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存在工具变量时的非参数推断方法AI 解读

We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence rates, and show that they are attained by particular estimators. In the presence of instrumental variables the relation that identifies the regression function also defines an ill-posed inverse problem, the “difficulty” of which depends…

基于最大熵密度的部分自适应估计AI 解读

We propose a partially adaptive estimator based on information theoretic maximum entropy estimates of the error distribution. The maximum entropy (maxent) densities have simple yet flexible functional forms to nest most of the mathematical distributions. Unlike the non-parametric fully adaptive estimators, our parametric estimators do not involve choosing a bandwidth or trimming, and only require estimating a small number of nuisance parameters, which is desirable when the…

用于天气雷达反射率即时预报的核时空动态模型AI 解读

A good short-period forecast of heavy rainfall is essential for many meteorological and hydrological applications. Traditional deterministic and stochastic nowcasting methodologies have been inadequate in their characterization of pixelwise rainfall reflectivity propagation, intensity, and uncertainty. The methodology presented herein uses an approach that efficiently parameterizes spatio-temporal dynamic models in terms of integro-difference equations within a hierarchical…

协变量缺失时比例风险回归的加权估计量AI 解读

Missing covariate data are common in epidemiologic studies and disease prevention trials. In this article regression parameter estimation in the Cox proportional hazards model is considered when certain covariates are observed for all study subjects and other covariate data are collected only for a subset. The article presents both simple weighted and kernel-assisted fully augmented weighted estimators that use the partially incomplete data nonparametrically. We use…

聚类数据广义部分线性模型的稳健估计AI 解读

In this article we consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear models (GPLMs) for longitudinal data or clustered data in general. We approximate the nonparametric function in the GPLM by a regression spline, and use bounded scores and leverage-based weights in the estimating equation to achieve robustness against outliers. We show that the regression spline approach avoids some of the intricacies associated…

调查抽样中的非参数模型校准估计AI 解读

Calibration is commonly used in survey sampling to include auxiliary information at the estimation stage of a population parameter. Calibrating the observation weights on population means (totals) of a set of auxiliary variables implies building weights that when applied to the auxiliaries give exactly their population mean (total). Implicitly, calibration techniques rely on a linear relation between the survey variable and the auxiliary variables. However, when auxiliary…

异方差与自相关稳健检验的新渐近理论AI 解读

A new first-order asymptotic theory for heteroskedasticity-autocorrelation (HAC) robust tests based on nonparametric covariance matrix estimators is developed. The bandwidth of the covariance matrix estimator is modeled as a fixed proportion of the sample size. This leads to a distribution theory for HAC robust tests that explicitly captures the choice of bandwidth and kernel. This contrasts with the traditional asymptotics (where the bandwidth increases more slowly than the…

高阶核估计量的精确平均积分平方误差AI 解读

The exact mean integrated squared error (MISE) of the nonparametric kernel density estimator is derived for the asymptotically optimal smooth polynomial kernels of Müller (1984, Annals of Statistics 12, 766–774) and the trapezoid kernel of Politis and Romano (1999, Journal of Multivariate Analysis 68, 1–25) and is used to contrast their finite-sample efficiency with the higher order Gaussian kernels of Wand and Schucany (1990Canadian Journal of Statistics 18, 197–204). We…

空间点过程的残差分析（附讨论）AI 解读

Summary We define residuals for point process models fitted to spatial point pattern data, and we propose diagnostic plots based on them. The residuals apply to any point process model that has a conditional intensity; the model may exhibit spatial heterogeneity, interpoint interaction and dependence on spatial covariates. Some existing ad hoc methods for model checking (quadrat counts, scan statistic, kernel smoothed intensity and Berman's diagnostic) are recovered as…

GARCH 模型残差的高阶矩部分和过程及其应用AI 解读

In this paper we construct high moment partial sum processes based on residuals of a GARCH model when the mean is known to be 0. We consider partial sums of kth powers of residuals, CUSUM processes and self-normalized partial sum processes. The kth power partial sum process converges to a Brownian process plus a correction term, where the correction term depends on the kth moment μk of the innovation sequence. If μk=0, then the correction term is 0 and, thus, the kth power…

一类 Matérn 型高斯随机场的固定域渐近理论AI 解读

Stein [Statist. Sci. 4 (1989) 432–433] proposed the Matérn-type Gaussian random fields as a very flexible class of models for computer experiments. This article considers a subclass of these models that are exactly once mean square differentiable. In particular, the likelihood function is determined in closed form, and under mild conditions the sieve maximum likelihood estimators for the parameters of the covariance function are shown to be weakly consistent with respect to…

含离群值非参数回归中的交叉验证AI 解读

A popular data-driven method for choosing the bandwidth in standard kernel regression is cross-validation. Even when there are outliers in the data, robust kernel regression can be used to estimate the unknown regression curve [Robust and Nonlinear Time Series Analysis. Lecture Notes in Statist. (1984) 26 163–184]. However, under these circumstances standard cross-validation is no longer a satisfactory bandwidth selector because it is unduly influenced by extreme prediction…

非必为高斯噪声下的小波阈值法：功能表现AI 解读

For signals belonging to balls in smoothness classes and noise with enough moments, the asymptotic behavior of the minimax quadratic risk among soft-threshold estimates is investigated. In turn, these results, combined with a median filtering method, lead to asymptotics for denoising heavy tails via wavelet thresholding. Some further comparisons of wavelet thresholding and of kernel estimators are also briefly discussed.

离散分布混合密度的非参数估计AI 解读

By a mixture density is meant a density of the form πμ(⋅)=∫πθ(⋅)×μ(dθ), where (πθ)θ∈Θ is a family of probability densities and μ is a probability measure on Θ. We consider the problem of identifying the unknown part of this model, the mixing distribution μ, from a finite sample of independent observations from πμ. Assuming that the mixing distribution has a density function, we wish to estimate this density within appropriate function classes. A general approach is proposed…

对强序列相关稳健的高功效趋势函数检验：普雷维什—辛格假说的应用AI 解读

We propose tests for hypotheses on the parameters of the deterministic trend function of a univariate time series. The tests do not require knowledge of the form of serial correlation in the data, and they are robust to strong serial correlation. The data can contain a unit root and still have the correct size asymptotically. The tests that we analyze are standard heteroscedasticity autocorrelation robust tests based on nonparametric kernel variance estimators. We analyze…

非参数核估计中交叉验证平滑参数的唯一性AI 解读

We investigate the issue of the uniqueness of the cross-validation selected smoothing parameters in kernel estimation of multivariate nonparametric regression or conditional probability functions. When the covariates are all continuous variables, we provide a necessary and sufficient condition, and when the covariates are a mixture of categorical and continuous variables, we provide a simple sufficient condition that guarantees asymptotically the uniqueness of the…

This paper considers the analysis of current status data with a cured proportion in the population using a mixture model that combines a logistic regression formulation for the probability of cure with a semiparametric regression model for the time to occurrence of the event. The semiparametric regression model belongs to the flexible class of partly linear models that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A…

通过超球面对数样条建模方向性离散程度AI 解读

Summary We introduce the directionally dispersed class of multivariate distributions, a generalization of the elliptical class. By allowing dispersion of multivariate random variables to vary with direction it is possible to generate a very wide and flexible class of distributions. Directionally dispersed distributions have a simple form for their density, which extends a spherically symmetric density function by including a function D modelling directional dispersion. Under…

用于 cDNA 微阵列归一化与分析的双向半线性模型AI 解读

A basic question in analyzing cDNA microarray data is normalization, the purpose of which is to remove systematic bias in the observed expression values by establishing a normalization curve across the whole dynamic range. A proper normalization procedure ensures that the normalized intensity ratios provide meaningful measures of relative expression levels. We propose a two-way semilinear model (TW–SLM) for normalization and analysis of microarray data. This method does not…

一类变换风险率模型的统计推断AI 解读

A new class of transformed hazard rate models is considered that contains both the multiplicative hazards model and the additive hazards model as special cases. The sieve maximum likelihood estimators are derived for the model parameters, and the estimators for the regression coefficients are shown to be consistent and asymptotically normal with variance achieving the semiparametric efficiency bound. Simulation studies are conducted to examine the small-sample properties of…

平稳与非平稳分数阶时间序列推断的效率改进AI 解读

We consider a time series model involving a fractional stochastic component, whose integration order can lie in the stationary/invertible or nonstationary regions and be unknown, and an additive deterministic component consisting of a generalized polynomial. The model can thus incorporate competing descriptions of trending behavior. The stationary input to the stochastic component has parametric autocorrelation, but innovation with distribution of unknown form. The model is…

局部 Rademacher 复杂度AI 解读

We propose new bounds on the error of learning algorithms in terms of a data-dependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense that the Rademacher averages are computed from the data, on a subset of functions with small empirical error. We present some applications to classification and prediction with convex function classes, and with kernel classes in particular.

水平跃迁与经济时间序列中的长记忆假象AI 解读

When applied to time series processes containing occasional level shifts, the log-periodogram (GPH) estimator often erroneously finds long memory. For a stationary short-memory process with a slowly varying level, I show that the GPH estimator is substantially biased, and derive an approximation to this bias. The asymptotic bias lies on the (0, 1) interval, and its exact value depends on the ratio of the expected number of level shifts to a user-defined bandwidth parameter.…

惩罚偏离可加性的非参数回归AI 解读

Due to the curse of dimensionality, estimation in a multidimensional nonparametric regression model is in general not feasible. Hence, additional restrictions are introduced, and the additive model takes a prominent place. The restrictions imposed can lead to serious bias. Here, a new estimator is proposed which allows penalizing the nonadditive part of a regression function. This offers a smooth choice between the full and the additive model. As a byproduct, this penalty…