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一种自适应且具高功效的随机化检验AI 解读

Hogg & Lenth (1984) reviewed some adaptive tests. The main problems encountered while using such a procedure are the need for a good selector statistic and the size inflation due to the choice. At present, the solution to the latter problem is to construct a distribution-free procedure (Randies & Hogg, 1973). In this paper we propose a simple adaptive exact procedure. We then use it to construct an adaptive randomization test for matched pairs. This test has exactly size α,…

构造准确参数经验贝叶斯置信区间的样本再利用方法AI 解读

SUMMARY Parametric empirical Bayes (EB) methods of point estimation for a vector of unknown parameters date to the landmark paper of James and Stein (1961). The usual approach is to use the mean of the estimated posterior distribution of each parameter, where the estimation of the prior parameters (‘hyperparameters’) is accomplished through the marginal distribution of the data. While point estimates computed this way usually perform well, interval estimates based on the…

单变量连续分布对称性的若干自助法检验AI 解读

The Kolmogorov distance between the empirical $\operatorname{cdf} F_n$ and its symmetrization $sF_n$ with respect to an adequate estimator of the center of symmetry of $P$ is a natural statistic for testing symmetry. However, its limiting distribution depends on $P$. Using critical values from the symmetrically bootstrapped statistic (where the resampling is made from $sF_n$) produces tests that can be easily implemented and have asymptotically the correct levels as well as…

若干非参数变点估计量的渐近行为AI 解读

Consider a sequence $X_1, X_2,\ldots, X_n$ of independent random variables, where $X_1, X_2,\ldots, X_{n\theta}$ have distribution $P,$ and $X_{n\theta + 1}, X_{n\theta + 2},\ldots, X_n$ have distribution $Q$. The change-point $\theta \in (0,1)$ is an unknown parameter to be estimated, and $P$ and $Q$ are two unknown probability distributions. The nonparametric estimators of Darkhovskh and Carlstein are imbedded in a more general framework, where random seminorms are applied…

随机删失数据的条件秩检验AI 解读

The present paper derives various survival tests and their optimality results for randomly censored lifetime data by an extension of familiar rank tests arguments. The approach is based on local asymptotic normal models which have a natural interpretation in terms of hazard rates. In particular, the description of classical rank tests by hazard rates may be of separate interest. As an application of the new methods, a justification of conditional survival tests is given also…

约束极大似然：以单调凸逻辑回归为例AI 解读

Maximum likelihood estimates in problems in which the likelihood is smooth and the parameter space is defined by linear or smooth nonlinear inequality constraints can be obtained using available nonlinear optimization packages, such as NPSOL. This class of models includes generalized linear models with order restrictions, convexity, or smoothness constraints on the parameters (smoothness constraints being in the form of bounds on finite differences of the regression…

非参数回归中平滑程度范围的选择AI 解读

Most nonparametric regression estimates smooth the observed data in the process of generating a suitable estimate. The resulting curve estimate is sensitive to the amount of smoothing introduced, and it is important to examine the estimate over a range of smoothing choices. An objective way to specify such a range is to estimate the optimal value of the smoothing parameter (bandwidth) with respect to some loss function and then report a confidence interval for this parameter…

临床神经解剖学中重复空间点模式的方差分析AI 解读

Our application concerns the analysis of the spatial distributions of pyramidal neurons in the cingulate cortex of human subjects in three diagnostic groupings. Our purpose is to develop and apply several methods for the analysis of replicated spatial point patterns to identify anatomical differences between normal, schizoaffective, and schizophrenic persons at the time of death. We begin with a scaled Poisson analysis that uncovers significant differences between the groups…

光滑迭代程序的一步Bootstrap方法AI 解读

SUMMARY Resampling techniques have the potential to provide useful information about the sampling distribution of estimators of many population characteristics. Ambitious schemes such as the bootstrap and iterated bootstrap imply a substantial increase in computational effort. For some iterative procedures, such as generalized least squares or the EM algorithm, it is possible to avoid fully iterating each bootstrap replication to convergence. By analysing expansions of the…

时间序列重抽样：估计养老金抗通胀方案下的损失概率AI 解读

Abstract Any pension protection formula that falls short of complete compensation for inflation has associated with it a time‐series of probability distributions of future purchasing power losses. A method of estimating those distributions is proposed and applied. The method is based on the idea of representing inflation as a multivariate time‐series process and using a model fitted to historical data to generate a large artificial sample of ‘realized’ inflation sequences by…

不稳定一阶自回归过程的自助法AI 解读

Consider a first-order autoregressive process $X_t = \beta X_{t - 1} + \varepsilon_t$, where $\{\varepsilon_t\}$ are independent and identically distributed random errors with mean 0 and variance 1. It is shown that when $\beta = 1$ the standard bootstrap least squares estimate of $\beta$ is asymptotically invalid, even if the error distribution is assumed to be normal. The conditional limit distribution of the bootstrap estimate at $\beta = 1$ is shown to converge to a…

均匀重抽样与重要性重抽样的 Bahadur 表示及渐近相对效率AI 解读

We derive Bahadur-type representations for quantile estimates obtained from two different types of nonparametric bootstrap resampling--the commonly used uniform resampling method, where each sample value is drawn with the same probability, and importance resampling, where different sample values are assigned different resampling weights. These results are applied to obtain the relative efficiency of uniform resampling and importance resampling and to derive exact convergence…

经验似然可作 Bartlett 校正AI 解读

It is shown that, in a very general setting, the empirical likelihood method for constructing confidence intervals is Bartlett-correctable. This means that a simple adjustment for the expected value of log-likelihood ratio reduces coverage error to an extremely low $O(n^{-2})$, where $n$ denotes sample size. That fact makes empirical likelihood competitive with methods such as the bootstrap which are not Bartlett-correctable and which usually have coverage error of size $n^{-1}$…

非参数回归的 Bootstrap 同时误差带AI 解读

Simultaneous error bars are constructed for nonparametric kernel estimates of regression functions. The method is based on the bootstrap, where resampling is done from a suitably estimated residual distribution. The error bars are seen to give asymptotically correct coverage probabilities uniformly over any number of gridpoints. Applications to an economic problem are given and comparison to both pointwise and Bonferroni-type bars is presented through a simulation study.

利用非参数曲线进行模型检验AI 解读

The use of local likelihood curve estimates in model checking is described. Test statistics are based on deviance differences, and are interpreted using nonparametric bootstrap Monte Carlo. Some theoretical aspects are discussed. Methods are illustrated for regression with discrete data.

普通股收益分布偏度与尾部延展性的数据分析AI 解读

This article explores the nature of skewness and elongation in daily common-stock-return distributions of individual firms using estimates of g (for skewness) and h (for elongation) obtained form Turkey's g and h distributions. Both parametric and nonparametric (bootstrap) estimates of standard errors of the g estimates are computed and compared. Daily return distributions are first examined cross-sectionally over a large sample of firms. The estimates of the skewness…

用 Bootstrap 确定选址决策规则的应用AI 解读

This article provides a general methodology for determining and evaluating a decision rule for hotel site location. Given (1) an indicator of hotel success, (2) an ideal decision rule based on this indicator if it were known without error, and (3) a model for predicting the value of the success indicator at a proposed site, we propose a procedure for finding the optimal model-based decision rule for any specified optimality criterion and for evaluating the worth of the rule.…

分位数自助置信区间的覆盖概率AI 解读

An asymptotic expansion of length 2 is established for the coverage probabilities of confidence intervals for the underlying $q$-quantile which are derived by bootstrapping the sample $q$-quantile. The corresponding level error turns out to be of order $O(n^{-1/2})$ which is unexpectedly low. A confidence interval of even more practical use is derived by using backward critical points. The resulting confidence interval is of the same length as the one derived by ordinary…

学生化 U 统计量的 Edgeworth 展开与 Bootstrap 近似AI 解读

The asymptotic accuracy of the estimated one-term Edgeworth expansion and the bootstrap approximation for a Studentized $U$-statistic is investigated. It is shown that both the Edgeworth expansion estimate and the bootstrap approximation are asymptotically closer to the exact distribution of a Studentized $U$-statistic than the normal approximation. The conditions needed to obtain these results are weak moment assumptions on the kernel $h$ of the $U$-statistic and a…

Wielandt不等式及其在随机对称矩阵特征值渐近分布中的应用AI 解读

A relatively obscure eigenvalue due to Wielandt is used to give a simple derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix. The asymptotic distributions are obtained under a fairly general setting. An application of the general theory to the bootstrap distribution of the eigenvalues of the sample covariance matrix is given.

横截面生存数据的非参数估计AI 解读

In many follow-up studies survival data are often observed according to a cross-sectional sampling scheme. Data of this type are subject to left truncation in addition to the usual right censoring. A number of characteristics and properties of the product-limit estimate, for left-truncated and right-censored data, have been explored and found to be similar to those of the Kaplan-Meier estimate. Under the stationarity assumption, however, it is believed that an alternative…

学生化均值的鞍点近似及其 Bootstrap 应用AI 解读

A saddlepoint technique is used to approximate to the density and tail probability of the studentized mean of a random sample. The motivation was to replace bootstrapping of the studentized mean in the way Davison & Hinkley (1988) used the saddlepoint approximation for the unstudentized mean. The method involves first obtaining a bivariate saddlepoint approximation, then, after a nonlinear transformation, integrating out an unwanted variable either numerically or by a…

Bootstrap 的重要性重抽样AI 解读

We introduce an empirical method of importance resampling, which does not require analytical calculation of the resampling probabilities. Our method can easily be used as part of a general algorithm for Monte Carlo calculation of bootstrap confidence intervals and hypothesis tests. It produces consistent, efficient and unbiased Monte Carlo approximations. We also present a very general but elementary account of importance resampling, which shows that even optimal importance…

一种自适应且具有较高功效的随机化检验AI 解读

Hogg & Lenth (1984) reviewed some adaptive tests.The main problems encountered while using such a procedure are the need for a good selector statistic and the size inflation due to the choice.At present, the solution to the latter problem is to construct a distribution-free procedure (Randies & Hogg, 1973).In this paper we propose a simple adaptive exact procedure.We then use it to construct an adaptive randomization test for matched pairs.This test has exactly size a, the…