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关于删失下生存函数非参数广义信赖推断的讨论AI 解读

We expect that many readers will not be familiar with fiducial inference. This is in contrast to the well-founded alternatives given by Bayesian and classical inference known to every statistician today. Fiducial inference has not yet been established as a general theory, but there has been considerable progress over the past few decades, as demonstrated by the paper of Cui & Hannig (2019). To discuss their contribution, we first provide a context for fiducial inference as…

《删失下生存函数的非参数广义 fiducial 推断》讨论AI 解读

It is a pleasure to participate in the discussion of the article by Cui & Hannig (2019). The authors are to be congratulated for their efforts and ingenuity in developing what is, to my knowledge, the first fiducial solution to a problem involving an infinite-dimensional parameter of interest. Specifically, the authors build on some existing machinery, summarized recently in Hannig et al. (2016) and the references therein, to construct a generalized fiducial distribution for…

删失下生存函数的非参数广义信赖推断AI 解读

Summary Since the introduction of fiducial inference by Fisher in the 1930s, its application has been largely confined to relatively simple, parametric problems. In this paper, we present what might be the first time fiducial inference is systematically applied to estimation of a nonparametric survival function under right censoring. We find that the resulting fiducial distribution gives rise to surprisingly good statistical procedures applicable to both one-sample and…

基于互信息的非参数独立性检验AI 解读

Summary We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach is based on the estimation of mutual information, whose decomposition into joint and marginal entropies facilitates the use of recently developed efficient entropy estimators derived from nearest neighbour distances. The proposed critical values may be obtained by simulation in the case where an approximation to one marginal is available…

重新审视面板数据分位数回归的简便方法AI 解读

Summary This note discusses two errors in the approach proposed in Canay (2011) for constructing a computationally simple two-step estimator in a quantile regression model with quantile-independent fixed effects. Firstly, we show that Canay’s assumption about n/Ts → 0 for some s > 1 is not strong enough and can entail severe bias or even the non-existence of the limiting distribution for the estimator of the vector of coefficients. The condition n/T → 0 appears to be closer…

时变系数面板模型中的潜在分组结构估计AI 解读

Summary This paper studies the estimation of latent group structures in heterogeneous time-varying coefficient panel data models. While allowing the coefficient functions to vary over cross-sections provides a good way to model cross-sectional heterogeneity, it reduces the degree of freedom and leads to poor estimation accuracy when the time-series length is short. On the other hand, in a lot of empirical studies, it is not uncommon to find that heterogeneous coefficients…

基于分位数的平滑转换风险价值估计AI 解读

Summary Value at risk models are concerned with the estimation of conditional quantiles of a time series. Formally, these quantities are a function of conditional volatility and the respective quantile of the innovation distribution. The former is often subject to asymmetric dynamic behaviour, e.g., with respect to past shocks. In this paper, we propose a model in which conditional quantiles follow a generalised autoregressive process governed by two parameter regimes with…

引导式非参数拟合优度检验及其收入分布应用AI 解读

Summary We have developed a customizable goodness-of-fit test of a parametric density based on its distance to a consistently estimated density. This consistent estimate is obtained via a nonparametric density estimator with a parametric start, wherein the start is set to be the hypothesized parametric density. To cope with the influence of nonparametric estimation bias, nonparametric goodness-of-fit tests have resorted to remedies such as undersmoothing or convolution of…

贝叶斯非参数稀疏向量自回归模型AI 解读

High dimensional vector autoregressive (VAR) models require a large number of parameters to be estimated and may suffer of inferential problems. We propose a new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional VAR models that can improve estimation efficiency and prediction accuracy. Our hierarchical prior overcomes overparametrization and overfitting issues by clustering the VAR coefficients into groups and by shrinking the coefficients of each…

多个条件变量下大型动态协方差矩阵的半参数估计新方法AI 解读

This paper studies the estimation of large dynamic covariance matrices with multiple conditioning variables. We introduce an easy-to-implement semiparametric method to estimate each entry of the covariance matrix via model averaging marginal regression, and then apply a shrinkage technique to obtain the dynamic covariance matrix estimation. Under some regularity conditions, we derive the asymptotic properties for the proposed estimators including the uniform consistency with…

动态预测计量建模中的大数据AI 解读

The modern economic environment is awash in Big Data. The business models of many of today’s largest and most innovative firms, for example, are intimately connected to data collection and processing. Closely related, all of science is now similarly awash in Big Data, due to massive advances in data capture and storage technology, typically in conjunction with the internet.1 Time-series econometrics is no exception, and the time-series community is beginning to confront Big…

民主发展中的隐藏分组模式：分组异质性的贝叶斯推断AI 解读

Summary We propose a nonparametric Bayesian approach to estimate time‐varying grouped patterns of heterogeneity in linear panel data models. Unlike the classical approach in Bonhomme and Manresa ( Econometrica , 2015, 83 , 1147–1184), our approach can accommodate selection of the optimal number of groups and model estimation jointly, and also be readily extended to quantify uncertainties in the estimated group structure. Our proposed approach performs well in Monte Carlo…

含内生虚拟解释变量的广义双变量Probit模型估计AI 解读

Summary The purpose of this paper is to provide guidelines for empirical researchers who use a class of bivariate threshold crossing models with dummy endogenous variables. A common practice employed by the researchers is the specification of the joint distribution of unobservables as a bivariate normal distribution, which results in a bivariate probit model . To address the problem of misspecification in this practice, we propose an easy‐to‐implement semiparametric…

局部平稳过程的交叉验证AI 解读

We propose an adaptive bandwidth selector via cross validation for local M-estimators in locally stationary processes. We prove asymptotic optimality of the procedure under mild conditions on the underlying parameter curves. The results are applicable to a wide range of locally stationary processes such linear and nonlinear processes. A simulation study shows that the method works fairly well also in misspecified situations.

条件定性处理效应的检验AI 解读

Precision medicine is an emerging medical paradigm that focuses on finding the most effective treatment strategy tailored for individual patients. In the literature, most of the existing works focused on estimating the optimal treatment regime. However, there has been less attention devoted to hypothesis testing regarding the optimal treatment regime. In this paper, we first introduce the notion of conditional qualitative treatment effects (CQTE) of a set of variables given…

重尾误差下最小二乘回归估计量的收敛速度AI 解读

We study the performance of the least squares estimator (LSE) in a general nonparametric regression model, when the errors are independent of the covariates but may only have a $p$th moment ($p\geq1$). In such a heavy-tailed regression setting, we show that if the model satisfies a standard “entropy condition” with exponent $\alpha\in(0,2)$, then the $L_{2}$ loss of the LSE converges at a rate \[\mathcal{O}_{\mathbf{P}}\bigl(n^{-\frac{1}{2+\alpha}}\vee n^{-\frac{1}{2}+\frac{1}{2p}}\bigr).\]…

广义聚类树与奇异测度AI 解读

In this paper we study the $\alpha $-cluster tree ($\alpha $-tree) under both singular and nonsingular measures. The $\alpha $-tree uses probability contents within a set created by the ordering of points to construct a cluster tree so that it is well defined even for singular measures. We first derive the convergence rate for a density level set around critical points, which leads to the convergence rate for estimating an $\alpha $-tree under nonsingular measures. For…

Lipschitz 损失正则化方法的估计界与尖锐预言不等式AI 解读

We obtain estimation error rates and sharp oracle inequalities for regularization procedures of the form \begin{equation*}\hat{f}\in\mathop{\operatorname{argmin}}_{f\in F}\Bigg(\frac{1}{N}\sum_{i=1}^{N}\ell_{f}(X_{i},Y_{i})+\lambda \Vert f\Vert \Bigg)\end{equation*} when $\Vert \cdot \Vert $ is any norm, $F$ is a convex class of functions and $\ell$ is a Lipschitz loss function satisfying a Bernstein condition over $F$. We explore both the bounded and sub-Gaussian stochastic…

局部平稳性与时变 Markov 链AI 解读

A primary motivation of this contribution is to define new locally stationary Markov models for categorical or integer-valued data. For this initial purpose, we propose a new general approach for dealing with time-inhomogeneity that extends the local stationarity notion developed in the time series literature. We also introduce a probabilistic framework which is very flexible and allows us to consider a much larger class of Markov chain models on arbitrary state spaces,…

超高维稀疏数据中基于条件严格凸损失的非参数筛选AI 解读

Sure screening technique has been considered as a powerful tool to handle the ultrahigh dimensional variable selection problems, where the dimensionality $p$ and the sample size $n$ can satisfy the NP dimensionality $\log p=O(n^{a})$ for some $a>0$ [J. R. Stat. Soc. Ser. B. Stat. Methodol. 70 (2008) 849–911]. The current paper aims to simultaneously tackle the “universality” and “effectiveness” of sure screening procedures. For the “universality,” we develop a general and…

深度学习缓解非参数回归维数灾难的理论研究AI 解读

Assuming that a smoothness condition and a suitable restriction on the structure of the regression function hold, it is shown that least squares estimates based on multilayer feedforward neural networks are able to circumvent the curse of dimensionality in nonparametric regression. The proof is based on new approximation results concerning multilayer feedforward neural networks with bounded weights and a bounded number of hidden neurons. The estimates are compared with…

回归不连续设计中分位数处理效应的稳健一致推断AI 解读

The practical importance of inference with robustness against large bandwidths for causal effects in regression discontinuity and kink designs is widely recognized. Existing robust methods cover many cases, but do not handle uniform inference for CDF and quantile processes in fuzzy designs. In this light, this paper extends the literature by developing a unified framework of inference with robustness against large bandwidths that applies to uniform inference for quantile…

双重差分平均处理效应推断：固定 b 方法AI 解读

This paper provides an analysis of the standard errors proposed by Driscoll and Kraay (1998) (DK) in linear Difference-in-Differences (DD) models with fixed effects and individual-specific time trends. The analysis is accomplished within the fixed-b asymptotic framework developed by Kiefer and Vogelsang (2005) for heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimator based tests. For both the fixed-N, large-T, and large-N, large-T cases, it is…

第一价格拍卖中基于 GPV 估计量的推断AI 解读

We consider inference on the probability density of valuations in the first-price sealed-bid auctions model within the independent private value paradigm. We show the asymptotic normality of the two-step nonparametric estimator of Guerre et al. (2000) (GPV), and propose an easily implementable and consistent estimator of the asymptotic variance. We prove the validity of the pointwise percentile bootstrap confidence intervals based on the GPV estimator. Lastly, we use the…