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高维完全独立性检验AI 解读

A simple statistic is proposed for testing the complete independence of random variables having a multivariate normal distribution. The asymptotic null distribution of this statistic, as both the sample size and the number of variables go to infinity, is shown to be normal. Consequently, this test can be used when the number of variables is not small relative to the sample size and, in particular, even when the number of variables exceeds the sample size. The finite sample…

能否兼得 AIC 与 BIC 的优势？模型识别与回归估计的冲突AI 解读

A traditional approach to statistical inference is to identify the true or best model first with little or no consideration of the specific goal of inference in the model identification stage. Can the pursuit of the true model also lead to optimal regression estimation? In model selection, it is well known that BIC is consistent in selecting the true model, and AIC is minimax-rate optimal for estimating the regression function. A recent promising direction is adaptive model…

单一监测时间下的双变量现时状态数据AI 解读

For bivariate current status data with univariate monitoring times, the identifiable part of the joint distribution is three univariate cumulative distribution functions, namely the two marginal distributions and the bivariate cumulative distribution function evaluated on the diagonal. We show that smooth functionals of these univariate cumulative distribution functions can be efficiently estimated with easily computed nonparametric maximum likelihood estimators based on…

利用最小二乘估计非参数回归的残差方差AI 解读

We propose a new estimator for the error variance in a nonparametric regression model. We estimate the error variance as the intercept in a simple linear regression model with squared differences of paired observations as the dependent variable and squared distances between the paired covariates as the regressor. For the special case of a one-dimensional domain with equally spaced design points, we show that our method reaches an asymptotic optimal rate which is not achieved…

无向高斯图模型中的协方差分解AI 解读

The covariance between two variables in a multivariate Gaussian distribution is decomposed into a sum of path weights for all paths connecting the two variables in an undirected independence graph. These weights are useful in determining which variables are important in mediating correlation between the two path endpoints. The decomposition arises in undirected Gaussian graphical models and does not require or involve any assumptions of causality. This covariance…

数据追踪与贝叶斯一致性的理解AI 解读

We deal with strong consistency for Bayesian density estimation. An awkward consequence of inconsistency is described. It is pointed out that consistency at some density f0 depends on the prior mass assigned to the ‘pathological’ set of those densities that are close to f0, in a weak sense, and far apart from f0, in a Hellinger sense. An analysis of these sets leads to the identification of the notion of ‘data tracking’. Specific examples in which this phenomenon cannot…

贝叶斯变量选择的自适应抽样AI 解读

Our paper proposes adaptive Monte Carlo sampling schemes for Bayesian variable selection in linear regression that improve on standard Markov chain methods. We do so by considering Metropolis–Hastings proposals that make use of accumulated information about the posterior distribution obtained during sampling. Adaptation needs to be done carefully to ensure that sampling is from the correct ergodic distribution. We give conditions for the validity of an adaptive sampling…

逆高斯分布参数最大似然估计量分布的另一种推导AI 解读

We provide a simpler derivation of the sampling properties of the maximum likelihood estimators of the parameters in an inverse Gaussian distribution.

降低近似贝叶斯 bootstrap 插补方差估计偏差的一则札记AI 解读

Rubin & Schenker (1986) proposed the approximate Bayesian bootstrap, a two-stage resampling procedure, as a method of creating multiple imputations when missing data are ignorable. Kim (2002) showed that the multiple imputation variance estimator is biased for moderate sample sizes when this method is used. To reduce the bias, Kim (2002) proposed modifying the number of samples drawn at the first stage of the Bayesian bootstrap procedure. In this note, we suggest an…

比例风险回归的一致性概率与区分能力AI 解读

The concordance probability is used to evaluate the discriminatory power and the predictive accuracy of nonlinear statistical models. We derive an analytical expression for the concordance probability in the Cox proportional hazards model. The proposed estimator is a function of the regression parameters and the covariate distribution only and does not use the observed event and censoring times. For this reason it is asymptotically unbiased, unlike Harrell's c-index based on…

空间统计中两种渐近框架的协调AI 解读

Two asymptotic frameworks, increasing domain asymptotics and infill asymptotics, have been advanced for obtaining limiting distributions of maximum likelihood estimators of covariance parameters in Gaussian spatial models with or without a nugget effect. These limiting distributions are known to be different in some cases. It is therefore of interest to know, for a given finite sample, which framework is more appropriate. We consider the possibility of making this choice on…

一阶内蕴自回归与 de Wijs 过程AI 解读

We discuss intrinsic autoregressions for a first-order neighbourhood on a two-dimensional rectangular lattice and give an exact formula for the variogram that extends known results to the asymmetric case. We obtain a corresponding asymptotic expansion that is more accurate and more general than previous ones and use this to derive the de Wijs variogram under appropriate averaging, a result that can be interpreted as a two-dimensional spatial analogue of Brownian motion…

一般依赖结构下多重关联检验中非真零假设数量的下界AI 解读

We propose probabilistic lower bounds for the number of false null hypotheses when testing multiple hypotheses of association simultaneously. The bounds are valid under general and unknown dependence structures between the test statistics. The power of the proposed estimator to detect the full proportion of false null hypotheses is discussed and compared to other estimators. The proposed estimator is shown to deliver a tight probabilistic lower bound for the number of false…

失效原因缺失的线性变换竞争风险模型：回归系数的半参数估计AI 解读

We consider the problem of estimating the regression coefficients in a competing risks model, where the relationship between the cause-specific hazard for the cause of interest and covariates is described using linear transformation models and when cause of failure is missing at random for a subset of individuals. Using the theory of Robins et al. (1994) for missing data problems and the approach of Chen et al. (2002) for estimating regression coefficients for linear…

复杂调查中基于惩罚样条的模型辅助估计AI 解读

Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on penalised spline regression is proposed. These estimators are weighted linear combinations of sample observations, with weights calibrated to known control totals. They allow straightforward extensions to multiple auxiliary variables and to complex designs. Under standard design conditions, the estimators are design consistent and asymptotically…

曲线样本结构均值的非参数最大似然估计AI 解读

A random sample of curves can be usually thought of as noisy realisations of a compound stochastic process X(t) = Z{W(t)}, where Z(t) produces random amplitude variation and W(t) produces random dynamic or phase variation. In most applications it is more important to estimate the so-called structural mean μ(t) = E{Z(t)} than the crosssectional mean E{X(t)}, but this estimation problem is difficult because the process Z(t) is not directly observable. In this paper we propose…

回归模型残差分析的对称诊断方法AI 解读

Typical alternative hypotheses in the analysis of residuals of a standard regression model are considered, and for each one a Bayesian diagnostic based on a symmetric form of the Kullback–Leibler divergence is determined. The results include an explicit expression for the diagnostic when the alternative hypothesis is that the errors are generated by an unknown distribution function with a Dirichlet process prior. This expression is immediately interpretable, exactly…

短记忆与长记忆高斯过程的 Stein–James 估计量AI 解读

We investigate the mean squared error of the Stein–James estimator for the mean when the observations are generated from a Gaussian vector stationary process with dimension greater than two. First, assuming that the process is short-memory, we evaluate the mean squared error, and compare it with that for the sample mean. Then a sufficient condition for the Stein–James estimator to improve upon the sample mean is given in terms of the spectral density matrix around the…

正态均值的非线性函数估计AI 解读

We derive a Monte-Carlo-amenable, minimum variance unbiased estimator of a nonlinear function of a normal mean and the variance of the estimator. Applications to problems arising in the analysis of data measured with error are described.

Logistic 回归模型的最小距离估计AI 解读

It is well known that the maximum likelihood fit of the logistic regression parameters can be greatly affected by atypical observations. Several robust alternatives have been proposed. However, if we consider the model from the case-control viewpoint, it is clear that current techniques can exhibit poor behaviour in many common situations. A new robust class of estimation procedures is introduced. The estimators are constructed via a minimum distance approach after…

脆弱性模型中层级似然与传统最佳线性无偏预测方法的比较AI 解读

Hierarchical likelihood provides a statistically efficient procedure for frailty models. Recently, a method using the computationally attractive orthodox best linear unbiased predictor has been proposed; this uses Pearson-type estimation. We compare both approaches and discuss their relative merits. With semiparametric frailty models difficulties can arise for the orthodox method, if the number of nuisance parameters increases with the sample size. This difficulty is avoided…

相关数据下的序约束均值估计AI 解读

In many applications, researchers are interested in estimating the mean of a multivariate normal random vector whose components are subject to order restrictions. Various authors have demonstrated that the likelihood-based methodology may perform poorly under certain conditions for such problems. The problem is much harder when the underlying covariance matrix is nondiagonal. In this paper a simple iterative algorithm is introduced that can be used for estimating the mean of…

比较非正态连续分布的正交基方法AI 解读

We present an orthonormal bases approach for detecting general differences among continuous distributions. An unknown density function is represented by a finite vector of its estimated Fourier coefficients with respect to a suitable orthonormal basis. For a wide class of orthonormal bases, we establish asymptotic normality of the vector of estimated Fourier coefficients and propose an unbiased and consistent estimator of its asymptotic covariance matrix. Fourier coeffients…

加速间隔时间模型AI 解读

This paper develops a new semiparametric model for the effect of covariates on the conditional intensity of a recurrent event counting process. The model is a transparent extension of the accelerated failure time model for univariate survival data. Estimation of the regression parameter is motivated by semiparametric efficiency considerations, extending the class of weighted log-rank estimating functions originally proposed in Prentice (1978) and subsequently studied in…