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Hawkes 及一般点过程的自助法推断AI 解读

Inference and testing in general point process models such as the Hawkes model is predominantly based on asymptotic approximations for likelihood-based estimators and tests. As an alternative, and to improve finite sample performance, this paper considers bootstrap-based inference for interval estimation and testing. Specifically, for a wide class of point process models we consider a novel bootstrap scheme labeled ‘fixed intensity bootstrap’ (FIB), where the conditional…

修正的 Clarke 检验及模型选择扩展AI 解读

We introduce a large family of model selection tests based on the expectation of an arbitrary, possibly non-smooth, parametric criterion function of the data. The considered methodology is illustrated for several econometric problems, including linear and quantile regression. It covers the case of strictly locally non-nested models and some overlapping models. The asymptotic theory of the proposed test statistic is stated. A general exchangeable bootstrap scheme allows the…

弱工具变量稳健推断中条件似然比及相关检验的功效AI 解读

Power curves of the Conditional Likelihood Ratio (CLR) and related tests for testing H0:β=β0 in linear models with a single endogenous variable, y=xβ+u, estimated using potentially weak instrumental variables have been presented for two different designs. One design keeps the variance matrix of the structural and first-stage errors, Σ, constant, the other instead keeps the variance matrix of the reduced-form and first-stage errors, Ω, constant. The values of Σ govern the…

依赖数据的高阶正确快速移动平均自助法AI 解读

We develop the theory of a novel fast bootstrap for dependent data. Our scheme deploys i.i.d. resampling of smoothed moment indicators. We characterize the class of parametric and semiparametric estimation problems for which the method is valid. We show the asymptotic refinements of the new procedure, proving that it is higher-order correct under mild assumptions on the time series, the estimating functions, and the smoothing kernel. We illustrate the applicability and the…

异质流动性下的已实现协方差建模：广义矩阵 Wishart 状态空间模型AI 解读

We propose to generalize the Wishart state-space model for realized covariance matrices of asset returns in order to capture complex measurement error structures induced by modern robust and data efficient realized covariance estimators and heterogeneous liquidity across assets. Our model assumes that the latent covariance matrix of the assets is observed through their realized covariance matrix with a Riesz measurement density, which generalizes the Wishart to monotone…

过度识别下的双重稳健识别与估计AI 解读

Consider two parametric models. At least one is correctly specified, but we do not know which. Both models include a common vector of parameters. An estimator for this common parameter vector is called Doubly Robust (DR) if it is consistent no matter which model is correct. We provide a general technique for constructing DR estimators (assuming the models are over identified). Our Over-identified Doubly Robust (ODR) technique is a simple extension of the Generalized Method…

线性工具变量模型中对识别强度稳健的非参数推断AI 解读

For a linear IV regression, we propose two new inference procedures on parameters of endogenous variables that are robust to any identification pattern, do not rely on a linear first-stage equation, and account for heteroskedasticity of unknown form. Building on Bierens (1982), we first propose an Integrated Conditional Moment (ICM) type statistic constructed by setting the parameters to the value under the null hypothesis. The ICM procedure tests at the same time the value…

马克思走向主流：俄国革命对其学术影响力的作用AI 解读

Karl Marx’s high academic stature outside of economics diverges sharply from his peripheral influence within the discipline, particularly after nineteenth-century developments rendered the labor theory of value obsolete. We hypothesize that the 1917 Russian Revolution is responsible for elevating Marx into the academic mainstream. Using the synthetic control method, we construct a counterfactual for Marx’s citation patterns in Google Ngram data. This allows us to predict how…

具有对抗性响应的普遍回归AI 解读

We provide algorithms for regression with adversarial responses under large classes of non-i.i.d. instance sequences, on general separable metric spaces, with provably minimal assumptions. We also give characterizations of learnability in this regression context. We consider universal consistency, which asks for strong consistency of a learner without restrictions on the value responses. Our analysis shows that such an objective is achievable for a significantly larger class…

贝叶斯多元保序回归中可信区间的覆盖率AI 解读

We consider the nonparametric multivariate isotonic regression problem, where the regression function is assumed to be nondecreasing with respect to each predictor. Our goal is to construct a Bayesian credible interval for the function value at a given interior point with assured limiting frequentist coverage. A natural prior on the regression function is given by a random step function with a suitable prior on increasing step-heights, but the resulting posterior…

序贯蒙特卡洛估计量的有限样本复杂度AI 解读

We present bounds for the finite-sample error of sequential Monte Carlo samplers on static spaces. Our approach explicitly relates the performance of the algorithm to properties of the chosen sequence of distributions and mixing properties of the associated Markov kernels. This allows us to give the first finite-sample comparison to other Monte Carlo schemes. We obtain bounds for the complexity of sequential Monte Carlo approximations for a variety of target distributions…

异质幂律数据的极值推断AI 解读

We extend extreme value statistics to independent data with possibly very different distributions. In particular, we present novel asymptotic normality results for the Hill estimator, which now estimates the extreme value index of the average distribution. Due to the heterogeneity, the asymptotic variance can be substantially smaller than that in the i.i.d. case. As a special case, we consider a heterogeneous scales model where the asymptotic variance can be calculated…

低秩模型的统计推断AI 解读

This paper studies inference in linear models with a high-dimensional parameter matrix that can be well approximated by a “spiked low-rank matrix.” A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero singular values that diverge to infinity. We show that this framework covers a broad class of models of latent variables, which can accommodate matrix completion problems, factor models, varying coefficient models and heterogeneous…

对抗损失下未知子流形上的分布估计极小极大速率AI 解读

Statistical inference from high-dimensional data with low-dimensional structures has recently attracted a lot of attention. In machine learning, deep generative modelling approaches implicitly estimate distributions of complex objects by creating new samples from the underlying distribution, and have achieved great success in generating synthetic realistic-looking images and texts. A key step in these approaches is the extraction of latent features or representations…

跨尺度的扩散密度估计AI 解读

We consider a space structured population model generated by two-point clouds: a homogeneous Poisson process M with intensity n→∞ as a model for a parent generation together with a Cox point process N as offspring generation, with conditional intensity given by the convolution of M with a scaled dispersal density σ−1f(·/σ). Based on a realisation of M and N, we study the nonparametric estimation of f and the estimation of the physical scale parameter σ>0 simultaneously for…

高维潜在因子模型中的最优判别分析AI 解读

In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower-dimensional space, and base the classification on the resulting lower-dimensional projections. In this paper, we formulate a latent-variable model with a hidden low-dimensional structure to justify this two-step procedure and to guide which projection to choose. We propose a computationally efficient classifier that takes certain principal…

非平稳时间序列的自回归近似、推断与应用AI 解读

Understanding the time-varying structure of complex temporal systems is one of the main challenges of modern time-series analysis. In this paper, we show that every uniformly-positive-definite-in-covariance and sufficiently short-range dependent nonstationary and nonlinear time series can be well approximated globally by a white-noise-driven autoregressive (AR) process of slowly diverging order. To our best knowledge, it is the first time such a structural approximation…

稠密正则图上 Ising 模型的统计推断AI 解读

In this paper, we derive the limit of experiments for one-parameter Ising models on dense regular graphs. In particular, we show that the limiting experiment is Gaussian in the “low temperature” regime, and non-Gaussian in the “critical” regime. We also derive the limiting distributions of the maximum likelihood and maximum pseudolikelihood estimators, and study limiting power for tests of hypothesis against contiguous alternatives. To the best of our knowledge, this is the…

利用基展开估计平稳 Gibbs 点过程的成对交互函数AI 解读

The class of Gibbs point processes (GPP) is a large class of spatial point processes able to model both clustered and repulsive point patterns. They are specified by their conditional intensity, which for a point pattern x and a location u, is roughly speaking the probability that an event occurs in an infinitesimal ball around u given the rest of the configuration is x. The most simple and natural class of models is the class of pairwise interaction point processes where…

残差子抽样的通用秩推断及其大型网络应用AI 解读

Determining the precise rank is an important problem in many large-scale applications with matrix data exploiting low-rank plus noise models. In this paper, we suggest a universal approach to rank inference via residual subsampling (RIRS) for testing and estimating rank in a wide family of models, including many popularly used network models such as the degree corrected mixed membership model as a special case. Our procedure constructs a test statistic via subsampling…

可达半径的最优估计与度量学习AI 解读

We study the estimation of the reach, an ubiquitous regularity parameter in manifold estimation and geometric data analysis. Given an i.i.d. sample over an unknown d-dimensional Ck-smooth submanifold M of RD, we provide optimal nonasymptotic bounds for the estimation of its reach. We build upon a formulation of the reach in terms of maximal curvature on one hand and geodesic metric distortion on the other. The derived rates are adaptive, with rates depending on whether the…

高维有向无环图模型及其等价类的贝叶斯学习复杂度AI 解读

Structure learning via MCMC sampling is known to be very challenging because of the enormous search space and the existence of Markov equivalent DAGs. Theoretical results on the mixing behavior are lacking. In this work, we prove the rapid mixing of a random walk Metropolis–Hastings algorithm, which reveals that the complexity of Bayesian learning of sparse equivalence classes grows only polynomially in n and p, under some high-dimensional assumptions. A series of…

使用 ℓp 正则化统计量的 Model-X knockoffs 功效分析AI 解读

Variable selection properties of procedures utilizing penalized-likelihood estimates is a central topic in the study of high-dimensional linear regression problems. Existing literature emphasizes the quality of ranking of the variables by such procedures as reflected in the receiver operating characteristic curve or in prediction performance. Specifically, recent works have harnessed modern theory of approximate message-passing (AMP) to obtain, in a particular setting, exact…

众包问题中的最优排列估计AI 解读

Motivated by crowdsourcing applications, we consider a model where we have partial observations from a bivariate isotonic n×d matrix with an unknown permutation π∗ acting on its rows. Focusing on the twin problems of recovering the permutation π∗ and estimating the unknown matrix, we introduce a polynomial-time procedure achieving the minimax risk for these two problems, this for all possible values of n, d, and all possible sampling efforts. Along the way we establish that,…