论文检索

摘要暂缺

具有第二类偏向的分布的一致估计及竞争风险应用AI 解读

A random variable X is symmetric about 0 if X and -X have the same distribution. There is a large literature on the estimation of a distribution function (DF) under the symmetry restriction and tests for checking this symmetry assumption. Often the alternative describes some notion of skewness or one-sided bias. Various notions can be described by an ordering of the distributions of X and -X. One such important ordering is that $P(0<X<X\le x)-P(-x\le X<0)$ is increasing in $x<0$…

单调平均剩余寿命的估计AI 解读

In survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age $x, M(x)$, defined by $$M(x) = E[X - x|X > x],$$ where $X$ is a lifetime. $M$ is called the mean residual life function.In many applications it is reasonable to assume that $M$ is decreasing (DMRL) or increasing (IMRL); we write decreasing (increasing) for nonincreasing (non-decreasing). There is some literature on empirical estimators of $M$ and…

一致随机序约束下的生存函数估计AI 解读

If S and T are survival functions for two life distributions, then S is said to be uniformly stochastically smaller than T, denoted by S ≪ T, if θ(x) ≡ S(x)/T(x) is nonincreasing in x on {x: T(x) > 0}. This ordering is transitive. Uniform stochastic ordering (USO) has found important applications in nonparametric accelerated life testing, among other areas. It has been shown that the nonparametric maximum likelihood estimator (NPMLE) of S under USO when T is known is…

一致随机序约束下的生存函数估计AI 解读

If S and T are survival functions for two life distributions, then S is said to be uniformly stochastically smaller than T, denoted by S ≪ T, if θ(x) ≡ S(x)/T(x) is nonincreasing in x on {x: T(x) > 0}. This ordering is transitive. Uniform stochastic ordering (USO) has found important applications in nonparametric accelerated life testing, among other areas. It has been shown that the nonparametric maximum likelihood estimator (NPMLE) of S under USO when T is known is…

线性回归中的序约束推断AI 解读

Regression analysis constitutes a large portion of the statistical repertoire in applications. In cases where such analysis is used for exploratory purposes with no previous knowledge of the structure, one would not wish to impose any constraints on the problem. But in many applications we are interested in curve fitting with a simple parametric model to describe the structure of a system with some prior knowledge about the structure. An important example of this occurs when…

线性回归中的序约束推断AI 解读

Regression analysis constitutes a large portion of the statistical repertoire in applications. In cases where such analysis is used for exploratory purposes with no previous knowledge of the structure, one would not wish to impose any constraints on the problem. But in many applications we are interested in curve fitting with a simple parametric model to describe the structure of a system with some prior knowledge about the structure. An important example of this occurs when…

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…

重尾误差下的最近邻回归AI 解读

There has been an increasing interest in modelling regression with heavy-tailed conditional error distributions, mostly in the parametric setting. Nonparametric regression procedures have been studied almost exclusively for the cases where the conditional variance of the regressed variable is finite in the region of interest. We initiate a study of the infinite variance case. Some results in strong uniform consistency of the nearest neighbor estimator with rates are proven.…

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.…

摘要暂缺

摘要暂缺

重复测量模型中的序约束推断AI 解读

There is an extensive literature on inferences from independent random samples about several normal means under order restrictions. The purpose of this note is to point out these results have very simple generalizations to one repeated measures model.

单调非参数回归AI 解读

In monotone regression procedures one utilizes only the monotonicity of the regression function. In nonparametric regression one utilizes only the assumed smoothness. The analytic and asymptotic properties of the estimator are superior in the latter case; however, monotonicity is not guaranteed. We study a hybrid procedure that produces monotone estimators with properties similar to those of nonparametric regression estimators.

重复测量模型中的顺序约束推断AI 解读

There is an extensive literature on inferences from independent random samples about several normal means under order restrictions. The purpose of this note is to point out these results have very simple generalizations to one repeated measures model.

用多重对比比较若干处理与对照AI 解读

A problem frequently encountered in the practice of statistics is the comparison of several treatments with a control or standard. We consider an experimental situation where prior knowledge indicates that all of the treatments are at least as effective as the control and the problem is to determine if any are significantly better than the control. A number of statistical procedures have been proposed for this situation, of which the best known is Dunnett's (1955) multiple…

椭圆等高密度的概率不等式及其在序约束推断中的应用AI 解读

Anderson (1955) established the monotonicity of the integral of a symmetric, unimodal density over translates of a symmetric, convex set. A similar result is developed for integrals of elliptically contoured, unimodal densities over translates of an asymmetric, convex set in certain directions related to the set. This result is used to establish some monotonicity properties of the power functions of the likelihood ratio tests for determining whether or not a vector of normal…