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具有潜在大量协变量的断点回归设计AI 解读

This paper studies the case of possibly high-dimensional covariates in the regression discontinuity design (RDD) analysis. In particular, we propose estimation and inference methods for the RDD models with covariate selection which perform stably regardless of the number of covariates. The proposed methods combine the local approach using kernel weights with $\ell_{1}$-penalization to handle high-dimensional covariates. We provide theoretical and numerical results which…

条件矩约束的函数型广义经验似然估计AI 解读

Important problems in causal inference, economics, and, more generally, robust machine learning can be expressed as conditional moment restrictions, but estimation becomes challenging as it requires solving a continuum of unconditional moment restrictions. Previous works addressed this problem by extending the generalized method of moments (GMM) to continuum moment restrictions. In contrast, generalized empirical likelihood (GEL) provides a more general framework and has…

密度加权平均导数估计的小带宽渐近高阶改进AI 解读

The density weighted average derivative (DWAD) of a regression function is a canonical parameter of interest in economics. Classical first-order large sample distribution theory for kernel-based DWAD estimators relies on tuning parameter restrictions and model assumptions that imply an asymptotic linear representation of the point estimator. These conditions can be restrictive, and the resulting distributional approximation may not be representative of the actual sampling…

局部平稳时间序列的偏自相关函数：刻画、估计与推断AI 解读

For stationary time series, it is common to use the plots of partial autocorrelation function (PACF) or PACF-based tests to explore the temporal dependence structure of such processes. To our best knowledge, such analogs for non-stationary time series have not been fully established yet. In this paper, we fill this gap for locally stationary time series with short-range dependence. First, we characterize the PACF locally in the time domain and show that the $j$th PACF,…

利用核密度估计选择非线性指标计算中的半径AI 解读

When nonlinear measures are estimated from sampled temporal signals with finite-length, a radius parameter must be carefully selected to avoid a poor estimation. These measures are generally derived from the correlation integral which quantifies the probability of finding neighbors, i.e. pair of points spaced by less than the radius parameter. While each nonlinear measure comes with several specific empirical rules to select a radius value, we provide a systematic selection…

非参数结构函数与弹性的自适应估计及一致置信带AI 解读

We introduce two data-driven procedures for optimal estimation and inference in nonparametric models using instrumental variables. The first is a data-driven choice of sieve dimension for a popular class of sieve two-stage least squares estimators. When implemented with this choice, estimators of both the structural function $h_0$ and its derivatives (such as elasticities) converge at the fastest possible (i.e., minimax) rates in sup-norm. The second is for constructing…

利用变点生存模型外推相对治疗效应AI 解读

Introduction: Modelling of relative treatment effects is an important aspect to consider when extrapolating the long-term survival outcomes of treatments. Flexible parametric models offer the ability to accurately model the observed data, however, the extrapolated relative treatment effects and subsequent survival function may lack face validity. Methods: We investigate the ability of change-point survival models to estimate changes in the relative treatment effects,…

通过条件分位数回归估计无条件分位数偏效应AI 解读

This paper develops a semi-parametric procedure for estimation of unconditional quantile partial effects using quantile regression coefficients. The estimator is based on an identification result showing that, for continuous covariates, unconditional quantile effects are a weighted average of conditional ones at particular quantile levels that depend on the covariates. We propose a two-step estimator for the unconditional effects where in the first step one estimates a…

异质性因果效应估计的极小极大收敛速率AI 解读

Estimation of heterogeneous causal effects - i.e., how effects of policies and treatments vary across subjects - is a fundamental task in causal inference. Many methods for estimating conditional average treatment effects (CATEs) have been proposed in recent years, but questions surrounding optimality have remained largely unanswered. In particular, a minimax theory of optimality has yet to be developed, with the minimax rate of convergence and construction of rate-optimal…

边界自适应的局部多项式条件密度估计AI 解读

We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the estimators, offering characterizations of both probability concentration and distributional approximation. In particular, we establish uniform convergence rates in probability and valid Gaussian distributional approximations for the…

协变量调整回归函数的去偏推断AI 解读

In this article, we study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. In particular, under certain causal conditions, this parameter corresponds to the average outcome had all units been assigned to a specific exposure level, known as the causal dose-response curve. We propose a debiased local linear estimator of the…

卷积核大小与人脸分析 CNN 泛化偏差的联系AI 解读

Training dataset biases are by far the most scrutinized factors when explaining algorithmic biases of neural networks. In contrast, hyperparameters related to the neural network architecture have largely been ignored even though different network parameterizations are known to induce different implicit biases over learned features. For example, convolutional kernel size is known to affect the frequency content of features learned in CNNs. In this work, we present a causal…

分层随机化下协变量调整的统一框架AI 解读

Randomization, as a key technique in clinical trials, can eliminate sources of bias and produce comparable treatment groups. In randomized experiments, the treatment effect is a parameter of general interest. Researchers have explored the validity of using linear models to estimate the treatment effect and perform covariate adjustment and thus improve the estimation efficiency. However, the relationship between covariates and outcomes is not necessarily linear, and is often…

内生序贯处理方案中的识别AI 解读

This paper develops a novel nonparametric identification method for treatment effects in settings where individuals self-select into treatment sequences. I propose an identification strategy which relies on a dynamic version of standard Instrumental Variables (IV) assumptions and builds on a dynamic version of the Marginal Treatment Effects (MTE) as the fundamental building block for treatment effects. The main contribution of the paper is to relax assumptions on the support…

用于函数型数据因果结构学习的核独立性检验AI 解读

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as realisations of an underlying smooth process sampled over the continuum. However, traditional methods for independence testing and causal learning are not directly applicable to such data, as they do not take into account the dependence along the…

商品组合选择的半参数离散选择模型AI 解读

We propose two approaches to estimate semiparametric discrete choice models for bundles. Our first approach is a kernel-weighted rank estimator based on a matching-based identification strategy. We establish its complete asymptotic properties and prove the validity of the nonparametric bootstrap for inference. We then introduce a new multi-index least absolute deviations (LAD) estimator as an alternative, of which the main advantage is its capacity to estimate preference…

因果发现中的预测不对称性：信息论方法AI 解读

Causal investigations in observational studies pose a great challenge in research where randomized trials or intervention-based studies are not feasible. We develop an information geometric causal discovery and inference framework of "predictive asymmetry". For $(X, Y)$, predictive asymmetry enables assessment of whether $X$ is more likely to cause $Y$ or vice-versa. The asymmetry between cause and effect becomes particularly simple if $X$ and $Y$ are deterministically…

多变量平稳与非平稳时间序列的核联合独立性检验AI 解读

Multivariate time series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the accurate statistical modelling and analysis of such systems. Here, we introduce kernel-based statistical tests of joint independence in multivariate time series by extending the $d$-variable Hilbert-Schmidt independence criterion (dHSIC) to…

非参数自回归的多步预测区间：自助法一致性、去偏与估计变异AI 解读

To address the difficult problem of multi-step ahead prediction of non-parametric autoregressions, we consider a forward bootstrap approach. Employing a local constant estimator, we can analyze a general type of non-parametric time series model, and show that the proposed point predictions are consistent with the true optimal predictor. We construct a quantile prediction interval that is asymptotically valid. Moreover, using a debiasing technique, we can asymptotically…

核处理效应的高效双重稳健检验AI 解读

The average treatment effect, which is the difference in expectation of the counterfactuals, is probably the most popular target effect in causal inference with binary treatments. However, treatments may have effects beyond the mean, for instance decreasing or increasing the variance. We propose a new kernel-based test for distributional effects of the treatment. It is, to the best of our knowledge, the first kernel-based, doubly-robust test with provably valid type-I error.…

超大样本半参数单调指数模型的随机学习AI 解读

I study the estimation of semiparametric monotone index models in the scenario where the number of observation points $n$ is extremely large and conventional approaches fail to work due to heavy computational burdens. Motivated by the mini-batch gradient descent algorithm (MBGD) that is widely used as a stochastic optimization tool in the machine learning field, I proposes a novel subsample- and iteration-based estimation procedure. In particular, starting from any initial…

通过函数型生存分析刻画动态处理效应类型AI 解读

In recent years, research interest in personalised treatments has been growing. However, treatment effect heterogeneity and possibly time-varying treatment effects are still often overlooked in clinical studies. Statistical tools are needed for the identification of treatment response patterns, taking into account that treatment response is not constant over time. We aim to provide an innovative method to obtain dynamic treatment effect phenotypes on a time-to-event outcome,…

非参数回归的涵盖检验AI 解读

We set up a formal framework to characterize encompassing of nonparametric models through the L2 distance. We contrast it to previous literature on the comparison of nonparametric regression models. We then develop testing procedures for the encompassing hypothesis that are fully nonparametric. Our test statistics depend on kernel regression, raising the issue of bandwidth's choice. We investigate two alternative approaches to obtain a "small bias property" for our test…

无需对工具变量平滑的部分线性工具变量回归AI 解读

We consider a semiparametric partly linear model identified by instrumental variables. We propose an estimation method that does not smooth on the instruments and we extend the Landweber-Fridman regularization scheme to the estimation of this semiparametric model. We then show the asymptotic normality of the parametric estimator and obtain the convergence rate for the nonparametric estimator. Our estimator that does not smooth on the instruments coincides with a typical…