论文检索

Stein估计的数据平滑性质AI 解读

The data smoothing aspect of Stein estimates is explored in the nonparametric regression settings. We show that appropriately shrinking the raw data towards any linear smoother will provide a robust "smoother" (which dominates the raw data and hence has a bounded maximum risk when the average squared error loss is concerned).

自回归过程的无穷小稳健性AI 解读

We define the influence function and construct optimal robust estimators for autoregressive processes. We show that the asymptotic bias caused by small contaminations of the marginals can be written as the integral of a certain function with respect to the contamination. This function is called the influence function. It is unique only up to an equivalence relation, but there is a natural unique version which describes the limiting influence of an additional observation…

平稳线性模型中两阶段最小二乘估计的自助法AI 解读

For models similar to those used in econometric work, under suitable regularity conditions, the bootstrap is shown to give asymptotically valid approximations to the distribution of errors in coefficient estimates.

非线性回归诊断的几何方法及其在配对病例对照研究中的应用AI 解读

A geometric approach is described for the detection of influential points in nonlinear regression. This work extends and gives geometric interpretation to recent results in logistic regression diagnostics. An application of this approach to matched case-control studies is discussed.

图形投影寻踪的渐近理论AI 解读

Mathematical tools are developed for describing low-dimensional projections of high-dimensional data. Theorems are given to show that under suitable conditions, most projections are approximately Gaussian.

先验随阶段变化的经验贝叶斯方法AI 解读

We consider modified empirical Bayes problems in which the prior distribution of $\Theta$ at stage $n + 1$ is $G^{(n+1)}(\theta)$. The Bayes optimality criterion is now given by the sequence of functionals $R(G^{(n+1)}$. The observations $X_1, \cdots, X_n$ are no longer i.i.d so decision procedures are constructed based on modified empirical density estimates for $f_G^{(n+1)}(x)$. Asymptotic optimality together with asymptotic convergence rates is established for two action…

对 Amemiya 二元 Logit 回归估计论文的评论AI 解读

Amemiya (1980) derived expressions for the $n^{-2}$-order mean squared errors of the maximum likelihood and the minimum logit chi-squared estimators in the dichotomous logit regression model. He numerically evaluated these expressions for a number of specific examples and in all examples found that the minimum chi-squared estimator has smaller $n^{-2}$-order mean squared error. In this paper, we demonstrate examples in which the maximum likelihood estimator has smaller $n^{-2}$…

非参数趋势一致性札记AI 解读

The question is discussed when of two ordered sets of continuous distribution functions one shows less positive trend than the other. The resulting ordering has applications to power function monotonicity of isotonic rank tests, and is related to certain orderings in parametric models.

密度、回归曲线与众数的光滑最优核估计AI 解读

Several criteria concerning the choice of kernels for the nonparametric estimation of functions and their derivatives are discussed. A specific optimality criterion is described which applies to kernels of compact support and of different orders of smoothness. The solutions of the corresponding variational problems are explicitly given. Many kernels discussed previously are obtained as special cases.

多元回归变量选择准则的渐近性质AI 解读

In normal linear regression analysis, many model selection rules proposed from various viewpoints are available. For the information criteria AIC, FPE, $C_p$, PSS and BIC, the asymptotic distribution of the selected model and the asymptotic quadratic risk based on each criterion are explicitly obtained.

不变置信区域与预测区域的一个条件性质AI 解读

This paper considers estimation and prediction problems invariant under an amenable group that is transitive on the parameter space. It is shown that an invariant confidence or prediction region does not admit super-relevant betting procedures if and only if its level of coverage is defined conditionally given the maximal invariant statistic.

非高斯无限可分及线性随机过程的似然比检测器AI 解读

We consider the problem of determining absolute continuity, and the distribution of the likelihood ratio (Radon-Nikodym derivative) of the measures induced on function space by two infinitely divisible stochastic processes. The results are applied to linear processes, which are shown to be infinitely divisible.

Cox 模型中部分似然与广义最大似然估计的渐近等价性AI 解读

The usual approach to estimating regression parameters in the Cox regression model uses the partial likelihood. If the covariates are not time-dependent, the model can be stated in terms of the survival function, which allows one to derive a generalized likelihood containing both regression and survival curve parameters. It is shown that, in the absence of ties, an estimator results which is asymptotically equivalent to the partial likelihood estimator. A joint information…

混合条件下符号检验的稳健化AI 解读

A robustified version of the two sample sign test is defined which is insensitive to certain deviations from the assumption of the independence of the observations. These deviations are described in terms of mixing conditions. The asymptotic value of the power function of this robustified sign test is computed on contiguous alternatives possessing the same dependence structure. This entails the calculation of its asymptotic relative efficiencies with respect to some tests…

尾部序所定义分布类的渐近相对效率界AI 解读

It is shown that large classes of asymptotic relative efficiencies (AREs) are isotonic with respect to various partial orderings on the heaviness of tails of symmetric distributions. The orderings include those of van Zwet (1964), Lawrence (1975), Barlow and Proschan (1975), and a new one that generalizes all three. Characterizations in terms of these orderings are given for many familiar families of distributions with restricted tail and central behavior. By restricting…

利用先验信息估计分层总体总量的可容许估计量AI 解读

We consider the problem of the estimation of the total of a stratified finite population. For two levels of prior knowledge about the stratification, we provide Bayes and pseudo-Bayes estimators that make use of this prior knowledge in sensible ways. We then note that admissibility results can be established for these estimators using the techniques of Meeden and Ghosh (1982, 1983) and indicate some possible natural extensions of the present work.

平稳时间序列的正弦极限AI 解读

We show that the Sinusoidal Limit Theorem of Slutsky in the Gaussian case is a consequence of the equality of certain higher order crossings.

非平稳时间序列的信号提取AI 解读

The nonstationary signal extraction problem is to estimate $s_t$ given observations on $z_t = s_t + n_t$ (signal plus noise) when either $s_t$ or $n_t$ or both is nonstationary. Homogeneous or explosive nonstationary time series described by models of the form $\delta(B)z_t = w_t$ where $\delta(B)$ has zeroes on or inside the unit circle and $w_t$ is stationary are considered. For certain cases, approximate solutions to the nonstationary signal extraction problem have been…

量性响应数据的贝叶斯非参数推断AI 解读

The problem of nonparametric Bayes estimation of a tolerance distribution based on quantal response data has been considered previously with a prior distribution based on the Dirichlet process. In the present article, a broad class of priors is developed for this problem by allowing the hazard function of the tolerance distribution to be a realization of a nonnegative stochastic process with independent increments. This class includes the Dirichlet prior as a special case.…

非参数回归函数估计量的重对数律AI 解读

We study the estimation of a regression function by two classes of estimators, the Nadaraya-Watson Kernel type estimators and the orthogonal polynomial estimators. We obtain sharp pointwise rates of strong consistency by establishing laws of the iterated logarithm for the two classes of estimators. These results parallel those of Hall (1981) on density estimation and extend those of Noda (1976) on strong consistency of kernel regression estimators.

一类回归函数估计量的一致一致性AI 解读

We study a wide class of nonparametric regression function estimators including kernel estimators and robust smoothers. Under different assumptions on the kernel and the sequence of bandwidths, we obtain weak uniform consistency rates on a bounded interval. The uniform consistency is shown in a "stochastic design model" and in a "fixed design model".

无限参数回归模型中有界线性泛函的一致估计AI 解读

Consider a linear model with infinitely many parameters given by $y = \sum^\infty_{i = 1} x_i\theta_i + \varepsilon$ where $\mathbf{x} = (x_1, x_2, \cdots)'$ and $\theta = (\theta_1, \theta_2, \cdots)'$ are infinite dimensional vectors such that $\sum^\infty_{i = 1}x^2_i < \infty$ and $\sum^\infty_{i = 1} \theta^2_i < \infty$. Suppose independent observations $y_1, y_2, \cdots, y_n$ are observed at levels $\mathbf{x}_1, \mathbf{x}_2, \cdots, \mathbf{x}_n$. Under suitable…

随机删失下两样本秩检验的渐近行为AI 解读

Two samples, $\{X_{ji}, 1 \leq i \leq n(j)\} (j = 1, 2)$ are assumed to be composed of iid random variables with survival functions $(1 - F_j)(1 - H_j)$, where $H$ is the cdf of the "censoring times" and $F$ is the cdf of the "true lifetimes." A unified derivation of the Pitman efficiencies of a class of rank statistics for censored samples is presented. The conditions under which the result holds do not require contiguous alternatives, since convergence to normality is…

两样本删失生存数据的序贯线性秩检验AI 解读

Under extremely general patterns of patient-arrival, allocation to treatment and loss to follow-up in (randomized) clinical trial settings, the sequentially computed logrank statistic (Mantel, 1966) is shown (under the null hypothesis of identically distributed lifetimes) to have exactly uncorrelated increments, and is shown via Rebolledo's (1980) martingale invariance principle to satisfy a functional central limit theorem, justifying sequential logrank tests of Jones and…