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改进交叉验证：.632+ 自助法AI 解读

A training set of data has been used to construct a rule for predicting future responses. What is the error rate of this rule? This is an important question both for comparing models and for assessing a final selected model. The traditional answer to this question is given by cross-validation. The cross-validation estimate of prediction error is nearly unbiased but can be highly variable. Here we discuss bootstrap estimates of prediction error, which can be thought of as…

摘要暂缺

M 估计、凸性与分位数AI 解读

The paper develops a class of extensions of the univariate quantile function to the multivariate case (M-quantiles), related in a certain way to M-parameters of a probability distribution and their M-estimators. The spatial (geometric) quantiles, recently introduced by Koltchinskii and Dudley and by Chaudhuri as well as the regression quantiles of Koenker and Basset, are the examples of the M-quantile function discussed in the paper. We study the main properties of…

受约束协方差分量模型中的估计与检验AI 解读

A cutting plane algorithm is proposed for estimating variance and covariance components by maximum likelihood or restricted maximum likelihood enforcing the constraints that covariance matrices be positive semidefinite. For tests of hypotheses involving these constrained estimates, an asymptotic parametric bootstrap is proposed for approximating the distribution of the likelihood ratio test statistic. Although the bootstrap is generally inconsistent when the true parameter…

基于数据深度与自助法的极限 P 值概念AI 解读

In this article we propose some new notions of limiting P values for hypothesis testing. The limiting P value (LP) here not only provides the usual attractive interpretation of a P value as the strength in support of the null hypothesis coming from the observed data, but also has several advantages. First, it allows us to resample directly from the empirical distribution (in the bootstrap implementations), rather than from the estimated population distribution satisfying the…

免疫测定中经自助法调整的校准置信区间AI 解读

In immunoassay, a nonlinear heteroscedastic regression model is used to characterize assay concentration-response, and the model fitted to data from standard samples is used to calibrate unknown test samples. Usual large-sample methods to construct individual confidence intervals for calibrated concentrations have been observed in empirical studies to be seriously inaccurate in terms of achieving the nominal level of coverage. We show theoretically that this inaccuracy is…

摘要暂缺

通过自助法对不平等指标进行统计推断AI 解读

In this paper we consider the use of bootstrap methods to compute interval estimates and perform hypothesis tests for decomposable measures of economic inequality. Two applications of this approach using the Gini coefficient and Theil's entropy measures of inequality, are provided. Our first application employs pre- and post-tax aggregate state income data, constructed from the Panel Study of Income Dynamics we find that although casual observation of the inequality measures…

配对实验中比较受试者工作特征曲线的分布无关方法AI 解读

A distribution-free permutation test procedure is proposed for comparing receiver operating characteristic curves based on continuous data from a paired design. The method tests the hypothesis that the two curves are identical for all operating points, unlike previously proposed methods which test the equivalence of the areas under the curves. The new test is shown by simulation to have very similar operating characteristics to the standard method based on comparisons of the…

模型选择中的广义信息准则AI 解读

The problem of evaluating the goodness of statistical models is investigated from an information-theoretic point of view. Information criteria are proposed for evaluating models constructed by various estimation procedures when the specified family of probability distributions does not contain the distribution generating the data. The proposed criteria are applied to the evaluation of models estimated by maximum likelihood, robust, penalised likelihood, Bayes procedures,…

一阶自回归模型的单位根自助法检验AI 解读

We propose bootstrap tests for unit roots in first-order autoregressive models and we establish their asymptotic validity both for independent and for autoregressive errors; in this case, the bootstrap methodology directly approaches the asymptotic distribution, making unnecessary the usual corrections due to dependence of innovations. We also present a Monte Carlo power study comparing these tests with existing alternative methods. For small samples, the power of the…

Maximum likelihood estimators for record-value data with a linear trend are quite sensitive to misspecification of the error distribution. Indeed, incorrect choice of that distribution can lead to inconsistent estimation of the intercept parameter and produce estimators of slope that do not enjoy the asymptotic convergence rate prescribed by the information matrix. These properties and the importance of linearly trended records lead us to suggest a distribution-free approach…

重抽样：代入估计量的一致性AI 解读

On the basis of N i.i.d. random variables with a common unknown distribution P we wish to estimate a functional $\tau_N(P)$. An obvious and very general approach to this problem is to find an estimator $\hat{P}_N$ of P first, and then construct a so-called substitution estimator $\tau_N (\hat{P}_N)$ of $\tau_N(P)$. In this paper we investigate how to choose the estimator $\hat{P}_N$ so that the substitution estimator $\tau_N (\hat{P}_N)$ will be consistent. Although our…

多个总体随机序关系的似然比检验AI 解读

The likelihood ratio test is often used to test hypotheses involving a stochastic ordering. Distribution theory for the likelihood ratio test has been developed only for two stochastically ordered distributions. For testing equality of distributions against a stochastic ordering in several populations, this paper derives the null asymptotic distribution of the likelihood ratio test statistic, which is characterized by minimization problems and has no closed form. A Monte…

回归与分类中的估计组合AI 解读

We consider the problem of how to combine a collection of general regression fit vectors to obtain a better predictive model. The individual fits may be from subset linear regression, ridge regression, or something more complex like a neural network. We develop a general framework for this problem and examine a cross-validation—based proposal called “model mix” or “stacking” in this context. We also derive combination methods based on the bootstrap and analytic methods and…

泊松点过程强度函数的自助法置信域AI 解读

Bootstrap methods are developed for constructing confidence regions for the intensity function of a nonstationary Poisson process. Several different resampling algorithms are suggested, ranging from resampling a Poisson process with intensity equal to that estimated nonparametrically from the data to resampling the data points themselves in the same manner that the bootstrap is used in problems involving independent and identically distributed observations. For each…

基于自助法的相依与独立观测控制图AI 解读

Shewhart charts are widely accepted as standard tools for monitoring manufacturing processes of univariate, independent “nearly” normal measurements. They are not as well developed beyond these types of data. We generalize the idea of Shewhart charts to cover other types of data commonly encountered in practice. More specifically, we develop some valid control charts for dependent data and for independent data that are not necessarily “nearly” normal. We derive the proposed…

基于频域自助法的传递函数模型拟合检验AI 解读

Transfer function models have been used for modeling the linear dependence between stationary time series and for improving the accuracy of forecasts. This article proposes a method to evaluate the fit of such a model by comparing certain frequency domain functionals of the model with those of the data using a model-based bootstrap algorithm. The method works by checking the ability of the fitted model to reproduce the dynamic relationship and the linear dependence structure…

基于频域自助法的传递函数模型拟合检验AI 解读

Transfer function models have been used for modeling the linear dependence between stationary time series and for improving the accuracy of forecasts. This article proposes a method to evaluate the fit of such a model by comparing certain frequency domain functionals of the model with those of the data using a model-based bootstrap algorithm. The method works by checking the ability of the fitted model to reproduce the dynamic relationship and the linear dependence structure…

时间序列比值统计量的频域自助法AI 解读

The asymptotic properties of the bootstrap in the frequency domain based on Studentized periodogram ordinates are studied. It is proved that this bootstrap approximation is valid for ratio statistics such as autocorrelations. By using Edgeworth expansions it is shown that the bootstrap approximation even outperforms the normal approximation. The results carry over to Whittle estimates. In a simulation study the behavior of the bootstrap is studied for empirical correlations…

平稳观测下分块自助法的二阶正确性AI 解读

We show that the blockwise bootstrap approximation for the distribution of a studentized statistic computed from dependent data is second-order correct provided we choose an appropriate variance estimator. We also show how to adapt the $BC_a$ confidence interval of Efron to the a dependent case. For the proofs we extend the results of Götze and Hipp on the validity of the formal Edgeworth expansion for a sum to the studentized mean.

典型变量分析的替代置信区域AI 解读

Recent papers have questioned the appropriateness of the circular confidence regions often drawn around group mean points in canonical variate analysis and proposed improved elliptical regions. This paper develops new theoretical and bootstrap regions of an alternative type, with those constructed using parametric bootstrapping being shown by simulation to perform consistently well.

The problem of estimating the number of binary responses that can be attributed to high levels of a continuous covariate is studied. The distribution of the covariate in the population is combined with the relative odds of response to produce a function, areas under which represent numbers of responses attributable to covariate values in that range. A combination of parametric and nonparametric smoothing is proposed. Consistent estimates of variance are developed as well as…

有限混合模型中的自助法似然比推断AI 解读

SUMMARY Statistical inference using the likelihood ratio statistic for the number of components in a mixture model is complicated when the true number of components is less than that of the proposed model since this represents a non-regular problem: the true parameter is on the boundary of the parameter space and in some cases the true parameter is in a nonidentifiable subset of the parameter space. The maximum likelihood estimator is shown to converge to the subset…