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高维谱统计量的自助法AI 解读

Summary Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of spectral statistics in low-dimensional problems, such methods are relatively unexplored in the high-dimensional setting. The aim of this article is to focus on linear spectral statistics as a class of prototypes for developing a…

通过统一偏斜正态分布实现 probit 回归的共轭贝叶斯推断AI 解读

Summary Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, these methods serve as building blocks in more complex formulations, such as density regression, nonparametric classification and graphical models. Within the Bayesian framework, inference proceeds by updating the priors for the coefficients, typically taken to be Gaussians, with the likelihood induced by probit or logit regressions for the…

双重截断下非参数最大似然估计的存在性与唯一性AI 解读

Summary Doubly truncated survival data arise if failure times are observed only within certain time intervals. The nonparametric maximum likelihood estimator is widely used to estimate the underlying failure time distribution. Using a directed graph representation of the data suggested by Vardi (1985), a certain graphical condition holds if and only if the nonparametric maximum likelihood estimate exists and is unique. If this condition does not hold, then such an estimate…

贝叶斯刀切经验似然AI 解读

Summary Empirical likelihood is a very powerful nonparametric tool that does not require any distributional assumptions. Lazar (2003) showed that in Bayesian inference, if one replaces the usual likelihood with the empirical likelihood, then posterior inference is still valid when the functional of interest is a smooth function of the posterior mean. However, it is not clear whether similar conclusions can be obtained for parameters defined in terms of $U$-statistics. We…

基于趋势滤波的加性模型AI 解读

We study additive models built with trend filtering, that is, additive models whose components are each regularized by the (discrete) total variation of their $k$th (discrete) derivative, for a chosen integer $k\geq0$. This results in $k$th degree piecewise polynomial components, (e.g., $k=0$ gives piecewise constant components, $k=1$ gives piecewise linear, $k=2$ gives piecewise quadratic, etc.). Analogous to its advantages in the univariate case, additive trend filtering…

非平稳过程均值的实质变化检测：超额质量方法AI 解读

This paper considers the problem of testing if a sequence of means $(\mu_{t})_{t=1,\ldots ,n}$ of a nonstationary time series $(X_{t})_{t=1,\ldots ,n}$ is stable in the sense that the difference of the means $\mu_{1}$ and $\mu_{t}$ between the initial time $t=1$ and any other time is smaller than a given threshold, that is $|\mu_{1}-\mu_{t}|\leq c$ for all $t=1,\ldots ,n$. A test for hypotheses of this type is developed using a bias corrected monotone rearranged local linear…

ARMAX 残差部分和过程的极限行为AI 解读

We establish general and versatile results regarding the limit behavior of the partial-sum process of ARMAX residuals. Illustrations include ARMA with seasonal dummies, misspecified ARMAX models with autocorrelated errors, nonlinear ARMAX models, ARMA with a structural break, a wide range of ARMAX models with infinite-variance errors, weak GARCH models and the consistency of kernel estimation of the density of ARMAX errors. Our results identify the limit distributions, and…

高维随机化不完全U统计量AI 解读

This paper studies inference for the mean vector of a high-dimensional $U$-statistic. In the era of big data, the dimension $d$ of the $U$-statistic and the sample size $n$ of the observations tend to be both large, and the computation of the $U$-statistic is prohibitively demanding. Data-dependent inferential procedures such as the empirical bootstrap for $U$-statistics is even more computationally expensive. To overcome such a computational bottleneck, incomplete $U$-statis…

排序凹惩罚回归AI 解读

The Lasso is biased. Concave penalized least squares estimation (PLSE) takes advantage of signal strength to reduce this bias, leading to sharper error bounds in prediction, coefficient estimation and variable selection. For prediction and estimation, the bias of the Lasso can be also reduced by taking a smaller penalty level than what selection consistency requires, but such smaller penalty level depends on the sparsity of the true coefficient vector. The sorted $\ell_{1}$ p…

动态异方差下非参数回归的有效估计AI 解读

We study the efficient estimation of nonparametric regression in the presence of heteroskedasticity. We focus our analysis on local polynomial estimation of nonparametric regressions with conditional heteroskedasticity in a time series setting. We introduce a weighted local polynomial regression smoother that takes account of the dynamic heteroskedasticity. We show that, although traditionally it is advised that one should not weight for heteroskedasticity in nonparametric…

广义半参数与非参数回归中参数及函数的有效估计与计算AI 解读

The efficiency of estimation for the parameters in semiparametric models has been widely studied in the literature (Bickel et al., 1993). In this paper, we study efficient estimators for both parameters and nonparametric functions in a class of generalized semi/non-parametric regression models, which cover commonly used semiparametric models such as partially linear models, partially linear single index models, and two-sample semiparametric models. We propose a maximum…

含解释变量测量误差的非参数回归一致置信带AI 解读

This paper develops a method to construct uniform confidence bands for a nonparametric regression function where a predictor variable is subject to a measurement error. We allow for the distribution of the measurement error to be unknown, but assume the availability of validation data or repeated measurements on the latent predictor variable. The proposed confidence band builds on the deconvolution kernel estimation and a novel application of the multiplier bootstrap method.…

具有一致性的非高斯伪最大似然估计量AI 解读

We characterise the mean and variance parameters that distributionally misspecified maximum likelihood estimators can consistently estimate in location-scale models, and provide simple closed-form consistent estimators for the rest. Including means and a multivariate coverage make our procedures useful for Garch-M models and empirically relevant macro and finance applications involving Vars and multivariate regressions. We study the statistical properties of our proposed…

计数时间序列的半参数独立性检验与支持集作用AI 解读

This article considers testing for independence in a time series of small counts within an Integer Autoregressive (INAR) model, taking a semiparametric approach that avoids any distributional assumption on the arrivals process of the model. The nature of the testing problem is shown to differ depending on whether or not the support of the arrivals distribution is the full set of natural numbers (as would be the case for Poisson or Negative Binomial distributions for example)…

存在中介—结局混杂时路径特定效应的半参数估计AI 解读

Summary Path-specific effects constitute a broad class of mediated effects from an exposure to an outcome via one or more causal pathways along a set of intermediate variables. Most of the literature concerning estimation of mediated effects has focused on parametric models, with stringent assumptions regarding unmeasured confounding. We consider semiparametric inference of a path-specific effect when these assumptions are relaxed. In particular, we develop a suite of…

融合密度估计：理论与方法AI 解读

Summary We introduce a method for non-parametric density estimation on geometric networks. We define fused density estimators as solutions to a total variation regularized maximum likelihood density estimation problem. We provide theoretical support for fused density estimation by proving that the squared Hellinger rate of convergence for the estimator achieves the minimax bound over univariate densities of log-bounded variation. We reduce the original variational…

利用极值方法估计随访不足下的非参数治愈率AI 解读

Summary An important research topic in survival analysis is related to the modelling and estimation of the cure rate, i.e. the proportion of subjects who will never experience the event of interest. However, most estimation methods proposed so far in the literature do not handle the case of insufficient follow-up, i.e. when the right end point of the support of the censoring time is strictly less than that of the survival time of the susceptible subjects, and consequently…

非参数分位数工具变量回归加权平均导数的惩罚筛广义经验似然AI 解读

This paper considers estimation and inference for a weighted average derivative (WAD) of a nonparametric quantile instrumental variables regression (NPQIV). NPQIV is a non-separable and nonlinear ill-posed inverse problem, which might be why there is no published work on the asymptotic properties of any estimator of its WAD. We first characterize the semiparametric efficiency bound for a WAD of a NPQIV, which, unfortunately, depends on an unknown conditional derivative…

基于级数或大量回归变量的条件分位数过程AI 解读

Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric QR-series framework, covering many regressors as a special case, for performing inference on the entire conditional quantile function and its linear functionals. In this framework, we approximate the entire conditional quantile function by a…

极端收益与交易强度AI 解读

Summary Asymmetric information models of market microstructure claim that variables such as trading intensity are proxies for latent information on the value of financial assets. We consider the interval‐valued time series (ITS) of low/high returns and explore the relationship between these extreme returns and the intensity of trading. We assume that the returns (or prices) are generated by a latent process with some unknown conditional density. At each period of time, from…

大型时变参数VAR：一种非参数方法AI 解读

Summary In this paper we introduce a nonparametric estimation method for a large Vector Autoregression (VAR) with time‐varying parameters. The estimators and their asymptotic distributions are available in closed form. This makes the method computationally efficient and capable of handling information sets as large as those typically handled by factor models and Factor Augmented VARs. When applied to the problem of forecasting key macroeconomic variables, the method…

连续时间过程中的结构失效时间模型半参数估计AI 解读

Summary Structural failure time models are causal models for estimating the effect of time-varying treatments on a survival outcome. G-estimation and artificial censoring have been proposed for estimating the model parameters in the presence of time-dependent confounding and administrative censoring. However, most existing methods require manually pre-processing data into regularly spaced data, which may invalidate the subsequent causal analysis. Moreover, the computation…

患者偏好试验的设计、识别与敏感性分析AI 解读

Social and medical scientists are often concerned that the external validity of experimental results may be compromised because of heterogeneous treatment effects. If a treatment has different effects on those who would choose to take it and those who would not, the average treatment effect estimated in a standard randomized controlled trial (RCT) may give a misleading picture of its impact outside of the study sample. Patient preference trials (PPTs), where participants’…

连接脑区的纤维曲线的非参数贝叶斯模型AI 解读

In studying structural inter-connections in the human brain, it is common to first estimate fiber bundles connecting different regions relying on diffusion MRI. These fiber bundles act as highways for neural activity. Current statistical methods reduce the rich information into an adjacency matrix, with the elements containing a count of fibers or a mean diffusion feature along the fibers. The goal of this article is to avoid discarding the rich geometric information of…