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非参数不可分模型中的条件秩估计与外生性检验AI 解读

Consider a nonparametric nonseparable regression model Y = ϕ(Z, U), where ϕ(Z, U) is strictly increasing in U and U ∼ U[0, 1]. We suppose that there exists an instrument W that is independent of U. The observable random variables are Y, Z, and W, all one-dimensional. We construct test statistics for the hypothesis that Z is exogenous, that is, that U is independent of Z. The test statistics are based on the observation that Z is exogenous if and only if V = FY|Z(Y|Z) is…

均值中非线性Granger因果性的度量AI 解读

We propose model-free measures for Granger causality in mean between random variables. Unlike the existing measures, ours are able to detect and quantify nonlinear causal effects. The new measures are based on nonparametric regressions and defined as logarithmic functions of restricted and unrestricted mean square forecast errors. They are easily and consistently estimated by replacing the unknown mean square forecast errors by their nonparametric kernel estimates. We derive…

高维 U 统计量的高斯与自助法近似及其应用AI 解读

This paper studies the Gaussian and bootstrap approximations for the probabilities of a nondegenerate U-statistic belonging to the hyperrectangles in $\mathbb{R}^{d}$ when the dimension $d$ is large. A two-step Gaussian approximation procedure that does not impose structural assumptions on the data distribution is proposed. Subject to mild moment conditions on the kernel, we establish the explicit rate of convergence uniformly in the class of all hyperrectangles in $\mathbb{R}^{d}$…

未知阶异方差 VAR 模型的协整秩确定AI 解读

We investigate the asymptotic and finite sample properties of a number of methods for estimating the cointegration rank in integrated vector autoregressive systems of unknown autoregressive order driven by heteroskedastic shocks. We allow for both conditional and unconditional heteroskedasticity of a very general form. We establish the conditions required on the penalty functions such that standard information criterion-based methods, such as the Bayesian information…

无限方差创新驱动的非平稳线性过程的单位根推断AI 解读

The contribution of this paper is two-fold. First, we derive the asymptotic null distribution of the familiar augmented Dickey-Fuller [ADF] statistics in the case where the shocks follow a linear process driven by infinite variance innovations. We show that these distributions are free of serial correlation nuisance parameters but depend on the tail index of the infinite variance process. These distributions are shown to coincide with the corresponding results for the case…

通过条件边际回归检验遗漏协变量的显著性AI 解读

Researchers sometimes have a priori information on the relative importance of predictors that can be used to screen out covariates. An important question is whether any of the discarded covariates have predictive power when the most relevant predictors are included in the model. We consider testing whether any discarded covariate is significant conditional on some pre-chosen covariates. We propose a maximum-type test statistic and show that it has a nonstandard asymptotic…

随机化视角下的方差分析：对处理效应异质性稳健的检验统计量AI 解读

Fisher randomization tests for Neyman’s null hypothesis of no average treatment effect are considered in a finite-population setting associated with completely randomized experiments involving more than two treatments. The consequences of using the |$F$| statistic to conduct such a test are examined, and we argue that under treatment effect heterogeneity, use of the |$F$| statistic in the Fisher randomization test can severely inflate the Type I error under Neyman’s null…

分位数回归中的边际线性效应检验AI 解读

Summary The paper develops a new marginal testing procedure to detect significant predictors that are associated with the conditional quantiles of a scalar response. The idea is to fit the marginal quantile regression on each predictor one at a time, and then to base the test on the t-statistics that are associated with the most predictive predictors. A resampling method is devised to calibrate this test statistic, which has non-regular limiting behaviour due to the…

非参数工具变量回归的最优上确界范数收敛率与非线性泛函一致推断AI 解读

This paper makes several important contributions to the literature about nonparametric instrumental variables (NPIV) estimation and inference on a structural function h0 and functionals of h0. First, we derive sup‐norm convergence rates for computationally simple sieve NPIV (series two‐stage least squares) estimators of h0 and its derivatives. Second, we derive a lower bound that describes the best possible (minimax) sup‐norm rates of estimating h0 and its derivatives, and…

新型自助法置信界的渐近理论AI 解读

We propose a new method, based on sample splitting, for constructing bootstrap confidence bounds for a parameter appearing in the regular smooth function model. It has been demonstrated in the literature, for example, by Hall [Ann. Statist. 16 (1988) 927–985; The Bootstrap and Edgeworth Expansion (1992) Springer], that the well-known percentile-$t$ method for constructing bootstrap confidence bounds typically incurs a coverage error of order $O(n^{-1})$, with $n$ being the…

基于U统计量的估计量：更简便的渐近方差自助法估计AI 解读

The bootstrap is a popular and useful tool for estimating the asymptotic variance of complicated estimators. Ironically, the fact that the estimators are complicated can make the standard bootstrap computationally burdensome because it requires repeated recalculation of the estimator. In this paper, we propose a method that is specific to extremum estimators based on U‐statistics. The contribution here is that rather than repeated recalculation of the U‐statistic‐based…

内生样本选择下的非参数估计AI 解读

This paper addresses the problem of estimation of a nonparametric regression function from selectively observed data when selection is endogenous. Our approach relies on independence between covariates and selection conditionally on potential outcomes. Endogeneity of regressors is also allowed for. In the exogenous and endogenous case, consistent two-step estimation procedures are proposed and their rates of convergence are derived. Pointwise asymptotic distribution of the…

噪声与异步交易下二元平均已实现波动率矩阵的两阶段平稳自助法AI 解读

Under the two important modern financial market features of noise and non-synchronicity for multiple assets, for consistent estimators of the integrated covariations, we adopt the two-time scale average realized volatility matrix (ARVM) which is a matrix extension of the two-time scale realized volatilities of Zhang et al. (2005). An asymptotic normal theory is provided for the two-time scale ARVM and resulting realized covariations. The asymptotic normality is not directly…

存在干扰时两阶段随机实验的分析AI 解读

Two-stage randomization is a powerful design for estimating treatment effects in the presence of interference; that is, when one individual’s treatment assignment affects another individual’s outcomes. Our motivating example is a two-stage randomized trial evaluating an intervention to reduce student absenteeism in the School District of Philadelphia. In that experiment, households with multiple students were first assigned to treatment or control; then, in treated…

时变系数已实现波动率模型的非参数估计与预测AI 解读

This article introduces a new specification for the heterogenous autoregressive (HAR) model for the realized volatility of S&P 500 index returns. In this modeling framework, the coefficients of the HAR are allowed to be time-varying with unspecified functional forms. The local linear method with the cross-validation (CV) bandwidth selection is applied to estimate the time-varying coefficient HAR (TVC-HAR) model, and a bootstrap method is used to construct the point-wise…

最大线性竞争因子模型AI 解读

Models incorporating “latent” variables have been commonplace in financial, social, and behavioral sciences. Factor model, the most popular latent model, explains the continuous observed variables in a smaller set of latent variables (factors) in a matter of linear relationship. However, complex data often simultaneously display asymmetric dependence, asymptotic dependence, and positive (negative) dependence between random variables, which linearity and Gaussian…

基于核的联合独立性检验AI 解读

Summary We investigate the problem of testing whether d possibly multivariate random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two-variable Hilbert–Schmidt independence criterion but allows for an arbitrary number of variables. We embed the joint distribution and the product of the marginals in a reproducing kernel Hilbert space and define the d-variable Hilbert–Schmidt independence criterion dHSIC…

有限空间上经验 Wasserstein 距离的统计推断AI 解读

Summary The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive the asymptotic distribution of empirical Wasserstein distances as the optimal value of a linear programme with random objective function. This facilitates statistical inference (e.g. confidence intervals for sample-based Wasserstein…

高维线性模型的拟合优度检验AI 解读

Summary We propose a framework for constructing goodness-of-fit tests in both low and high dimensional linear models. We advocate applying regression methods to the scaled residuals following either an ordinary least squares or lasso fit to the data, and using some proxy for prediction error as the final test statistic. We call this family residual prediction tests. We show that simulation can be used to obtain the critical values for such tests in the low dimensional…

基于核的半参数估计量：小带宽渐近与自助法一致性AI 解读

This paper develops asymptotic approximations for kernel‐based semiparametric estimators under assumptions accommodating slower‐than‐usual rates of convergence of their nonparametric ingredients. Our first main result is a distributional approximation for semiparametric estimators that differs from existing approximations by accounting for a bias. This bias is nonnegligible in general, and therefore poses a challenge for inference. Our second main result shows that some (but…

长记忆下重抽样方法的有效性AI 解读

For long-memory time series, inference based on resampling is of crucial importance, since the asymptotic distribution can often be non-Gaussian and is difficult to determine statistically. However, due to the strong dependence, establishing the asymptotic validity of resampling methods is nontrivial. In this paper, we derive an efficient bound for the canonical correlation between two finite blocks of a long-memory time series. We show how this bound can be applied to…

自助法迭代的离散模型AI 解读

The bootstrap can be validated by considering the sequence of P values obtained by bootstrap iteration, rather than asymptotically. If this sequence converges to a random variable with the uniform U(0,1) distribution, the bootstrap is valid. Here, the model is made discrete and finite, characterised by a three-dimensional array of probabilities. This renders bootstrap iteration to any desired order feasible. A unit-root test for a process driven by a stationary MA(1) process…

混合时间尺度跳跃回归与自助法推断AI 解读

We develop an efficient mixed-scale estimator for jump regressions using high-frequency asset returns. A fine time scale is used to accurately identify the locations of large rare jumps in the explanatory variables such as the price of the market portfolio. A coarse scale is then used in the estimation in order to attenuate the effect of trading frictions in the dependent variable such as the prices of potentially less liquid assets. The proposed estimator has a non-standard…

稳健预测比较AI 解读

Forecast accuracy is typically measured in terms of a given loss function. However, as a consequence of the use of misspecified models in multiple model comparisons, relative forecast rankings are loss function dependent. In order to address this issue, a novel criterion for forecast evaluation that utilizes the entire distribution of forecast errors is introduced. In particular, we introduce the concepts of general-loss (GL) forecast superiority and convex-loss (CL)…