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基于任意阶自回归计算的 bootstrap 置信域AI 解读

Summary Given a linear time series, e.g. an autoregression of infinite order, we may construct a finite order approximation and use that as the basis for confidence regions. The sieve or autoregressive bootstrap, as this method is often called, is generally seen as a competitor with the better-understood block bootstrap approach. However, in the present paper we argue that, for linear time series, the sieve bootstrap has significantly better performance than blocking methods…

多重二次惩罚下的建模与平滑参数估计AI 解读

Summary Penalized likelihood methods provide a range of practical modelling tools, including spline smoothing, generalized additive models and variants of ridge regression. Selecting the correct weights for penalties is a critical part of using these methods and in the single-penalty case the analyst has several well-founded techniques to choose from. However, many modelling problems suggest a formulation employing multiple penalties, and here general methodology is lacking.…

函数线性模型的两步估计及其纵向数据应用AI 解读

Summary Functional linear models are useful in longitudinal data analysis. They include many classical and recently proposed statistical models for longitudinal data and other functional data. Recently, smoothing spline and kernel methods have been proposed for estimating their coefficient functions nonparametrically but these methods are either intensive in computation or inefficient in performance. To overcome these drawbacks, in this paper, a simple and powerful two-step…

半参数平均导数估计的 Edgeworth 展开AI 解读

A valid Edgeworth expansion is established for the limit distribution of density-weighted semiparametric averaged derivative estimates of single index models. The leading term that corrects the normal limit varies in magnitude, depending on the choice of bandwidth and kernel order. In general this term has order larger than the n−1/2 that prevails in standard parametric problems, but we find circumstances in which it is O(n−1/2), thereby extending the achievement of an n−1/2…

非平稳布尔模型的平滑估计及覆盖过程应用AI 解读

Kernel smoothing methods are applied to nonparametric estimation for nonstationary Boolean models. In many applications only exposed tangent points of the models are observable rather than full realisations. Several methods are developed for estimating the distribution of the underlying Boolean model from observation of the exposed tangent points. In particular, estimation methods for coverage processes are studied in detail and applied to neurobiological data.

自变量无测量误差或有测量误差时的聚类数据非参数函数估计AI 解读

We consider local polynomial kernel regression with a single covariate for clustered data using estimating equations. We assume that at most m < ∞ observations are available on each cluster. In the case of random regressors, with no measurement error in the predictor, we show that it is generally the best strategy to ignore entirely the correlation structure within each cluster and instead pretend that all observations are independent. In the further special case of…

利用序贯重要性抽样拟合计数与捕杀数据的种群动态模型AI 解读

For prudent wildlife management based on population dynamics models, it is important to incorporate parameter uncertainty into the management advice. Much parameter uncertainty originates when it is not possible to parameterize the population management model for a population of interest using data from that population alone. Instead, information about parameter values obtained from other populations of the same species, or even from similar species, must be used. In…

利用序贯重要性抽样拟合种群计数与扑杀数据的动态模型AI 解读

For prudent wildlife management based on population dynamics models, it is important to incorporate parameter uncertainty into the management advice. Much parameter uncertainty originates when it is not possible to parameterize the population management model for a population of interest using data from that population alone. Instead, information about parameter values obtained from other populations of the same species, or even from similar species, must be used. In…

平滑单调密度与单峰密度的极大似然估计AI 解读

We study the nonparametric estimation of univariate monotone and unimodal densities usingthe maximum smoothed likelihood approach. The monotone estimator is the derivative of the least concave majorant of the distribution correspondingto a kernel estimator.We prove that the mapping on distributions $\Phi$ with density $\varphi$, $$\varphi \mapsto \text{the derivative of the least concave majorant of $\Phi},$$ is a contraction in all $L^P$ norms $(1 \leq p \leq \infty)$, and…

非参数扩散模型的自适应漂移估计AI 解读

We consider a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable. The goal is to estimate the unknown drift coefficient.We apply a locally linear smoother with a data-driven bandwidth choice. The procedure is fully adaptive and nearly optimal up to a log log factor. The results about the quality of estimation are nonasymptotic and do not require any ergodic or mixing properties of the observed process.

光滑高斯随机场模型中结构化相关矩阵的估计AI 解读

This article considers the estimation of structured correlation matrices in infinitely differentiable Gaussian random field models.The problem is essentially motivated by the stochastic modeling of smooth deterministic responses in computer experiments.In particular, the log-likelihood function is determined explicitly in closed-form and the sieve maximum likelihood estimators are shown to be strongly consistent under mild conditions.

第一价格拍卖中的最优非参数估计AI 解读

This paper proposes a general approach and a computationally convenient estimation procedure for the structural analysis of auction data. Considering first-price sealed-bid auction models within the independent private value paradigm, we show that the underlying distribution of bidders' private values is identified from observed bids and the number of actual bidders without any parametric assumptions. Using the theory of minimax, we establish the best rate of uniform…

后验分布的收敛速率AI 解读

We consider the asymptotic behavior of posterior distributions and Bayes estimators for infinite-dimensional statistical models. We give general results on the rate of convergence of the posterior measure. These are applied to several examples, including priors on finite sieves, log-spline models, Dirichlet processes and interval censoring.

异方差与自相关协方差矩阵核估计量的一致性AI 解读

Conditions are derived for the consistency of kernel estimators of the covariance matrix of a sum of vectors of dependent heterogeneous random variables, which match those of the currently best-known conditions for the central limit theorem, as required for a unified theory of asymptotic inference. These include finite moments of order no more than 2 + for > 0, trending variances, and variables which are near-epoch dependent on a mixing process, but not necessarily mixing.…

通过线性函数校准检验回归均值的单调性AI 解读

A new approach to testing for monotonicity of a regression mean, not requiring computation of a curve estimator or a bandwidth, is suggested. It is based on the notion of “running gradients ” over short intervals, although from some viewpoints it may be regarded as an analogue for monotonicity testing of the dip/excess mass approach for testing modality hypotheses about densities. Like the latter methods, the new technique does not suffer difficulties caused by almost-flat…

样本极值的局部似然平滑AI 解读

Summary Trends in sample extremes are of interest in many contexts, an example being environmental statistics. Parametric models are often used to model trends in such data, but they may not be suitable for exploratory data analysis. This paper outlines a semiparametric approach to smoothing sample extremes, based on local polynomial fitting of the generalized extreme value distribution and related models. The uncertainty of fits is assessed by using resampling methods. The…

杂论：密度估计前的数据锐化AI 解读

We introduce a data-perturbation method for reducing bias of a wide variety of density estimators, in univariate, multivariate, spatial and spherical data settings. The method involves 'sharpening' the data by making them slightly more clustered than before, and then computing the estimator in the usual way, but from the sharpened data rather than the original data. The transformation depends in a simple, explicit way on the smoothing parameter employed for the density…

杂记：惩罚样条回归的最优平滑程度AI 解读

The optimal amount of smoothing in penalised spline regression is investigated. In particular, a simple closed form approximation to the optimal smoothing parameter is derived. Comparisons with its exact counterpart show it to be a useful starting point for measuring the optimal amount of smoothing in penalised spline regression. It also lends itself to the development of quick and simple rules for automatic smoothing parameter selection.

平滑判别分析AI 解读

Discriminant analysis for two data sets in $\mathbb{R}^d$ with probability densities $f$ and $g$ can be based on the estimation of the set $G = \{x: f(x) \geq g(x)\}$. We consider applications where it is appropriate to assume that the region $G$ has a smooth boundary or belongs to another nonparametric class of sets. In particular, this assumption makes sense if discrimination is used as a data analytic tool. Decision rules based on minimization of empirical risk over the…

存在可观测截断时变换模型的秩估计AI 解读

This paper introduces rank estimators for a general transformation model with observable truncation points. The estimators, which are modified versions of the rank estimators of Han (1987) and Cavanagh and Sherman (1998), are asymptotically normal and require no bandwidth choice. Log-concavity of the error disturbance?s survival function is a sufficient condition for the associated monotonicity conditions. Monte Carlo simulations investigate the estimators? behavior for…

边界处密度函数的改进估计量AI 解读

We propose a new method of boundary correction for kernel density estimation. The technique is a kind of generalized reflection method involving reflecting a transformation of the data. The transformation depends on a pilot estimate of the logarithmic derivative of the density at the boundary. In simulations, the new method is seen to clearly outperform an earlier generalized reflection idea. It also has overall advantages over boundary kernel methods and a nonnegative…

基于经验特征函数的时间序列假设检验：广义谱密度方法AI 解读

The standardized spectral density completely describes serial dependence of a Gaussian process. For non-Gaussian processes, however, it may become an inappropriate analytic tool, because it misses the nonlinear processes with zero autocorrelation. By generalizing the concept of the standardized spectral density, I propose a new spectral tool suitable for both linear and nonlinear time series analysis. The generalized spectral density is indexed by frequency and a pair of…

一步局部拟似然估计AI 解读

Summary Local quasi-likelihood estimation is a useful extension of local least squares methods, but its computational cost and algorithmic convergence problems make the procedure less appealing, particularly when it is iteratively used in methods such as the back-fitting algorithm, cross-validation and bootstrapping. A one-step local quasi-likelihood estimator is introduced to overcome the computational drawbacks of the local quasi-likelihood method. We demonstrate that as…

利用 Fourier 表示进行半参数回归的贝叶斯推断AI 解读

Summary This paper presents the Bayesian analysis of a semiparametric regression model that consists of parametric and nonparametric components. The nonparametric component is represented with a Fourier series where the Fourier coefficients are assumed a priori to have zero means and to decay to 0 in probability at either algebraic or geometric rates. The rate of decay controls the smoothness of the response function. The posterior analysis automatically selects the amount…