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高维中心极限定理与自助法近似的改进AI 解读

This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its distribution plays a key role in many high-dimensional estimation and testing problems. Using a novel iterative randomized Lindeberg method, the paper derives new bounds for the distributional approximation errors. These new bounds…

具有有限样本保证的新型 Edgeworth 展开AI 解读

We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean balls and the set of all half-spaces. These results allow to account for an impact of higher-order moments or cumulants of the considered distributions; the obtained error terms depend on a sample size and a dimension explicitly. The new…

干预特定平均结局的连续时间目标最小损失估计AI 解读

This paper generalizes the targeted minimum loss-based estimation (TMLE) framework to allow for estimating the effects of time-varying interventions in settings where both interventions, covariates, and outcome can happen at subject-specific time-points on an arbitrarily fine time-scale. TMLE is a general template for constructing asymptotically linear substitution estimators for smooth low-dimensional parameters in infinite-dimensional models. Existing longitudinal TMLE…

具有测量误差的李群非参数回归AI 解读

This paper develops a foundation of methodology and theory for nonparametric regression with Lie group-valued predictors contaminated by measurement errors. Our methodology and theory are based on harmonic analysis on Lie groups, which is largely unknown in statistics. We establish a novel deconvolution regression estimator, and study its rate of convergence and asymptotic distribution. We also provide asymptotic confidence intervals based on the asymptotic distribution of…

使用近似共充分抽样检验拟合优度与条件独立性AI 解读

Goodness-of-fit (GoF) testing is ubiquitous in statistics, with direct ties to model selection, confidence interval construction, conditional independence testing, and multiple testing, just to name a few applications. While testing the GoF of a simple (point) null hypothesis provides an analyst great flexibility in the choice of test statistic while still ensuring validity, most GoF tests for composite null hypotheses are far more constrained, as the test statistic must…

参数估计应如何适配使用目标？AI 解读

We study parameter estimation from the sample X, when the objective is to maximize the expected value of a criterion function, Q, for a distinct sample, Y. This is the situation that arises when a model is estimated for the purpose of describing other data than those used for estimation, such as in forecasting problems. A natural candidate for solving maxT∈σ(X)EQ(Y,T) is the innate estimator, θˆ=argmaxθQ(X,θ). While the innate estimator has certain advantages, we show that…

局部错误定价与市场微观结构噪声：参数化视角AI 解读

We extend the classic ”martingale-plus-noise” model for high-frequency returns to accommodate an error correction mechanism and endogenous pricing errors. It is motivated by (i) novel empirical evidence documenting that microstructure noise exhibits frequently changing patterns of serial dependence which are interwoven with innovations to the efficient price; (ii) building a bridge between high-frequency econometrics and market microstructure models. We identify temporal…

跳跃扩散模型中跳跃成分的存在性检验AI 解读

In this paper we propose a nonparametric test to determine whether an underlying jump diffusion process indeed contains jump component, or equivalently, is indeed a diffusion. Our test is based upon a robust threshold estimation of diffusive volatility and the kernel estimation of the conditional moment function of the squared instantaneous increments of the underlying process. We show that our test statistic has asymptotic standard normal distribution under the null…

含平稳协变量的分位数协整非参数推断AI 解读

This paper considers the inference problems in nonlinear quantile regressions with both stationary and nonstationary covariates. The nonparametric local constant quantile estimator is proposed to estimate the unknown quantile regression function, whose asymptotic properties are established under quite general conditions. Specification testing of the quantile regression function is further considered through a statistic constructed based on the integrated squared distance…

分位数回归的广义矩估计AI 解读

This paper develops generalized method of moments (GMM) estimation and inference procedures for quantile regression models. We propose a GMM estimator for simultaneous estimation across multiple quantiles. This estimator allows us to model quantile regression coefficients using flexible parametric restrictions across quantiles. The restrictions and simultaneous estimation lead to efficiency gains compared to standard methods. We establish the asymptotic properties of the GMM…

厚尾、非对称或异方差误差下高维均值回归的稳健选择后推断AI 解读

We propose a robust post-selection inference method based on the Huber loss for the regression coefficients, when the error distribution is heavy-tailed and asymmetric in a high-dimensional linear model with an intercept term. The asymptotic properties of the resulting estimators are established under mild conditions. We also extend the proposed method to accommodate heteroscedasticity assuming the error terms are symmetric and other suitable conditions. Statistical tests…

存在测量误差的变系数模型估计AI 解读

We propose a semiparametric estimator for varying coefficient models when the regressors in the nonparametric components are measured with error. Varying coefficient models are an extension of other popular semiparametric models , including partially linear and nonparametric additive models, and deliver an attractive solution to the curse-of-dimensionality. We use deconvolution kernel estimation in a two-step procedure and show that the estimator is consistent and…

尾部删失数据下尾部特征的估计与推断AI 解读

This paper considers estimation and inference about tail features such as tail index and extreme quantile when the observations beyond some threshold are censored. Ignoring such tail censoring could lead to substantial bias and size distortion, even if the censored probability is tiny. We first propose a new maximum likelihood estimator (MLE) based on the Pareto tail approximation and derive its asymptotic properties. Then, we propose an alternative method of constructing…

协方差—均值回归的统计推断AI 解读

In this article, we introduce a covariance-mean regression model with heterogeneous similarity matrices. It not only links the covariance of responses to heterogeneous similarity matrices induced by auxiliary information, but also establishes the relationship between the mean of responses and covariates. Under this new model setting, however, two statistical inference challenges are encountered. The first challenge is that the consistency of the covariance estimator based on…

多潜变量模型的快速精确变分推断AI 解读

Models with a large number of latent variables are often used to utilize the information in big or complex data, but can be difficult to estimate. Variational inference methods provide an attractive solution. These methods use an approximation to the posterior density, yet for large latent variable models existing choices can be inaccurate or slow to calibrate. Here, we propose a family of tractable variational approximations that are more accurate and faster to calibrate…

贝叶斯后验均值的抽样性质及其在 WALS 估计中的应用AI 解读

Many statistical and econometric learning methods rely on Bayesian ideas. When applied in a frequentist setting, their precision is often assessed using the posterior variance. This is permissible asymptotically, but not necessarily in finite samples. We explore this issue focusing on weighted-average least squares (WALS), a Bayesian-frequentist ‘fusion’. Exploiting the sampling properties of the posterior mean in the normal location model, we derive estimators of the…

具有内生同步效应的马尔可夫转换面板模型AI 解读

This paper introduces a new dynamic panel model with multi-layer network effects. Series-specific latent Markov chain processes drive the dynamics of the observable processes, and several types of interaction effects among the hidden chains allow for various degrees of endogenous synchronization of both latent and observable processes. The interaction is driven by a multi-layer network with exogenous and endogenous connectivity layers. We provide some theoretical properties…

基于期权的非参数跳跃变差度量AI 解读

This paper proposes a novel nonparametric method for estimating tail jump variation measures from short-dated options, which can achieve rate-efficiency and works in a general infinite jump activity setting, avoiding parametric or semiparametric assumptions for the jump measure. The method is based on expressing the measures of interest as integrals of the Laplace transforms of the jump compensator and developing methods for recovering nonparametrically the latter from the…

全球气温与温室气体：共同特征方法AI 解读

We propose a common features approach for testing for common trends and estimating long-run relationships between variables with complex trends. Using this approach, we establish that global temperatures and the concentration of greenhouse gases share a common trend and we estimate their long-run relationship without conditioning on the exact nature of this trend.

具有递增半参数单指标交互项的预测型函数线性模型AI 解读

When predicting crop yield using both functional and multivariate predictors, the prediction performances benefit from the inclusion of the interactions between the two sets of predictors. We assume the interaction depends on a nonparametric, single-index structure of the multivariate predictor and reduce each functional predictor’s dimension using functional principal component analysis (FPCA). Allowing the number of FPCA scores to diverge to infinity, we consider a…

含 GARCH 创新的预测回归系统：最小二乘与 IVX 极限理论AI 解读

The paper examines the effect of conditional heteroskedasticity on least squares inference in stochastic regression models of unknown integration order and proposes an inference procedure that is robust to models within the (near) I(0)–(near) I(1) range with GARCH innovations. We show that a regressor signal of exact order $O_{p}\left ( n\kappa _{n}\right ) $ for arbitrary $\,\kappa _{n}\rightarrow \infty $ is sufficient to eliminate stationary GARCH effects from the limit…

对潜在非平稳性稳健的结构 VAR 工具变量估计AI 解读

This paper considers the estimation of dynamic causal effects using a proxy structural vector-autoregressive model with possibly nonstationary regressors. We provide general conditions under which the asymptotic normal approximation remains valid. In this case, the asymptotic variance depends on the persistence property of each series. We further provide a consistent asymptotic covariance matrix estimator that requires neither knowledge of the presistence properties of the…

Kronecker 协方差模型的二次型估计AI 解读

We propose a new estimator, the quadratic form estimator, of the Kronecker product model for covariance matrices. We show that this estimator has good properties in the large dimensional case (i.e., the cross-sectional dimension n is large relative to the sample size T ). In particular, the quadratic form estimator is consistent in a relative Frobenius norm sense provided ${\log }^3n/T\to 0$ . We obtain the limiting distributions of the Lagrange multiplier and Wald tests…

混合鞅假设下时间序列与横截面的联合极限理论AI 解读

In this paper, we complement joint time-series and cross-section convergence results derived in a companion paper Hahn, Kuersteiner, and Mazzocco (2016, Central Limit Theory for Combined Cross-Section and Time Series) by allowing for serial correlation in the time-series sample. The implications of our analysis are limiting distributions that have a well-known form of long-run variances for the time-series limit. We obtain these results at the cost of imposing strict…