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平滑非参数多元混合数据的位置—尺度检验AI 解读

A number of tests have been proposed for assessing the location-scale assumption that is often invoked by practitioners. Existing approaches include Kolmogorov–Smirnov and Cramer–von Mises statistics that each involve measures of divergence between unknown joint distribution functions and products of marginal distributions. In practice, the unknown distribution functions embedded in these statistics are typically approximated using nonsmooth empirical distribution functions…

回归不连续设计、白噪声模型与极小极大理论AI 解读

This paper studies an approximation of sharp regression discontinuity (RD) designs with normal homoskedastic errors by ideal Gaussian white noise models with discontinuous drifts. After establishing an asymptotic equivalence of the two models, we first provide a simple derivation of a lower bound on the minimax optimal convergence rate for estimating the discontinuity size in a derivative (of an arbitrary order) of the regression function. We show that the optimal…

半参数持续期模型的简便秩估计方法AI 解读

Modeling nonnegative financial variables (e.g. durations between trades or volatilities) is central to a number of studies across econometrics, and still poses several statistical challenges. Among them, the efficiency aspects of semiparametric estimation remain pivotal. In this paper, we concentrate on estimation problems in autoregressive conditional duration models with unspecified innovation densities. Exponential quasi-likelihood estimators (QMLE) are the usual practice…

通过空间填充基函数选择提高平滑样条近似效率AI 解读

Summary We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size $n$, the smoothing spline estimator can be expressed as a linear combination of $n$ basis functions, requiring $O(n^3)$ computational time when the number $d$ of predictors is two or more. Such a sizeable computational cost hinders the broad applicability of smoothing splines. In practice, the full-sample smoothing spline…

可视化黑箱监督学习模型中预测变量的效应AI 解读

Summary In many supervised learning applications, understanding and visualizing the effects of the predictor variables on the predicted response is of paramount importance. A shortcoming of black box supervised learning models (e.g. complex trees, neural networks, boosted trees, random forests, nearest neighbours, local kernel-weighted methods and support vector regression) in this regard is their lack of interpretability or transparency. Partial dependence plots, which are…

非平稳时间序列精度矩阵的估计与推断AI 解读

We consider the estimation of and inference on precision matrices of a rich class of univariate locally stationary linear and nonlinear time series, assuming that only one realization of the time series is observed. Using a Cholesky decomposition technique, we show that the precision matrices can be directly estimated via a series of least squares linear regressions with smoothly time-varying coefficients. The method of sieves is utilized for the estimation and is shown to…

生存分析中治愈模型的一般方法AI 解读

In survival analysis it often happens that some subjects under study do not experience the event of interest; they are considered to be “cured.” The population is thus a mixture of two subpopulations, one of cured subjects and one of “susceptible” subjects. We propose a novel approach to estimate a mixture cure model when covariates are present and the lifetime is subject to random right censoring. We work with a parametric model for the cure proportion, while the…

筛先验下贝叶斯可信集的渐近频率学覆盖性质AI 解读

We investigate the frequentist coverage properties of (certain) Bayesian credible sets in a general, adaptive, nonparametric framework. It is well known that the construction of adaptive and honest confidence sets is not possible in general. To overcome this problem (in context of sieve type of priors), we introduce an extra assumption on the functional parameters, the so-called “general polished tail” condition. We then show that under standard assumptions, both the…

单位根中度偏离下核估计的渐近理论与非参数检验的水平AI 解读

We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered only nearly integrated and stationary autoregressive processes. These results have applications to nonparametric predictive regression models. In particular, we show that the null rejection probability of a nonparametric t test is controlled…

简便的局部多项式密度估计量AI 解读

This paper introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not require pre-binning or any other transformation of the data. We study the main asymptotic properties of the estimator, and use these results to provide principled estimation, inference, and bandwidth selection methods. As a substantive application of our results, we develop a novel…

长度偏倚抽样与信息性删失下 Copula 及依赖度量的非参数推断AI 解读

Length-biased data are often encountered in cross-sectional surveys and prevalent-cohort studies on disease durations. Under length-biased sampling subjects with longer disease durations have greater chance to be observed. As a result, covariate values linked to the longer survivors are favored by the sampling mechanism. When the sampled durations are also subject to right censoring, the censoring is informative. Modeling dependence structure without adjusting for these…

空间数据密度估计的带宽选择AI 解读

Summary Bandwidth choice is crucial in spatial kernel estimation in exploring non-Gaussian complex spatial data. The paper investigates the choice of adaptive and non-adaptive bandwidths for density estimation given data on a spatial lattice. An adaptive bandwidth depends on local data and hence adaptively conforms with local features of the spatial data. We propose a spatial cross-validation (SCV) choice of a global bandwidth. This is done first with a pilot density…

日内与隔夜波动率的耦合成分 DCS-EGARCH 模型AI 解读

We propose a semi-parametric coupled component exponential GARCH model for intraday and overnight returns that allows the two series to have different dynamical properties. We adopt a dynamic conditional score model with t-distributed innovations that captures the very heavy tails of overnight returns. We propose a several-step estimation procedure that captures the nonparametric slowly moving components by kernel estimation and the dynamic parameters by maximum likelihood.…

具有随机未观测异质性的持续期模型非参数分析AI 解读

This paper develops nonparametric identification and estimation results for a single-spell hazard model, where the unobserved heterogeneity is specified as a Lévy subordinator. The identification approach solves a nonlinear Volterra integral equation of the first kind with an unknown kernel function. Both the kernel of the integral operator, which models the distribution of the unobserved heterogeneity, and the functions that enter it are identified given regularity…

一类矩条件模型中函数值参数的导数估计AI 解读

We develop a general approach to estimating the derivative of a function-valued parameter θo(u) that is identified for every value of u as the solution to a moment condition. This setup in particular covers interesting models for conditional distributions, such as quantile regression or distribution regression. Exploiting that θo(u) solves a moment condition, we obtain an explicit expression for its derivative from the Implicit Function Theorem, and then estimate the…

条件独立性检验的困难与广义协方差度量AI 解读

It is a common saying that testing for conditional independence, that is, testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In this paper, we prove that conditional independence is indeed a particularly difficult hypothesis to test for. Valid statistical tests are required to have a size that is smaller than a pre-defined significance level, and different tests…

GRID：高维非参数回归的变量选择与结构发现方法AI 解读

We consider nonparametric regression in high dimensions where only a relatively small subset of a large number of variables are relevant and may have nonlinear effects on the response. We develop methods for variable selection, structure discovery and estimation of the true low-dimensional regression function, allowing any degree of interactions among the relevant variables that need not be specified a-priori. The proposed method, called the GRID, combines empirical…

基于分区的级数估计量的大样本性质AI 解读

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics and machine learning. First, we obtain a general characterization of their leading asymptotic bias. Second, we establish integrated mean squared error approximations for the point estimator and propose feasible tuning parameter selection. Third, we develop pointwise inference methods…

直接插值：无岭惩罚核回归也能泛化AI 解读

In the absence of explicit regularization, Kernel “Ridgeless” Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still generalize well on test data. We isolate a phenomenon of implicit regularization for minimum-norm interpolated solutions which is due to a combination of high dimensionality of the input data, curvature of the kernel function and favorable…

期权市场交易活动与定价核估计：贝叶斯方法AI 解读

We propose a nonparametric Bayesian approach for the estimation of the pricing kernel. Historical stock returns and option market data are combined through the Dirichlet Process (DP) to construct an option-adjusted physical measure. The precision parameter of the DP process is calibrated to the amount of trading activity in deep-out-of-the-money options. We use the option-adjusted physical measure to construct an option-adjusted pricing kernel. An empirical investigation on…

存在出口时的企业生产率估计：中国制造业证据AI 解读

Summary Motivated by the long‐standing interest of economists in understanding the nexus between firm productivity and export behavior, this paper develops a novel structural framework for control‐function‐based nonparametric identification of the gross production function and latent firm productivity in the presence of endogenous export opportunities that is robust to recent unidentification critiques of proxy estimators. We provide a workable identification strategy,…

双重差分模型中的双重／去偏机器学习AI 解读

Summary This paper provides an orthogonal extension of the semiparametric difference-in-differences estimator proposed in earlier literature. The proposed estimator enjoys the so-called Neyman orthogonality (Chernozhukov et al., 2018), and thus it allows researchers to flexibly use a rich set of machine learning methods in the first-step estimation. It is particularly useful when researchers confront a high-dimensional data set in which the number of potential control…

断点回归中稳健偏差校正推断的最优带宽选择AI 解读

Summary Modern empirical work in regression discontinuity (RD) designs often employs local polynomial estimation and inference with a mean square error (MSE) optimal bandwidth choice. This bandwidth yields an MSE-optimal RD treatment effect estimator, but is by construction invalid for inference. Robust bias-corrected (RBC) inference methods are valid when using the MSE-optimal bandwidth, but we show that they yield suboptimal confidence intervals in terms of coverage error.…

双重非线性协整的估计AI 解读

In recent years statistical inference for nonlinear cointegration has attracted attention from both academics and practitioners. This paper proposes a new type of cointegration in the sense that two univariate time series yt and xt are cointegrated via two (unknown) smooth nonlinear transformations, further generalizing the notion of cointegration initially revealed by Box and Tiao (1977), and more systematically studied by Engle and Granger (1987). More precisely, it holds…