论文检索

存在干扰参数时后验分位数的频率学有效性：高阶渐近分析AI 解读

Given a random sample from a distribution with density function that depends on an unknown parameter θ = (θ1, θ2), we are concerned with frequentist validity, up to o(n−1), of posterior quantiles of θ1, treating θ2 as a nuisance parameter. We propose to make the best choice of the prior on θ by matching, as far as practicable, the posterior and frequentist coverage probabilities up to o(n−1).

基于经验分布函数的序列独立性非参数检验AI 解读

The Blum, Kiefer & Rosenblatt (1961) statistic for testing independence is considered in a time series setting. This test is, under mild conditions, shown to be consistent against lag one dependent alternatives. The null distribution of the test statistic is established, both when the marginal distribution is continuous and when it is discrete. Simulation results giving information on the size and the power of the test are provided, and comparisons are made with other tests…

癌症临床试验中生活质量分布函数的估计AI 解读

The analysis of quality-of-life data collected at periodic intervals in a cancer clinical trial must account for those patients' data that are ‘missing’ because of death or administrative censoring. We examine estimates of the cumulative distribution function of an interpolated area under a quality-of-life curve as summaries of the quality-of-life experience of a treatment group. A proposed estimator, although biased, offers an improvement over a Kaplan-Meier estimator that…

插值构造的非参数预测区间与置信区间AI 解读

SUMMARY In several important statistical problems, prediction intervals and confidence intervals can be constructed with coverage levels which are known precisely but cannot be rendered equal to predetermined levels such as 0.95. One solution to this difficulty is to interpolate between such intervals. We show that simple linear interpolation reduces the order of coverage error, but that higher orders of interpolation produce no further improvement. The error is reduced by a…

改进的单调条件分位数估计量AI 解读

Suppose that $(X_1, Y_1),\cdots, (X_n, Y_n)$ are i.i.d. bivariate random vectors and that $\xi_p(x)$ is the $p$-quantile of $Y_1$ given $X_1 = x$ for $0 < p < 1$. Estimation of $\xi_p(x)$, when it is monotone in $x$, has been studied in the literature. In the nonparametric conditional quantile estimation one uses only some smoothness assumptions. The asymptotic properties are superior in the latter case; however, monotonicity is not guaranteed. We introduce a new estimator…

谱分布的拟合优度检验AI 解读

The spectral distribution function of a stationary stochastic process standardized by dividing by the variance of the process is a linear function of the autocorrelations. The integral of the sample standardized spectral density (periodogram) is a similar linear function of the autocorrelations. As the sample size increases, the difference of these two functions multiplied by the square root of the sample size converges weakly to a Gaussian stochastic process with a…

一致随机序约束下的生存曲线估计AI 解读

If F and G are cumulative distribution functions on [0, ∞) governing the lifetimes of specific systems under study, and if F and G are their corresponding survival functions, then F is said to be uniformly stochastically smaller than G, denoted by F <(+) G, if and only if the ratio l(x) = G (x)/ F (x) is nondecreasing for x ∈ [0, sup{t: [0, sup {(t: F (t) > 0}). When F and G are absolutely continuous, F (+) G is equivalent to the assumption that the corresponding failure…

摘要暂缺

MA(1) 与局部水平模型最大似然估计量的分布AI 解读

Although considerable attention has recently been paid to the behavior of the maximum likelihood estimator of simple moving average models, little progress has been made in finding a good approximation to its distribution in cases where the process is close to being noninvertible. In this paper a method is produced that gives an excellent approximation to the distribution function, even in the case where the process is strictly noninvertible. Also studied is the related…

效率约束下的位置参数偏差稳健估计AI 解读

In 1964, P. Huber established the following minimax bias robustness result for estimating the location $\mu$ in the $\varepsilon$-contamination family $F(x)=(1-\varepsilon)\phi[(x-\mu)/s]+\varepsilon H(x)$, where $\phi$ is the standard normal distribution and H is an arbitrary distribution function: The median minimizes the maximum asymptotic bias among all translation equivariant estimates of location. However, the median efficiency of $2/\pi$ at the Gaussian model may be…

局部线性回归平滑器及其极小极大效率AI 解读

In this paper we introduce a smooth version of local linear regression estimators and address their advantages. The MSE and MISE of the estimators are computed explicitly. It turns out that the local linear regression smoothers have nice sampling properties and high minimax efficiency-they are not only efficient in rates but also nearly efficient in constant factors. In the nonparametric regression context, the asymptotic minimax lower bound is developed via the heuristic of…

具有非单调依赖结构的二元分布AI 解读

A new ordering for nonmonotone dependence is proposed, and a method is presented for describing parametric families of bivariate distributions with fixed marginals and specified dependence structures. The method is easy to use and allows for arbitrary marginals and arbitrary dependence structures (e.g., structures of nonmonotone dependence). Any parametric family of bivariate distributions is ordered by the nonmonotone dependence ordering constructed from the desirable…

利用非参数校准进行有限总体偏差稳健估计AI 解读

A Standard problem in sample survey inference is that of predicting the finite population total H of a function h(y) of a random variable Y. The model-based approach to this problem first defines a working model ξ for Y and then predicts H by estimating its expectation under ξ, conditional on the sample values of Y. This approach leads to biased predictions if ξ is incorrect. We explore an automatic solution to this misspecification bias that uses nonparametric regression to…

基于数据深度的质量指数与多元秩检验AI 解读

Let F and G be the distribution functions of two given populations on Rp, p ≥ 1. We introduce and study a Parameter Q = Q(F, G), which measures the Overall “outlyingness” of population G relative to population F. The Parameter Q can be defined using any concept of data depth. Its value ranges from 0 to 1, and is .5 when F and G are identical. We show that within the dass of elliptical distributions when G departs from F in location or G has a larger spread, or both, the…

协变量存在测量误差的病例对照研究AI 解读

We devise methods for estimating the parameters of a prospective logistic model with dichotomous response D and arbitrary covariates X from case-control data when these covariates are measured with error. We suppose that some fraction of the cases and controls provide only the error-prone covariate measurements, W (the “incomplete” or “reduced” data), whereas some of the cases and controls provide measurements on X and W (the “complete” data). We assume a measurement error…

因果推断所依赖的假设AI 解读

SUMMARY Statisticians commonly make causal inferences from the results of randomized experiments, but usually question causal inferences from observational studies on the grounds that untestable assumptions are required. This paper explains the basis for this situation and examines, within quite a general framework, various assumptions that appear in the literature. It is demonstrated how the role of each assumption is intimately related to the sort of causal inference being…

伪回归、协整与近协整渐近理论的另一种研究方法AI 解读

An alternative approach is taken to the asymptotic theory of cointegration. The present approach gives a different expression for the limiting distributions of statistics associated with cointegration, which enables us to compute accurately the distribution functions. Alternative interpretations of cointegration are given and a notion of near cointegration is introduced. We then devise tests which take cointegration as the null and discuss the limiting local power under the…

摘要暂缺

癌症临床试验中生活质量分布函数的估计AI 解读

The analysis of quality-of-life data collected at periodic intervals in a cancer clinical trial must account for those patients' data that are ‘missing’ because of death or administrative censoring. We examine estimates of the cumulative distribution function of an interpolated area under a quality-of-life curve as summaries of the quality-of-life experience of a treatment group. A proposed estimator, although biased, offers an improvement over a Kaplan-Meier estimator that…

基于经验分布函数的序列独立性非参数检验AI 解读

The Blum, Kiefer & Rosenblatt (1961) statistic for testing independence is considered in a time series setting. This test is, under mild conditions, shown to be consistent against lag one dependent alternatives. The null distribution of the test statistic is established, both when the marginal distribution is continuous and when it is discrete. Simulation results giving information on the size and the power of the test are provided, and comparisons are made with other tests…

存在干扰参数时后验分位数的频率学有效性：高阶渐近分析AI 解读

Given a random sample from a distribution with density function that depends on an unknown parameter θ = (θ1, θ2), we are concerned with frequentist validity, up to o(n−1), of posterior quantiles of θ1, treating θ2 as a nuisance parameter. We propose to make the best choice of the prior on θ by matching, as far as practicable, the posterior and frequentist coverage probabilities up to o(n−1).

利用辅助信息估计有限总体分布函数的核方法AI 解读

This paper considers the use of auxiliary information to improve the estimation of the distribution function of a finite population. A method is proposed which combines the known distribution of the auxiliary variable with a kernel estimate of the conditional distribution of the survey variable given the value of the auxiliary variable. The resulting estimator compares favourably with existing estimators in terms of efficiency, conditional behaviour and robustness. The…

有限总体经验似然估计与辅助信息的有效利用AI 解读

SUMMARY In finite population inference problems, auxiliary population information is often available. We show in this paper that the empirical likelihood method can be naturally applied to such problems to make effective use of the auxiliary information. We prove that the resulting estimates have smaller asymptotic variances than the usual estimates which do not use auxiliary information. A Bahadur-type representation for empirical likelihood sample quantiles is given.…

Kolmogorov–Smirnov 损失下最佳不变分布函数估计量的极小极大性AI 解读

For the invariant decision problem of estimating a continuous distribution function with the Kolmogorov-Smirnov loss, it is proved that the best invariant estimator is minimax.