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多元时间序列频域检验的自助法：谱密度比较应用AI 解读

Summary We propose a general bootstrap procedure to approximate the null distribution of non-parametric frequency domain tests about the spectral density matrix of a multivariate time series. Under a set of easy-to-verify conditions, we establish asymptotic validity of the bootstrap procedure proposed. We apply a version of this procedure together with a new statistic to test the hypothesis that the spectral densities of not necessarily independent time series are equal. The…

时间序列中一般非参数回归函数的一致估计AI 解读

We propose an estimator of the conditional distribution of XtXt-1,Xt-2,..., and the corresponding regression function , where the conditioning set is of infinite order. We establish consistency of our estimator under stationarity and ergodicity conditions plus a mild smoothness condition.

残差可能不光滑的半参数条件矩模型的有效估计AI 解读

This paper considers semiparametric efficient estimation of conditional moment models with possibly nonsmooth residuals in unknown parametric components ([theta]) and unknown functions (h) of endogenous variables. We show that: (1) the penalized sieve minimum distance (PSMD) estimator can simultaneously achieve root-n asymptotic normality of and nonparametric optimal convergence rate of , allowing for noncompact function parameter spaces; (2) a simple weighted bootstrap…

弱识别或部分识别下条件矩限制的半参数检验AI 解读

We propose two new semiparametric specification tests which test whether a vector of conditional moment conditions is satisfied for any vector of parameter values [theta]0. Unlike most existing tests, our tests are asymptotically valid under weak and/or partial identification and can accommodate discontinuities in the conditional moment functions. Our tests are moreover consistent provided that identification is not too weak. We do not require the availability of a…

基于转移分布的跳跃扩散非参数检验AI 解读

We develop a specification test for the transition density of a discretely sampled continuous-time jump-diffusion process, based on a comparison of a nonparametric estimate of the transition density or distribution function with their corresponding parametric counterparts assumed by the null hypothesis. As a special case, our method applies to pure diffusions. We provide a direct comparison of the two densities for an arbitrary specification of the null parametric model…

含测量误差协变量平滑效应的 Cox 模型AI 解读

We propose, develop, and implement a fully Bayesian inferential approach for the Cox model when the log hazard function contains unknown smooth functions of the variables measured with error. Our approach is to model nonparametrically both the log-baseline hazard and the smooth components of the log-hazard functions using low-rank penalized splines. Careful implementation of the Bayesian inferential machinery is shown to produce remarkably better results than the naive…

测量误差模型中的非参数预测AI 解读

Predicting the value of a variable Y corresponding to a future value of an explanatory variable X, based on a sample of previously observed independent data pairs (X(1), Y(1)), …, (X(n), Y(n)) distributed like (X, Y), is very important in statistics. In the error-free case, where X is observed accurately, this problem is strongly related to that of standard regression estimation, since prediction of Y can be achieved via estimation of the regression curve E(Y|X). When the…

利用半参数变换与加速失效时间模型分析长度偏倚数据AI 解读

Right-censored time-to-event data are often observed from a cohort of prevalent cases that are subject to length-biased sampling. Informative right censoring of data from the prevalent cohort within the population often makes it difficult to model risk factors on the unbiased failure times for the general population, because the observed failure times are length biased. In this paper, we consider two classes of flexible semiparametric models: the transformation models and…

用单调 B 样条半参数估计面板计数数据AI 解读

We study semiparametric likelihood-based methods for panel count data with proportional mean model E[ℕ(t)|Z]=Λ0(t)exp(β0TZ), where Z is a vector of covariates and Λ0(t) is the baseline mean function. We propose to estimate Λ0(t) and β0 jointly with Λ0(t) approximated by monotone B-splines and to compute the estimators using generalized Rosen algorithm proposed by Jamshidian (2004). We show that the proposed spline-based likelihood estimators of Λ0(t) are consistent with a…

允许依赖删失的一类半参数混合治愈生存模型AI 解读

Modern cancer treatments have substantially improved cure rates and have generated a great interest in and need for proper statistical tools to analyze survival data with non-negligible cure fractions. Data with cure fractions are often complicated by dependent censoring, and the analysis of this type of data typically involves untestable parametric assumptions on the dependence of the censoring mechanism and the true survival times. Motivated by the analysis of prostate…

区间删失数据的半参数回归治愈模型AI 解读

Motivated by medical studies in which patients could be cured of disease but the disease event time may be subject to interval censoring, we presents a semiparametric non-mixture cure model for the regression analysis of interval-censored time-to-event datxa. We develop semiparametric maximum likelihood estimation for the model using the expectation-maximization method for interval-censored data. The maximization step for the baseline function is nonparametric and…

多元无序分类数据的非参数贝叶斯建模AI 解读

Modeling of multivariate unordered categorical (nominal) data is a challenging problem, particularly in high dimensions and cases in which one wishes to avoid strong assumptions about the dependence structure. Commonly used approaches rely on the incorporation of latent Gaussian random variables or parametric latent class models. The goal of this article is to develop a nonparametric Bayes approach, which defines a prior with full support on the space of distributions for…

正定矩阵的内蕴回归模型及其扩散张量成像应用AI 解读

The aim of this paper is to develop an intrinsic regression model for the analysis of positive-definite matrices as responses in a Riemannian manifold and their association with a set of covariates, such as age and gender, in a Euclidean space. The primary motivation and application of the proposed methodology is in medical imaging. Because the set of positive-definite matrices do not form a vector space, directly applying classical multivariate regression may be inadequate…

广义多参数似然模型的统计估计AI 解读

Multiparameter likelihood models (MLMs) with multiple covariates have a wide range of applications; however, they encounter the “curse of dimensionality” problem when the dimension of the covariates is large. We develop a generalized multiparameter likelihood model that copes with multiple covariates and adapts to dynamic structural changes well. It includes some popular models, such as the partially linear and varying-coefficient models, as special cases. We present a…

回归中的核降维AI 解读

We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate X from the response Y, given the projection of X on the central subspace [cf. J. Amer. Statist. Assoc. 86 (1991) 316–342 and Regression Graphics (1998) Wiley]. We show that this conditional independence assertion can be characterized in terms of conditional covariance operators on…

后验风险率的渐近理论AI 解读

An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a completely random measure. In this paper we provide a comprehensive analysis of the asymptotic behavior of such models. We investigate consistency of the posterior distribution and derive fixed sample size central limit theorems for both linear and…

高维正态均值向量估计的非参数经验贝叶斯与复合决策方法AI 解读

We consider the classical problem of estimating a vector μ=(μ1, …, μn) based on independent observations Yi∼N(μi, 1), i=1, …, n. Suppose μi, i=1, …, n are independent realizations from a completely unknown G. We suggest an easily computed estimator μ̂, such that the ratio of its risk E(μ̂−μ)2 with that of the Bayes procedure approaches 1. A related compound decision result is also obtained. Our asymptotics is of a triangular array; that is, we allow the distribution G to…

多元波动率非参数估计的傅里叶变换方法AI 解读

We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the prices process and the Fourier transform of the co-volatility process. A nonparametric estimator is derived given a discrete unevenly spaced and asynchronously sampled observations…

Lasso 与 Dantzig selector 的统一分析AI 解读

We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector exhibit similar behavior. For both methods, we derive, in parallel, oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the ℓp estimation loss for 1≤p≤2 in the linear model when the number of variables can be much larger than the sample size.

长记忆估计量：傅里叶方法与小波方法的比较AI 解读

Semi-parametric estimation methods of the long-memory exponent of a time series have been studied in several papers, some applied, others theoretical, some using Fourier methods, others using a wavelet-based technique. In this paper, we compare the Fourier and wavelet approaches to the local regression method and to the local Whittle method. We provide an overview of these methods, describe what has been done and indicate the available results and the conditions under which…

基于经验谱测度的局部平稳时间序列局部推断AI 解读

The time varying empirical spectral measure plays a major role in the treatment of inference problems for locally stationary processes. The properties of the empirical spectral measure and related statistics are studied -- both when its index function is fixed or when dependent on the sample size. In particular we prove a general central limit theorem. Several applications and examples are given including semiparametric Whittle estimation, local least squares estimation and…

新西兰经济周期AI 解读

Our paper is in the spirit of Rex Bergstrom's interests and research in cyclical growth models and his meticulous attention to underlying data series. We develop a new quarterly real GDP series for post–World War II New Zealand, derive a new “benchmark” set of classical business cycle turning points, and establish nonparametric classical cycle characteristics. Markov-switching models, estimated by Gibbs-sampling methods, are used to derive mean growth rate and volatility…

计量经济学的边界：Hilbert 空间中的非参数估计AI 解读

We extend Bergstrom's 1985 results on nonparametric (NP) estimation in Hilbert spaces to unbounded sample sets. The motivation is to seek the most general possible framework for econometrics, NP estimation with no a priori assumptions on the functional relations nor on the observed data. In seeking the boundaries of the possible, however, we run against a sharp dividing line, which defines a necessary and sufficient condition for NP estimation. We identify this condition…

指数异方差下二元响应与连续结果的半参数模型AI 解读

Abstract This paper formulates a likelihood‐based estimator for a double‐index, semiparametric binary response equation. A novel feature of this estimator is that it is based on density estimation under local smoothing. While the proofs differ from those based on alternative density estimators, the finite sample performance of the estimator is significantly improved. As binary responses often appear as endogenous regressors in continuous outcome equations, we also develop an…