions. One possible remedy is to use a nonparametric method to estimate the…

右截断数据的二元估计AI 解读

Bivariate estimation with survival data has received considerable attention recently; however, most of the work has focused on random censoring models. Another common feature of survival data, random truncation, is considered in this study. Truncated data may arise if the time origin of the events under study precedes the observation period. In a random right-truncation model, one observes the iid samples of (Y, T) only if (Y ≤ T), where Y is the variable of interest and T…

右截断数据下的二元估计AI 解读

Bivariate estimation with survival data has received considerable attention recently; however, most of the work has focused on random censoring models. Another common feature of survival data, random truncation, is considered in this study. Truncated data may arise if the time origin of the events under study precedes the observation period. In a random right-truncation model, one observes the lid samples of (Y, T) only if (Y less than or equal to T), where Y is the variable…

收入分布随机占优的非参数检验AI 解读

A class of tests for first, second, and third order stochastic dominance, together with modifications to the Pearson goodness of fit test are proposed for the nonparametric comparison of income distributions. They are implemented and compared with tests for generalised Lorenz dominance (which is the indirect test of second order stochastic dominance currently employed in income distribution studies) utilizing Canadian family income data. Copyright 1996 by The Econometric…

劳动市场制度与工资分布，1973—1992：半参数方法AI 解读

This paper provides evidence that the decline in the real value of the minimum wage and in the rate of unionization account for a significant share of the increase in wage inequality in the United States between 1979 and 1988. The role of the minimum wage is particularly important for women, while deunionization has the largest impact on men. The authors develop a semiparametric procedure that applies kernel density methods to appropriately weighted samples. The procedure…

平均剩余寿命过程AI 解读

Yang and Hall and Wellner initiated investigations of the asymptotic uniform behaviour of mean residual life (MRL) processes. They obtained results holding true over fixed and expanding compact subintervals of $[0, \infty)$. In this exposition we study MRL processes over the whole positive half-line $[0, \infty)$. We describe classes of weight functions which enable us to establish the (a) strong uniform-over-$[0, \infty)$ consistency and (b)weak uniform-over-$[0, \infty)$ ap…

区间删失数据分布函数非参数极大似然估计札记AI 解读

Gentleman & Geyer (1994) discuss the analysis of interval censored data and present results based on standard convex optimisation theory. Here, this problem is viewed from the perspective of a mixing problem of indicator functions. Using an analogy with the problem of mixture distributions a variety of results are easily derived, including a characterisation theorem for the maximum likelihood estimator and various reliably convergent algorithms. Software for the analysis of…

有限总体累积分布函数估计的模拟外推去卷积AI 解读

We study estimation of a finite population cumulative distribution function when sample units are measured with error. We propose a simple, bias-adjusted estimator that eliminates much of the bias induced by measurement error. A variance estimator for the proposed cumulative distribution function estimator is also obtained.

使多个参数函数的贝叶斯推断具有频率学有效性的先验AI 解读

We characterise priors which match, up to O(n−1), the posterior joint cumulative distribution function of multiple parametric functions with the corresponding frequentist cumulative distribution function. This work extends and unifies the work of Ghosh & Mukerjee (1993) and Datta & Ghosh (1995a) on the topic of probability-matching priors. A set of necessary and sufficient conditions is obtained for the above characterisation. Some of these conditions depend only on the…

分布函数垂直切线位置的稳健估计AI 解读

It is shown that the location of the set of $m + 1$ observations with minimal diameter, within local data, is a robust estimator of the location of a vertical tangent in a distribution function. The rate of consistency of these estimators is shown to be the same as that of asymptotically efficient estimators for the same model. Robustness means (1) only properties of the distribution local to the vertical tangent play a role in the asymptotics, and (2) these asymptotics can…

长记忆移动平均过程经验过程的渐近展开AI 解读

Let $X_n = \Sigma_{i=1}^{\infty} a_i \varepsilon_{n-i}$, where the $\varepsilon_i$ are iid with mean 0 finite fourth moment and the $a_i$ are regularly varying with index $-\beta$ where $\beta \epsilon (1/2, 1)$ so that ${X_n}$ has long-range dependence. This covers an important class of the fractional ARIMA process. For $r \geq 0$, let $Y_{N, r} = \sum_{n=1}^N \sum_{1\leq j_1 < \dots < j_r} \Pi_{s=1}^r a_{j_s}, Y_{N, 0} = N, \sigma_{N, r}^2 = \Var(Y_{N, r})$ and $F^{(r)} =$…

多元分布的洛伦兹 zonoidAI 解读

The article extends the usual Lorenz curve and Lorenz order of univariate distributions to the multivariate case. For a given probability distribution in nonnegative d space, d ≥ 1, we define and investigate the Lorenz zonoid and the Lorenz surface, which are sets in (d + 1) space. The surface equals the usual Lorenz curve when d = 1. Included is the definition of the Lorenz surface of a finite number of vectors that may be interpreted as the endowments of economic units in…

多元数据分位数的几何定义AI 解读

An extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered. The approach is based on blending as well as generalization of the key ideas used in the construction of spatial median and regression quantiles, both of which have been extensively studied in the literature. These geometric quantiles are potentially useful in constructing trimmed multivariate means as well as many other L estimates of…

两样本分位数比较函数及其诊断标志物应用AI 解读

In this article a control percentile test, a chi-squared test, and a Kolmogorov-type test are proposed for comparing two distributions from incomplete survival data. These tests are obtained by examining a vertical shift comparison function at a single point, a finite number of points, and an entire set of points on an interval. The proposed methods also have applications in receiver operating characteristic (ROC) analysis, which has been widely used in such diverse fields…

基于小波阈值与 Neyman 截断的显著性检验AI 解读

Traditional nonparametric tests, such as the Kolmogorov—Smirnov test and the Cramér—Von Mises test, are based on the empirical distribution functions. Although these tests possess root-n consistency, they effectively use only information contained in the low frequencies. This leads to low power in detecting fine features such as sharp and short aberrants as well as global features such as high-frequency alternations. The drawback can be repaired via smoothing-based test…

两样本问题中的分位数比较函数及诊断标志物比较应用AI 解读

In this article a control percentile test, a chi-squared test, and a Kolmogorov-type test are proposed for comparing two distributions from incomplete survival data. These tests are obtained by examining a vertical shift comparison function at a single point, a finite number of points, and an entire set of points on an interval. The proposed methods also have applications in receiver operating characteristic (ROC) analysis, which has been widely used in such diverse fields…

线性回归中的参数恒定性检验：经验分布函数方法AI 解读

This paper proposes some tests for parameter constancy in linear regressions. The tests use weighted empirical distribution functions of estimated residuals and are asymptotically distribution free. The proposed tests have nontrivial local power against a wide range of alternatives. In particular, the tests are capable of detecting error heterogeneity that is not necessarily manifested in the form of changing variances. The model allows for both dynamic and trending…

不完整生存数据中分位数函数的非参数似然比置信带AI 解读

The purpose of this paper is to derive confidence bands for quantile functions using a nonparametric likelihood ratio approach. The method is easy to implement and has several appealing properties. It applies to right-censored and left-truncated data, and it does not involve density estimation or even require the existence of a density. Previous approaches (e.g., bootstrap) have imposed smoothness conditions on the density. The performance of the proposed method is…

二参数指数族中后验分位数的频率学有效性AI 解读

Berger & Bernardo's (1989) reference priors and Tibshirani (1989) priors are derived for distributions in Bar-Lev & Reiser's (1982) two-parameter exponential family when either the location or the scale parameter is of interest. The reference prior is shown to be a Tibshirani prior. Furthermore, conditions under which a Tibshirani prior is a higher-order matching prior are investigated. When both the parameters are of interest, it is also shown that the reference prior…

中位数回归模型的拟似然AI 解读

This article proposes quasi-likelihood equations for median regression models. The quasi-likelihood can be used for dependent observations such as repeated measurements or time series data. To construct a quasi-likelihood equation, we need to specify the relation between the median and the dispersion and also specify the dependency of the observations. If a monotone transformation of the original observation has a Laplace distribution, then the quasi-likelihood is the exact…

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