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自适应近似贝叶斯计算AI 解读

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.’s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the…

病例对照研究中风险预测标志物评价的半参数方法AI 解读

The performance of a well-calibrated risk model for a binary disease outcome can be characterized by the population distribution of risk and displayed with the predictiveness curve. Better performance is characterized by a wider distribution of risk, since this corresponds to better risk stratification in the sense that more subjects are identified at low and high risk for the disease outcome. Although methods have been developed to estimate predictiveness curves from cohort…

横截面抽样下疾病—死亡模型患病概率的非参数估计AI 解读

Cross-sectional sampling is an attractive design that saves resources but results in biased data. For proper inference, one should first discover the bias function and then weigh observations appropriately. We consider cross-sectioning of the illness-death model with the aim of estimating the probability of visiting the illness state before death. We develop simple consistent and asymptotically normal estimators under various assumptions on the model and data collection and,…

基于 Copula 的半参数马尔可夫模型的有效估计AI 解读

This paper considers the efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant (one-dimensional marginal) distributions and parametric bivariate copula functions where the copulas capture temporal dependence and tail dependence of the processes. The Markov processes generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications.…

带参数引导的局部拟似然AI 解读

Generalized linear models and quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification and the resulting model is completely determined by the data themselves. However nonparametric estimation schemes generally have a slower convergence rate such as the local polynomial smoothing estimation of nonparametric generalized linear models…

非线性主成分与多元扩散过程的长期含义AI 解读

We investigate a method for extracting nonlinear principal components (NPCs). These NPCs maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate probability densities, including densities without compact support and even densities with algebraic tails. We provide primitive sufficient conditions for the existence of these NPCs. By exploiting the theory of continuous-time, reversible Markov…

非线性非平稳时间序列自回归的设定检验AI 解读

This paper considers a class of nonparametric autoregressive models with nonstationarity. We propose a nonparametric kernel test for the conditional mean and then establish an asymptotic distribution of the proposed test. Both the setting and the results differ from earlier work on nonparametric autoregression with stationarity. In addition, we develop a new bootstrap simulation scheme for the selection of a suitable bandwidth parameter involved in the kernel test as well as…

部分线性变系数模型中的分位数回归AI 解读

Semiparametric models are often considered for analyzing longitudinal data for a good balance between flexibility and parsimony. In this paper, we study a class of marginal partially linear quantile models with possibly varying coefficients. The functional coefficients are estimated by basis function approximations. The estimation procedure is easy to implement, and it requires no specification of the error distributions. The asymptotic properties of the proposed estimators…

状态空间模型中的趋势估计：渐近均方误差与收敛速度AI 解读

The focus of this paper is on trend estimation for a general state-space model Yt=μt+ɛt, where the dth difference of the trend {μt} is assumed to be i.i.d., and the error sequence {ɛt} is assumed to be a mean zero stationary process. A fairly precise asymptotic expression of the mean square error is derived for the estimator obtained by penalizing the dth order differences. Optimal rate of convergence is obtained, and it is shown to be “asymptotically equivalent” to a…

多元时间序列模型协方差结构的突变检测AI 解读

In this paper, we introduce an asymptotic test procedure to assess the stability of volatilities and cross-volatilites of linear and nonlinear multivariate time series models. The test is very flexible as it can be applied, for example, to many of the multivariate GARCH models established in the literature, and also works well in the case of high dimensionality of the underlying data. Since it is nonparametric, the procedure avoids the difficulties associated with parametric…

随机过程半参数Z估计量的渐近理论：遍历扩散与时间序列应用AI 解读

This paper generalizes a part of the theory of Z-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to derive the asymptotic behavior of the solution to an estimating equation θ↝Ψn(θ, ĥn)=0 with an abstract nuisance parameter h when the compensator of Ψn is random. As its application, we consider the estimation problem in an ergodic diffusion…

泛函导数的估计AI 解读

Situations of a functional predictor paired with a scalar response are increasingly encountered in data analysis. Predictors are often appropriately modeled as square integrable smooth random functions. Imposing minimal assumptions on the nature of the functional relationship, we aim to estimate the directional derivatives and gradients of the response with respect to the predictor functions. In statistical applications and data analysis, functional derivatives provide a…

随机设计与异方差相关误差下的小波回归AI 解读

We investigate function estimation in nonparametric regression models with random design and heteroscedastic correlated noise. Adaptive properties of warped wavelet nonlinear approximations are studied over a wide range of Besov scales, $f\in\mathcal{B}_{\pi,r}^{s}$, and for a variety of Lp error measures. We consider error distributions with Long-Range-Dependence parameter α, 0<α≤1; heteroscedasticity is modeled with a design dependent function σ. We prescribe a tuning…

稳健非参数回归的渐近等价与自适应估计AI 解读

Asymptotic equivalence theory developed in the literature so far are only for bounded loss functions. This limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded. In this paper we develop asymptotic equivalence results for robust nonparametric regression with unbounded loss functions. The results imply that all the Gaussian nonparametric regression procedures can be robustified in a unified way. A key…

非参数回归误差的拟合优度问题：分布无关方法AI 解读

This paper discusses asymptotically distribution free tests for the classical goodness-of-fit hypothesis of an error distribution in nonparametric regression models. These tests are based on the same martingale transform of the residual empirical process as used in the one sample location model. This transformation eliminates extra randomization due to covariates but not due the errors, which is intrinsically present in the estimators of the regression function. Thus, tests…

多元线性时间序列的非参数与半参数检验AI 解读

We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting distributions of these test statistics under null hypotheses are always normal distributions, and they can be implemented easily for practical use. If null hypotheses are false, as the sample size goes to infinity, they diverge to infinity and…

参数多项分布模型的半参数容忍区域：构建与应用AI 解读

We introduce a semiparametric “tubular neighborhood” of a parametric model in the multinomial setting. It consists of all multinomial distributions lying in a distance-based neighborhood of the parametric model of interest. Fitting such a tubular model allows one to use a parametric model while treating it as an approximation to the true distribution. In this paper, the Kullback–Leibler distance is used to build the tubular region. Based on this idea one can define the…

While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones, we demonstrate a general approach for establishing identifiability utilizing algebraic arguments. A theorem of J. Kruskal for a simple latent-class model with finite state space lies at the…

梯度场的路径密度AI 解读

We consider the problem of reliably finding filaments in point clouds. Realistic data sets often have numerous filaments of various sizes and shapes. Statistical techniques exist for finding one (or a few) filaments but these methods do not handle noisy data sets with many filaments. Other methods can be found in the astronomy literature but they do not have rigorous statistical guarantees. We propose the following method. Starting at each data point we construct the…

变系数模型的局部秩推断AI 解读

By allowing the regression coefficients to change with certain covariates, the class of varying coefficient models offers a flexible approach to modeling nonlinearity and interactions between covariates. This paper proposes a novel estimation procedure for the varying coefficient models based on local ranks. The new procedure provides a highly efficient and robust alternative to the local linear least squares method, and can be conveniently implemented using existing R…

已知参数强度形式下非齐次空间点过程二阶统计量的非参数方差估计AI 解读

We introduce new variance estimation procedures for second-order statistics that are computed from a single realization of intensity reweighted stationary spatial point processes. The statistics are defined either on a subset B of the observation window or on the whole window. For the former, we use subblocks that have the same size and shape as B as "replicates" of B in order to estimate the target variance. For the latter, we develop a subsampling estimator for a key…

具有参数模型特征的局部多项式分位数回归AI 解读

We propose a new approach to conditional quantile function estimation that combines both parametric and nonparametric techniques. At each design point, a global, possibly incorrect, pilot parametric model is locally adjusted through a kernel smoothing fit. The resulting quantile regression estimator behaves like a parametric estimator when the latter is correct and converges to the nonparametric solution as the parametric start deviates from the true underlying model. We…

基于特征函数的经验似然方法及其 Lévy 过程应用AI 解读

Lévy processes have been receiving increasing attention in financial modeling. One distinctive feature of such models is that their characteristic functions are readily available. Inference based on characteristic functions is very useful for studying Lévy processes. By incorporating the recent advances in nonparametric approaches, empirical likelihood methods based on characteristic functions are developed in this paper for parameter estimation, testing a particular…

结合变量选择的非参数贝叶斯条件分布建模AI 解读

This article considers a methodology for flexibly characterizing the relationship between a response and multiple predictors. Goals are (1) to estimate the conditional response distribution addressing the distributional changes across the predictor space, and (2) to identify important predictors for the response distribution change both within local regions and globally. We first introduce the probit stick-breaking process (PSBP) as a prior for an uncountable collection of…