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时间序列分析中的非参数多步预测AI 解读

Summary We consider the problem of multistep-ahead prediction in time series analysis by using nonparametric smoothing techniques. Forecasting is always one of the main objectives in time series analysis. Research has shown that non-linear time series models have certain advantages in multistep-ahead forecasting. Traditionally, nonparametric k-step-ahead least squares prediction for non-linear autoregressive AR(d) models is done by estimating E(Xt+k |Xt, …, Xt−d+1) via…

周期高斯再生核正则化方法的统计性质AI 解读

The method of regularization with the Gaussian reproducing kernel is popular in the machine learning literature and successful in many practical applications. In this paper we consider the periodic version of the Gaussian kernel regularization. We show in the white noise model setting, that in function spaces of very smooth functions, such as the infinite-order Sobolev space and the space of analytic functions, the method under consideration is asymptotically minimax; in…

美国医院行业规模报酬的非参数分析AI 解读

Abstract This paper presents new estimates of scale economies for US hospitals. We show that the common translog specification of hospital costs is a misspecification, and employ nonparametric, local linear estimation with both continuous and discrete covariates. A bootstrap method is used to provide inferences regarding ray scale economies and expansion path scale economies for a large sample of hospitals covering 1984–1996. We find evidence of changes in the structure of…

相关回归误差的非参数检测AI 解读

In regression problems it is hard to detect correlated errors since the errors are not observed. In this paper, a nonparametric method is proposed for the detection of correlated errors when the design points are equally spaced. It turns out that the first‐order sample autocovariance of the residuals from the kernel regression estimates provides essential information about correlated errors and its bootstrap is quite effective in implementing such information.

We study the profile‐kernel and backfitting methods in partially linear models for clustered/longitudinal data. For independent data, despite the potential root‐n inconsistency of the backfitting estimator noted by Rice (1986), the two estimators have the same asymptotic variance matrix, as shown by Opsomer & Ruppert (1999). In this paper, theoretical comparisons of the two estimators for multivariate responses are investigated. We show that, for correlated data, backfitting…

基于局部 L2 拟合的半参数密度估计AI 解读

This article examines density estimation by combining a parametric approach with a nonparametric factor. The plug-in parametric estimator is seen as a crude estimator of the true density and is adjusted by a nonparametric factor. The nonparametric factor is derived by a criterion called local L2-fitting. A class of estimators that have multiplicative adjustment is provided, including estimators proposed by several authors as special cases, and the asymptotic theories are…

通过加权后验核密度估计计算状态空间蒙特卡洛似然AI 解读

Maximum likelihood estimation and likelihood ratio tests for nonlinear, non-Gaussian state-space models require numerical integration for likelihood calculations. Several methods, including Monte Carlo (MC) expectation maximization, MC likelihood ratios, direct MC integration, and particle filter likelihoods, are inefficient for the motivating problem of stage-structured population dynamics models in experimental settings. An MC kernel likelihood (MCKL) method is presented…

当前状态数据半参数回归模型的筛最大似然估计AI 解读

In a randomized controlled clinical trial study where the response variable of interest is the time to occurrence of a certain event, it is often too expensive or even impossible to observe the exact time. However, the current status of the subject at a random time of inspection is much more natural, feasible, and practical in terms of cost-effectiveness. This article considers a semiparametric regression model that consists of parametric and nonparametric regression…

同时建模条件异方差与尺度变化AI 解读

This paper proposes a semiparametric approach by introducing a smooth scale function into the standard generalized autoregressive conditional heteroskedastic (GARCH) model so that conditional heteroskedasticity (CH) and scale change in financial returns can be modeled simultaneously. An estimation procedure combining kernel estimation of the scale function and maximum likelihood estimation of the GARCH parameters is proposed. Asymptotic properties of the estimators are…

伯恩斯坦 Copula 及其在多元分布建模与逼近中的应用AI 解读

We define the Bernstein copula and study its statistical properties in terms of both distributions and densities. We also develop a theory of approximation for multivariate distributions in terms of Bernstein copulas. Rates of consistency when the Bernstein copula density is estimated empirically are given. In order of magnitude, this estimator has variance equal to the square root of the variance of common nonparametric estimators, e.g., kernel smoothers, but it is biased…

风险率函数的平均导数AI 解读

This paper develops semiparametric kernel-based estimators of risk-specific hazard functions for competing risks data. Both discrete and continuous failure times are considered. The maintained assumption is that the hazard function depends on explanatory variables only through an index. In contrast to existing semiparametric estimators, proportional hazards is not assumed. The new estimators are asymptotically normally distributed. The estimator of index coefficients is…

非线性加性自回归模型的滞后识别AI 解读

Summary We propose a lag selection method for non-linear additive autoregressive models that is based on spline estimation and the Bayes information criterion. The additive structure of the autoregression function is used to overcome the ‘curse of dimensionality’, whereas the spline estimators effectively take into account such a structure in estimation. A stepwise procedure is suggested to implement the method proposed. A comprehensive Monte Carlo study demonstrates good…

平滑样条高斯回归：通过有效近似实现更可扩展的计算AI 解读

Summary Smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with Gaussian responses. The computation of smoothing splines is generally of the order O(n3), n being the sample size, which severely limits its practical applicability. We study more scalable computation of smoothing spline regression via certain low dimensional approximations that are asymptotically as efficient. A simple algorithm is…

脑成像中重复非均匀点模式的空间强度建模AI 解读

Summary Pharmacological experiments in brain microscopy study patterns of cellular activ- ation in response to psychotropic drugs for connected neuroanatomic regions. A typical ex- perimental design produces replicated point patterns having highly complex spatial variability. Modelling this variability hierarchically can enhance the inference for comparing treatments. We propose a semiparametric formulation that combines the robustness of a nonparametric kernel method with…

The purpose of this note is to show how semiparametric estimators with a small bias property can be constructed. The small bias property (SBP) of a semiparametric estimator is that its bias converges to zero faster than the pointwise and integrated bias of the nonparametric estimator on which it is based. We show that semiparametric estimators based on twicing kernels have the SBP. We also show that semiparametric estimators where nonparametric kernel estimation does not…

摘要暂缺

利用渐近枢轴估计函数推断无限维参数AI 解读

Suppose that a consistent estimator for an infinite‐dimensional parameter can be readily obtained via a set of estimating functions which has a ‘good’ local linear approximation around the true value of the parameter. However, it may be difficult to estimate the variance function of this estimator well. We show that, if the set of estimating functions evaluated at the true parameter value is ‘asymptotically pivotal’, then the ‘fiducial’ distribution of the parameter can be…

提升核密度估计：一种偏差缩减技术？AI 解读

This paper proposes an algorithm for boosting kernel density estimates. We show that boosting is closely linked to a previously proposed method of bias reduction and indicate how it should enjoy similar properties. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research.

聚类与纵向数据非参数回归中平滑样条的等价核AI 解读

For independent data, it is well known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman, 1984). However, recent work of Welsh et al. (2002) shows that the same is not true for clustered/longitudinal data. Splines and conventional kernels are different in localness and ability to account for the within‐cluster correlation. We show that a smoothing spline estimator is asymptotically equivalent to a recently proposed seemingly…

依赖数据的多峰性检验AI 解读

We propose a test for multimodality with dependent data by resampling from a suitably constructed transition probability kernel, which includes Silverman's test with independent data as a special case. We extend some theoretical properties of Silverman's test with independent and identically distributed data to weakly dependent data, and also discuss the robustness of Silverman's test against departure from independence.

基于加权伽马过程的乘法强度模型计算方法AI 解读

We develop computational procedures for a class of Bayesian nonparametric and semiparametric multiplicative intensity models incorporating kernel mixtures of spatial weighted gamma measures. A key feature of our approach is that explicit expressions for posterior distributions of these models share many common structural features with the posterior distributions of Bayesian hierarchical models using the Dirichlet process. Using this fact, along with an approximation for the…

用半参数惩罚样条估计公司债利率期限结构AI 解读

This article provides a new methodology for estimating the term structure of corporate debt using a semiparametric penalized spline model. The method is applied to a case study of AT&T bonds. Typically, very few data are available on individual corporate bond prices, too little to find a nonparametric estimate of term structure from these bonds alone. This problem is solved by “borrowing strength” from Treasury bond data. More specifically, we combine a nonparametric model…

通过最大化“脏”马尔可夫随机场后验进行平滑的统计分析AI 解读

We consider Bayesian nonparametric function estimation using a Markov random field prior based on the Laplace distribution. We describe efficient methods for finding the exact maximum a posteriori estimate, which handle constraints naturally and avoid the problems posed by nondifferentiability of the posterior distribution; the methods also make links to spline and wavelet smoothers and to a dual posterior distribution. Three automatic smoothing parameter selection…

基于似然的条件方差函数局部线性估计AI 解读

We consider estimation of mean and variance functions with kernel-weighted local polynomial fitting in a heteroscedastic nonparametric regression model. Our preferred estimators are based on a localized normal likelihood, using a standard local linear form for estimating the mean and a local log-linear form for estimating the variance. It is important to allow two bandwidths in this problem, separate ones for mean and variance estimation. We provide data-based methods for…