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回归函数根处的条件分位数估计AI 解读

The Robbins-Monro process $X_{n+1} = X_n - c_n Y_n$ is a standard stochastic approximation method for estimating the root $\theta$ of an unknown regression function. There is a vast literature on the convergence properties of $X_n$ to $\theta$. In practice, one is also interested in the conditional distribution of the system under the sequential control when the control is set at $\theta$ or near $\theta$. This problem appears to have received no attention in the literature.…

An estimator for the proportion of ‘immunes’ in a population is proposed, when a sample of censored failure times is available. Our suggestion is to use one minus the maximum observed value of the Kaplan-Meier empirical distribution function. This estimator is shown to be consistent and asymptotically normal, under modest conditions on the censoring mechanism. Simulations suggest that the estimator is approximately normal for quite small sample sizes, provided the immune…

多个收入分布的同时密度估计AI 解读

The size distributions of net income in Great Britain changed systematically in the 1970s. This can be shown by visual comparison of nonparametric density estimates. Typical bandwidth selection methods, such as least squares and biased cross-validation, tend to hinder comparison, because of too much variability across curves. Hence, a method for finding an appropriate pooled bandwidth is developed. It is seen that this method is much more reliable than single curve…

通过条件独立性刻画指数分布AI 解读

SUMMARY Let Y 1, Y 2, . . ., Yn be mutually independent non-negative random variables having an absolutely continuous distribution function Fi(y) over its support [0, ∞) and the corresponding density function f i(y) > 0 for y > 0. Let A denote the event that Yi – Y i+1 > 0 for all i = 1, 2, . . ., n – 1. Then we show that, conditional on the event A, Yi – Y i+1 and Y i+1 are independent for all i = 1, 2,. . ., k if and only if Yi (i = 1, 2, . . ., k) are exponentially…

用秩统计理论研究一般 Bootstrap 的一致性AI 解读

A general notion of a bootstrapped mean constructed by exchangeably weighting sample points is introduced. Consistency of this generalized bootstrapped mean, which includes proposals of Efron and Rubin among others, is proved by classical linear rank statistics theory. The consistency of generalized bootstrapped empirical and quantile processes is also established.

样本分位数的平衡重复复制法之渐近性质AI 解读

Inference, including variance estimation, can be made from stratified samples by selecting a balanced set of subsamples. This balanced subsampling method is generically called the balanced repeated replication method in survey data analysis, which includes McCarthy's balanced half-samples method and its extensions for more general stratified designs. We establish the asymptotic consistency of the balanced repeated replication variance estimators when the parameter of…

作为稳健位置估计量的距离截尾均值AI 解读

The metrically trimmed mean is defined as the average of observations remaining after a fixed number of outlying observations have been removed. A metric, the distance from the median, is used to determine which points are outlying. The influence curve and the asymptotic normality of the metrically trimmed mean are derived using von Mises expansions. The relative merits of the median, the trimmed mean and the metrically trimmed mean are discussed in neighborhoods of…

带非参数回归趋势的自回归过程均值平稳性检验AI 解读

In this paper, we suggest tests of stationarity in the mean of autoregressive time series versus arbitrary trend alternatives. As an intermediate, though essential, step local asymptotic normality of autoregressive models with a nonparametric regression trend is established. Moreover, a functional central limit theorem for the underlying likelihood ratio processes is derived. These results then offer a general construction principle by which every goodness of fit test (case…

删失数据下尺度参数的最小距离估计AI 解读

This article examines how the level of censoring affects the performance of estimators of scale that minimize a weighted Cramérvon Mises distance between the Kaplan-Meier product-limit estimator of the survival distribution function and an assumed model. The article shows that under certain conditions these estimators are asymptotically normal if the survival function is a member of the assumed scale family. Weights that minimize the asymptotic variance under these…

非独立同分布数据下弹着精度分位数的可行贝叶斯估计AI 解读

An important measure of accuracy for problems of directing projectiles at targets is the circular error probable (CEP), a bivariate version of a 50% quantile point. This article presents a Bayesian procedure for estimating CEP when the projectile impact measurements are not iid, which is the case of usual practical interest. Our interest in a Bayesian procedure is motivated by a desire to combine accuracy information from several different sources. Except for the simplest…

分位数过程弱收敛的初等方法及其在删失生存数据中的应用AI 解读

Let ξ be a continuously differentiable function with positive derivative, and let ξ n be a sequence of right-continuous increasing processes. We show that if n 1/2(ξ n − ξ) W, where W is continuous, then n 1/2(ξ−1 n − ξ−1) − W(ξ−1)/ξ′(ξ−1). This result is applied to classical processes such as the empirical distribution function, the Kaplan-Meier estimator, and some other situations. We also prove an analogous result for the bootstrapped version of n 1/2(ξ n − ξ) and show…

利用条件密度混合估计层级模型边际后验密度AI 解读

A technique called quantile integration is proposed for the estimation of marginal posterior densities arising in Bayesian models having hierarchical representations. The method is based on approximating marginal densities as mixtures of conditional densities, where the conditioning variables are selected deterministically from the mixing distributions. The form of the approximation makes it easy to implement, and the resulting approximations are computationally efficient to…

利用条件密度混合估计层级模型边际后验密度的方法AI 解读

A technique called quantile integration is proposed for the estimation of marginal posterior densities arising in Bayesian models having hierarchical representations. The method is based on approximating marginal densities as mixtures of conditional densities, where the conditioning variables are selected deterministically from the mixing distributions. The form of the approximation makes it easy to implement, and the resulting approximations are computationally efficient to…

删失数据的尺度最小距离估计AI 解读

This article examines how the level of censoring affects the performance of estimators of scale that minimize a weighted Cramérvon Mises distance between the Kaplan-Meier product-limit estimator of the survival distribution function and an assumed model. The article shows that under certain conditions these estimators are asymptotically normal if the survival function is a member of the assumed scale family. Weights that minimize the asymptotic variance under these…

非独立同分布数据下弹着精度分位数的可行贝叶斯估计AI 解读

An important measure of accuracy for problems of directing projectiles at targets is the circular error probable (CEP), a bivariate version of a 50% quantile point. This article presents a Bayesian procedure for estimating CEP when the projectile impact measurements are not iid, which is the case of usual practical interest. Our interest in a Bayesian procedure is motivated by a desire to combine accuracy information from several different sources. Except for the simplest…

渐近展开启发的插值规则AI 解读

We suggest a simple interpolation rule, based on Edgeworth and Cornish-Fisher expansions, which permits highly accurate numerical approximation in problems involving calculation of distributions or quantiles without requiring explicit calculation of terms in the expansions.

有限总体分布函数估计量的性质AI 解读

Two leading estimators of the finite population distribution function are studied. Their large-sample mean squared errors are compared, under a given model. Neither estimator is universally better; circumstances are identified where the model-based estimator would do poorly, despite employing the correct model.

经济学中一类线性过程模型的经验分布渐近性质AI 解读

Let … be a moving average process of infinite order where the innovations ε( k ) are in the domain of attraction of a stable law with index α ε (0, 2) and the parameter sequence decreases at a polynomial or exponential rate. These and similar processes have recently received increased attention both in the econometrics and statistics/probability literature. The present paper studies almost sure uniform rates of convergence of the empirical distribution function. Applications…

随机展开与渐近近似AI 解读

Under general conditions the distribution function of the first few terms in a stochastic expansion of an econometric estimator or test statistic provides an asymptotic approximation to the distribution function of the original estimator or test statistic with an error of order less than that of the limiting normal or chi-square approximation. This can be used to establish the validity of several refined asymptotic methods, including the comparison of Nagar-type moments and…

定期观测三状态马尔可夫过程的非参数估计及艾滋病应用AI 解读

SUMMARY Estimation in a three-state Markov process with irreversible transitions in the presence of interval-censored data is considered. A nonparametric maximum likelihood procedure for the estimation of the cumulative transition intensities is presented. A self-consistent estimator of the parameters is defined and it is shown that the maximum likelihood estimator is a self-consistent estimator. This extends the idea of self-consistency introduced by Efron to the estimation…

广义分位数过程AI 解读

For random vectors taking values in $\mathbb{R}^d$ we introduce a notion of multivariate quantiles defined in terms of a class of sets and study an associated process which we call the generalized quantile process. This process specializes to the well known univariate quantile process. We obtain functional central limit theorems for our generalized quantile process and show that both Gaussian and non-Gaussian limiting processes can arise. A number of interesting example are…

随机乘法删失模型中经验分布的大样本研究AI 解读

Consider an incomplete data problem with the following specifications. There are three independent samples $(X_1, \ldots, X_m), (Z_1, \ldots, Z_n)$ and $(U_1, \ldots, U_n)$. The first two samples are drawn from a common lifetime distribution function $G$, while the third sample is drawn from the uniform distribution over the interval $(0,1)$. In this paper we derive the large sample properties of $\hat{G}_{m,n}$, the nonparametric maximum likelihood estimate of $G$ based on…

条件曲线的统计推断：泊松过程方法AI 解读

A Poisson approximation of a truncated, empirical point process enables us to reduce conditional statistical problems to unconditional ones. Let $(\mathbf{X,Y})$ be a $(d + m)$-dimensional random vector and denote by $F(\cdot\mid\mathbf{x})$ the conditional d.f. of $\mathbf{Y}$ given $\mathbf{X} = \mathbf{x}$. Applying our approach, one may study the fairly general problem of evaluating a functional parameter $T(F(\cdot\mid\mathbf{x}_1),\ldots,F(\cdot\mid\mathbf{x}_p))$ based…

非参数回归中的 Bootstrap 置信区间AI 解读

Several authors have developed bootstrap methods for constructing confidence intervals in nonparametric regression. On each occasion a nonpivotal approach has been employed. Nonpivotal methods are still the overwhelmingly popular choice when statisticians use the bootstrap to compute confidence intervals, but they are not necessarily the most appropriate. In this paper we point out some of the theoretical advantages of pivoting. They include a reduction in the error of the…