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四种乘积极限估计量的偏差比较AI 解读

The bias of the product-limit estimator depends entirely on the method used to ‘complete’ the estimator beyond the last observation when it is censored. The bias has been investigated for the upper (Gill, 1980) and lower (Efron, 1967) bounds on these methods. Rather than using a completion method, investigators in practice commonly truncate the estimator using data-driven rules. The bias under two common truncation rules are considered: (i) truncating at the last observation…

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Reinsch 样条与 Speckman 样条的比较AI 解读

In the context of nonparametric regression, spline smoothers can be used both for the estimation of the curve itself and for the estimation of the error variance. We compare two approaches that have been suggested: the Reinsch spline, i.e. roughness penalty, and the Speckman spline, minimax. The comparison is made on the basis of the summed mean squared error for curve estimation and on the basis of a closely related criterion for variance estimation. We show in both…

位置参数估计中的条件稳健性AI 解读

Let Y1,…, Yn denote independent real-valued observations, each distributed according to a density p(y − θ ), where θ is an unknown parameter and p is a symmetric density function. This paper considers robust point estimation of θ from the point of view of conditional inference. Specific measures of the conditional robustness of a location estimator are introduced, as well as measures of the conditional robustness of a particular sample. Location-scale models are also…

标志点数据的大小与形状分析AI 解读

The paper deals with statistical analysis of landmark data using the exact joint distribution theory for the size and shape of planar Gaussian configurations. This is an extension of earlier work which considered marginal shape analysis. Special cases of the size and shape distribution are examined and the isotropic Gaussian model is investigated in particular detail. Various properties are studied, including conditional distributions and a curve of regression. Finally we…

点过程统计分析的动态方法AI 解读

An approach to the analysis of point processes based on sequential analysis of successive intervals assuming a piecewise constant intensity rate is presented. Bayesian inference for processes with explanatory variables is derived in terms of on-line estimation, filtering and prediction. Limiting equations for the time-continuous intensity rate are obtained and solved for the no-covariates case. Examples are provided and the approach is applied in a numerical example.

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失效类型缺失的竞争风险检验札记AI 解读

The modified log rank test for competing risks with missing failure type suggested by Goet-ghebeur & Ryan (1990) is derived from a partial likelihood which leaves out some information. This extra information is incorporated to give a new partial likelihood and hence a new test statistic.

混合比例已知时正态混合模型中的检验AI 解读

The aim of this paper is to study the behaviour of the likelihood ratio test statistic in mixture models when the proportions of the distributions are known a priori. The results depend on the value of the proportion, the dimenstionality of the problem and whether or not the variance of the distributions is known.

右删失线性模型中的 M 估计AI 解读

We propose a method of obtaining an M-estimator in a linear model when the responses are subject to right censoring. The central limit theorem for the estimator using squared error loss, i.e. least squares, is derived using counting process martingale techniques. The estimation method is applied to the Stanford heart transplant data for illustration.

热卡插补调查数据的刀切法方差估计AI 解读

Hot deck imputation is commonly employed for item nonresponse in sample surveys. It is also a common practice to treat the imputed values as if they are true values, and then compute the variance estimates using standard formulae. This procedure, however, could lead to serious underestimation of the true variance, when the proportion of missing values for an item is appreciable. We propose a jackknife variance estimator for stratified multistage surveys which is obtained by…

残差相关时核回归的带宽选择AI 解读

Standard techniques for selecting the bandwidth of a kernel estimator from the data in a nonparametric regression model perform badly when the errors are correlated. In this paper we propose a modified version of an existing plug-in bandwidth selector. The method is generalized to stationary error variables by estimating a functional of the residual covariance function. The proposed bandwidth selector shows good properties in asymptotic theory and in simulations without…

核密度估计的自动带宽选择器AI 解读

To select a proper bandwidth is a critical step in kernel density estimation. It is well known that the bandwidth selected by cross-validation has a large variability. This difficulty limits the applicability of cross-validation. To reduce the variability, we suggested modifying the sample characteristic function beyond some cut-off frequency in estimating the bias term of the mean integrated squared error. It is proposed to select the cut-off frequency by a generalization…

线性回归模型中变量选择后的推断AI 解读

We explore the impact of variable selection on statistical inferences in linear regression models. In particular, the generalized final prediction error criterion of Shibata (1984) is considered and it is found, among other things, that inferences on the regression coefficients are impaired by the variable selection procedure. Most notably, the size of the nominal confidence sets tend to be inflated if they are derived based on the selected model. On the other hand, variable…

删失样本中免疫个体比例的估计AI 解读

An estimator for the proportion of ‘immunes’ in a population is proposed, when a sample of censored failure times is available. Our suggestion is to use one minus the maximum observed value of the Kaplan-Meier empirical distribution function. This estimator is shown to be consistent and asymptotically normal, under modest conditions on the censoring mechanism. Simulations suggest that the estimator is approximately normal for quite small sample sizes, provided the immune…

多元分析中 Bartlett–Nanda–Pillai 迹统计量的鞍点近似AI 解读

The null distribution of the Bartlett-Nanda-Pillai trace statistic is shown to be equivalent to the conditional distribution of canonical sufficient statistics in a multiparameter exponential family setting. As such, sequential and double saddlepoint approximations are used to approximate the distribution. The existence of tabulated percentiles for the distribution allows for comparison of the accuracy of the various saddlepoint approximations. The ability of the…

修正有符号似然统计量与鞍点近似AI 解读

For a number of tests in exponential families we show that the use of a normal approximation to the modified signed likelihood ratio statistic r* is equivalent to the use of a saddlepoint approximation. This is also true in a large deviation region where the signed likelihood ratio statistic r is of order √ n.

利用 Gibbs 抽样进行捕获—再捕获估计AI 解读

Capture-recapture models are widely used in the estimation of population sizes. Based on data augmentation considerations, we show how Gibbs sampling can be applied to calculate Bayes estimates in this setting. As a result, formulations which were previously avoided because of analytical and numerical intractability can now be easily considered for practical application. We illustrate this potential by using Gibbs sampling to calculate Bayes estimates for a hierarchical…

非线性假设的贝叶斯因子与似然分布AI 解读

New methods are proposed which allow Bayes factors to be computed for hypotheses which impose nonlinear restrictions on the parameters. Projection methods are used to induce the prior distribution over the restricted parameter space which is required for computation of the Bayes factor. Various distance metrics are introduced to define the projection, including a utility-based metric which gives Kullback-Leibler divergence as a special case. Draws from the restricted and…

非线性回归模型二次设计的一则说明AI 解读

Hamilton & Watts (1985) state that their quadratic design criterion results in designs with only p points of support. In this note we demonstrate how their design criterion may be used to obtain designs with p+1 design points, thus allowing for a check of the adequacy of the assumed model.

捕获概率异质的再捕获实验：修正鞅估计AI 解读

An estimation method of Lloyd & Yip (1991), based on martingales and the assumption of beta distributed capture probabilities, is modified to improve its performance for all but highly heterogeneous populations. This estimator is compared to the jackknife estimator by simulation under both beta and non-beta conditions. Some expressions for standard error are developed but found to behave poorly for realistic sample sizes. Bootstrap estimates of standard error appear superior…

二元极值分布的Fisher信息AI 解读

A representation of Lee (1979) is used to give an explicit algebraic formula for the 5×5-dimensional Fisher information matrix for Gumbel's (1960) bivariate Type II distribution of extreme values with Weibull marginals. Numerical evaluations show that our parameterization makes the dependence parameter almost exactly orthogonal to the two marginal scale parameters.

正态分布下线性倾向得分匹配效果的刻画AI 解读

Matched sampling is a standard technique for controlling bias in observational studies due to specific covariates. Since Rosenbaum & Rubin (1983), multivariate matching methods based on estimated propensity scores have been used with increasing frequency in medical, educational, and sociological applications. We obtain analytic expressions for the effect of matching using linear propensity score methods with normal distributions. These expressions cover cases where the…