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适应非参数回归稀疏设计的插值方法：评论AI 解读

We suggest interpolation methods for overcoming the problem of sparse design in local linear smoothing. These methods are based on simple rules, determined by the kernel and bandwidth, for deciding when and where pseudo-design points should be added to augment the original design sequence. New ordinates for the added design points are computed by simple interpolation, then local linear smoothing is applied directly to the expanded dataset. The method is competitive with…

非参数回归中适应稀疏设计的插值方法AI 解读

We suggest interpolation methods for overcoming the problem of sparse design in local linear smoothing. These methods are based on simple rules, determined by the kernel and bandwidth, for deciding when and where pseudo-design points should be added to augment the original design sequence. New ordinates for the added design points are computed by simple interpolation, then local linear smoothing is applied directly to the expanded dataset. The method is competitive with…

毒性严重程度数据中的无可观察不良效应水平AI 解读

Toxicity data are often categorized by severity of response and dose level with the assumption that there is a tolerated dose below which there is no toxicity. For data from a controlled experiment, the largest observed dose at or below the tolerated dose is called the no-observed-adverse-effect level (NOAEL). The problem of identifying the NOAEL can be viewed statistically as estimating the maximal observed dose for which there is no increased severity or frequency of toxic…

高维回归中的非线性混杂AI 解读

It is not uncommon to find nonlinear patterns in the scatterplots of regressor variables. But how such findings affect standard regression analysis remains largely unexplored. This article offers a theory on nonlinear confounding, a term for describing the situation where a certain nonlinear relationship in regressors leads to difficulties in modeling and related analysis of the data. The theory begins with a measure of nonlinearity between two regressor variables. It is…

线性回归模型的贝叶斯模型平均AI 解读

We consider the problem of accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. A Bayesian solution to this problem involves averaging over all possible models (i.e., combinations of predictors) when making inferences about quantities of interest. This approach is often not practical. In this…

广义线性混合模型的最大似然算法AI 解读

Maximum likelihood algorithms are described for generalized linear mixed models. I show how to construct a Monte Carlo version of the EM algorithm, propose a Monte Carlo Newton-Raphson algorithm, and evaluate and improve the use of importance sampling ideas. Calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously. I also use the Newton-Raphson algorithm as a framework to compare maximum likelihood to the…

局部自适应回归样条AI 解读

Least squares penalized regression estimates with total variation penalties are considered. It is shown that these estimators are least squares splines with locally data adaptive placed knot points. The definition of these variable knot splines as minimizers of global functionals can be used to study their asymptotic properties. In particular, these results imply that the estimates adapt well to spatially inhomogeneous smoothness. We show rates of convergence in bounded…

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,…

基于特征值分解的正则化高斯判别分析AI 解读

Friedman proposed a regularization technique (RDA) of discriminant analysis in the Gaussian framework. RDA uses two regularization parameters to design an intermediate classifier between the linear, the quadratic the nearest-means classifiers. In this article we propose an alternative approach, called EDDA, that is based on the reparameterization of the covariance matrix [Σ k ] of a group Gk in terms of its eigenvalue decomposition Σ k = λ k D k A k D k ′, where λk specifies…

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…

离散持续期与竞争风险模型中风险率及时变效应的平滑估计AI 解读

State-space or dynamic approaches to discrete or grouped duration data with competing risks or multiple terminating events allow simultaneous modeling and smooth estimation of hazard functions and time-varying effects in a flexible way. Full Bayesian or posterior mean estimation, using numerical integration techniques or Monte Carlo methods, can become computationally rather demanding or even infeasible for higher dimensions and larger datasets. Therefore, based on previous…

四人家庭收入中位数估计：贝叶斯时间序列方法AI 解读

This article develops a general methodology for small domain estimation based on data from repeated surveys. The results are directly applied to the estimation of median income of four-person families for the 50 states and the District of Columbia. These estimates are needed by the U.S. Department of Health and Human Services (HHS) to formulate its energy assistance program for low income families. The U.S. Bureau of the Census, by an informal agreement, has provided such…

离散持续期与竞争风险模型中风险函数和时变效应的平滑AI 解读

State-space or dynamic approaches to discrete or grouped duration data with competing risks or multiple terminating events allow simultaneous modeling and smooth estimation of hazard functions and time-varying effects in a flexible way. Full Bayesian or posterior mean estimation, using numerical integration techniques or Monte Carlo methods, can become computationally rather demanding or even infeasible for higher dimensions and larger datasets. Therefore, based on previous…

摘要暂缺

连续统回归并不总是连续AI 解读

SUMMARY Continuum regression (CR) is regression of a response y on that linear combination t γ of explanatory variables which maximizes r 2(y, t) var(t)γ, where γ is chosen from a continuum of candidates. CR includes several common methods as special cases: ordinary least squares, principal component regression, partial least squares and a modified ridge regression. We demonstrate that CR, despite its name, can yield a predictor that is a discontinuous function of γ and of…

非参数重要性抽样AI 解读

Importance sampling is a widely used variance reduction simulation technique for the evaluation of high-dimensional integrals. A key step in the implementation of importance sampling is to choose a proper distribution function from which pseudorandom numbers are generated. Parametric sampling distributions, if available at all, are often inadequate for high-dimensional integrals over irregular regions. One possible remedy is to use a nonparametric method to estimate the…

多离散度分量广义线性混合模型的偏差校正AI 解读

General formulas are derived for the asymptotic bias in regression coefficients and variance components estimated by penalized quasi-likelihood (PQL) in generalized linear mixed models with canonical link function and multiple sets of independent random effects. Easily computed correction matrices result in variance component estimates that have satisfactory asymptotic behavior for small values of the variance components and significantly reduce bias for larger values. Both…

二元时间序列互谱的自动估计AI 解读

The penalised Whittle likelihood has recently been shown to have good properties in nonparametric estimation of spectral density functions. This paper extends the approach to the estimation of the cross-spectrum of a bivariate time series. One major difference from the univariate case is that the cross-spectrum estimate is not constrained to be positive, but must result in a positive definite spectral density matrix. An efficient computational method based on iterative…

变量选择中模型先验概率的预测式设定AI 解读

We examine the problem of specifying prior probabilities for all possible subset models in the context of variable selection in normal linear models. A solution is proposed that uses a prior prediction for the observable, an associated weight, and prior opinion regarding error precision as the only required input. Numerical examples are given to illustrate the method.

基于数据依赖分区的直方图回归估计AI 解读

We establish general sufficient conditions for the $L_2$-consistency of multivariate histogram regression estimates based on data-dependent partitions. These same conditions insure the consistency of partitioning regression estimates based on local polynomial fits, and, with an additional regularity assumption, the consistency of histogram estimates for conditional medians. Our conditions require shrinking cells, subexponential growth of a combinatorial complexity measure…

切片逆回归核估计的渐近性质AI 解读

To explore nonlinear structures hidden in high-dimensional data and to estimate the effective dimension reduction directions in multivariate nonparametric regression, Li and Duan proposed the sliced inverse regression (SIR) method which is simple to use. In this paper, the asymptotic properties of the kernel estimate of sliced inverse regression are investigated. It turns out that regardless of the kernel function, the asymptotic distribution remains the same for a wide…

推断对先验边际分布的局部敏感性AI 解读

The sensitivity of posterior expectations to perturbations of prior marginals is investigated, using a local method. This approach is particularly well suited to high-dimensional parameter spaces. Qualitative and quantitative results are obtained regarding the propagation of sensitivity in multiparameter settings. More specifically, a posterior expectation is treated as a functional of the prior marginal. The derivative of this functional is evaluated at the nominal prior…

局部多项式的有限样本方差：分析与解决方法AI 解读

Fitting local polynomials in nonparametric regression has a number of advantages. The attractive theoretical features are in a partial contradiction to variance properties for random design and to practical experience over a broad range of situations. No upper bound can be given for the conditional variance. The unconditional variance is infinite when using optimal weights with compact support. Properties are better for Gaussian weights. We analyze local polynomials for…

高维线性模型残差的经验过程AI 解读

We give a stochastic expansion for the empirical distribution function $\hat{F}_n$ of residuals in a p-dimensional linear model. This expansion holds for p increasing with n. It shows that, for high-dimensional linear models, $\hat{F}_n$ strongly depends on the chosen estimator $\hat{\theta}$ of the parameter $\theta$ of the linear model. In particular, if one uses an ML-estimator $\hat{\theta}_{ML}$ which is ML motivated by a wrongly specified error distribution function G,…