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复杂区域上的样条平滑AI 解读

Summary It is occasionally necessary to smooth data over domains in ℝ2 with complex irregular boundaries or interior holes. Traditional methods of smoothing which rely on the Euclidean metric or which measure smoothness over the entire real plane may then be inappropriate. This paper introduces a bivariate spline smoothing function defined as the minimizer of a penalized sum-of-squares functional. The roughness penalty is based on a partial differential operator and is…

依赖性对密度估计随机精度度量的影响AI 解读

In kernel density estimation, those data values that make a nondegenerate contribution to the estimator (computed at a given point) tend to be spaced well apart. This property has the effect of suppressing many of the conventional consequences of long-range dependence, for example, slower rates of convergence, which might otherwise be revealed by a traditional loss-or risk-based assessment of performance. From that viewpoint, dependence has to be very long-range indeed…

时间序列筛自助法的不变原理AI 解读

This paper establishes an invariance principle applicable for the asymptotic analysis of sieve bootstrap in time series. The sieve bootstrap is based on the approximation of a linear process by a finite autoregressive process of order increasing with the sample size, and resampling from the approximated autoregression. In this context, we prove an invariance principle for the bootstrap samples obtained from the approximated autoregressive process. It is of the strong form…

聚合数据下的非参数估计AI 解读

We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intrafamily component but require that observations from different families be independent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behavior of the characteristic function at infinity. We investigate the practical…

不同密度估计方法下投影寻踪的判别能力AI 解读

We explore the properties of projection pursuit discriminant analysis. This discriminant method is very powerful but relies heavily on a univariate density estimate. We show that the procedure based on wavelets maintains the same rate of convergence as with univariate wavelet density estimation. We also show the Bayes risk strong consistency of both the kernel‐ and wavelet‐based methods. Simulated data and real data concerning character recognition show that the method is…

测量误差问题中的贝叶斯平滑样条与回归样条AI 解读

In the presence of covariate measurement error, estimating a regression function nonparametrically is extremely difficult, the problem being related to deconvolution. Various frequentist approaches exist for this problem, but to date there has been no Bayesian treatment. In this article we describe Bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error. The regression function is modeled with smoothing splines and…

染色体易位断点的聚集分析AI 解读

Translocation, a physical movement of genetic material from one chromosome to another, can result in the aberrant linkage of two cellular genes. This type of fusion may disrupt cellular function by producing novel, biologically active fused genes, or by triggering the activation of normally quiescent growth-associated genes. Either of these mechanisms provides a putative oncogenic stimulus, and indeed, several gene fusions from translocations have been identified in…

半参数工具变量估计量与检验统计量的 Edgeworth 近似AI 解读

We establish the validity of higher order asymptotic expansions to the distribution of a version of the nonlinear semiparametric instrumental variable considered in Newey (1990) as well as to the distribution of a Wald statistic derived from it. We employ local polynomial smoothing with variable bandwidth, which includes local linear, kernel, and [a version of] nearest neighbour estimates as special cases. Our expansions are valid to order n^(-2ϵ) for some 0 < ϵ < ½, where ϵ…

时间序列的回归分位数AI 解读

In this paper we study nonparametric estimation of regression quantiles for time series data by inverting a weighted Nadaraya–Watson (WNW) estimator of conditional distribution function, which was first used by Hall, Wolff, and Yao (1999, Journal of the American Statistical Association 94, 154–163). First, under some regularity conditions, we establish the asymptotic normality and weak consistency of the WNW conditional distribution estimator for α-mixing time series at both…

样条非参数回归中的模型选择AI 解读

Summary A Bayesian approach is presented for model selection in nonparametric regression with Gaussian errors and in binary nonparametric regression. A smoothness prior is assumed for each component of the model and the posterior probabilities of the candidate models are approximated using the Bayesian information criterion. We study the model selection method by simulation and show that it has excellent frequentist properties and gives improved estimates of the regression…

伯恩斯坦多项式后验的一致性AI 解读

Summary A Bernstein prior is a probability measure on the space of all the distribution functions on [0, 1]. Under very general assumptions, it selects absolutely continuous distribution functions, whose densities are mixtures of known beta densities. The Bernstein prior is of interest in Bayesian nonparametric inference with continuous data. We study the consistency of the posterior from a Bernstein prior. We first show that, under mild assumptions, the posterior is weakly…

聚类数据的半参数回归AI 解读

We consider estimation in a semiparametric partially generalised linear model for clustered data using estimating equations. A marginal model is assumed where the mean of the outcome variable depends on some covariates parametrically and a cluster‐level covariate nonparametrically. A profile‐kernel method allowing for working correlation matrices is developed. We show that the nonparametric part of the model can be estimated using standard nonparametric methods, including…

基于自由结点样条的贝叶斯曲线拟合AI 解读

We describe a Bayesian method, for fitting curves to data drawn from an exponential family, that uses splines for which the number and locations of knots are free parameters. The method uses reversible‐jump Markov chain Monte Carlo to change the knot configurations and a locality heuristic to speed up mixing. For nonnormal models, we approximate the integrated likelihood ratios needed to compute acceptance probabilities by using the Bayesian information criterion, BIC, under…

长程相依的贝叶斯半参数推断AI 解读

We develop a Bayesian semiparametric procedure for the analysis of stationary long‐range dependent time series. We use frequency domain methods to partition the infinite‐dimensional parameter space into regions where genuine prior information on the form of the spectral density is available, and others where vague prior beliefs are adopted; the solution to the partition problem, which is equivalent to bandwidth choice from a frequentist point of view, is obtained via Bayes…

凸函数估计的典范过程：积分布朗运动加四次漂移的“内包络”AI 解读

A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process “the invelope” and show that it is an almost surely uniquely defined function of integrated Brownian motion. Its role is comparable to the role of the greatest convex minorant of Brownian motion plus a parabolic drift in the problem…

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半参数非线性混合效应模型及其应用AI 解读

Nonlinear mixed effects models (NLMMs) and self-modeling nonlinear regression (SEMOR) models are often used to fit repeated measures data. They use a common function shared by all subjects to model variation within each subject and some fixed and/or random parameters to model variation between subjects. The parametric NLMM may be too restrictive, and the semiparametric SEMOR model ignores correlations within each subject. In this article we propose a class of semiparametric…

非凹惩罚似然变量选择及其 Oracle 性质AI 解读

Variable selection is fundamental to high-dimensional statistical modeling, including nonparametric regression. Many approaches in use are stepwise selection procedures, which can be computationally expensive and ignore stochastic errors in the variable selection process. In this article, penalized likelihood approaches are proposed to handle these kinds of problems. The proposed methods select variables and estimate coefficients simultaneously. Hence they enable us to…

通过部分 Lq 范数估计加性非参数模型：分数阶的代价AI 解读

We propose a new method for estimating additive nonparametric regression models based on taking the L q median of a sample of kernel estimators. We establish the consistency and asymptotic normality of our procedures. The rate of convergence depends on the value of q . For q > 3/2 one has the usual one-dimensional rate, but if q ≤ 3/2 the rate can be slower.

核平滑方法下的收益率曲线估计AI 解读

We introduce a new method for the estimation of discount functions, yield curves and forward curves from government issued coupon bonds. Our approach is nonparametric and does not assume a particular functional form for the discount function although we do show how to impose various restrictions in the estimation. Our method is based on kernel smoothing and is defined as the minimum of some localized population moment condition. The solution to the sample problem is not…

生存时间的广义加性回归模型AI 解读

We present a non-parametric survival model with two time-scales. The time-scales are equivalent up to a constant that varies over the subjects. Covariate effects are modelled linearly on each time scale by additive Aalen models. Estimators of the cumulative intensities on the two time-scales are suggested by solving approximate local maximum likelihood estimating equations. The local estimating equations necessitate only the choice of one bandwidth. The estimators are…

正态混合密度极大似然与贝叶斯估计的熵及收敛速度AI 解读

We study the rates of convergence of the maximum likelihood estimator (MLE) and posterior distribution in density estimation problems, where the densities are location or location-scale mixtures of normal distributions with the scale parameter lying between two positive numbers. The true density is also assumed to lie in this class with the true mixing distribution either compactly supported or having sub-Gaussian tails. We obtain bounds for Hellinger bracketing entropies…

We examine the way in which empirical bandwidth choice affects distributional properties of nonparametric density estimators. Two bandwidth selection methods are considered in detail: local and global plug-in rules. Particular attention is focussed on whether the accuracy of distributional bootstrap approximations is appreciably influenced by using the resample version $\hat{h}*$,rather than the sample version $\hat{h}$, of an empirical bandwidth. It is shown theoretically…