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基于分位数回归的面板数据聚类AI 解读

In panel data analysis, it is important to identify subgroups of units with heterogeneous parameters. This can not only increase the model flexibility but also produce more efficient estimation by pooling information across units within the same group. In this paper, we propose a new quantile-regression-based clustering method for panel data. We develop an iterative algorithm using a similar idea of k-means clustering to identify subgroups with heterogeneous slopes at a…

患者偏好试验的设计、识别与敏感性分析AI 解读

Social and medical scientists are often concerned that the external validity of experimental results may be compromised because of heterogeneous treatment effects. If a treatment has different effects on those who would choose to take it and those who would not, the average treatment effect estimated in a standard randomized controlled trial (RCT) may give a misleading picture of its impact outside of the study sample. Patient preference trials (PPTs), where participants’…

高阈值超越的广义可加模型及其在美国阵风重现水平估计中的应用AI 解读

Generalized additive model (GAM) forms offer a flexible approach to capturing marginal variation. Such forms are used here to represent distributional variation in extreme values and presented in terms of spatio-temporal variation, which is often evident in environmental processes. A two-stage procedure is proposed that identifies extreme values as exceedances of a high threshold, which is defined as a fixed quantile and estimated by quantile regression. Excesses of the…

多条时间序列的贝叶斯谱建模AI 解读

We develop a novel Bayesian modeling approach to spectral density estimation for multiple time series. The log-periodogram distribution for each series is modeled as a mixture of Gaussian distributions with frequency-dependent weights and mean functions. The implied model for the log-spectral density is a mixture of linear mean functions with frequency-dependent weights. The mixture weights are built through successive differences of a logit-normal distribution function with…

自回归模型的极端分位数估计AI 解读

A quantile autoregresive model is a useful extension of classical autoregresive models as it can capture the influences of conditioning variables on the location, scale, and shape of the response distribution. However, at the extreme tails, standard quantile autoregression estimator is often unstable due to data sparsity. In this article, assuming quantile autoregresive models, we develop a new estimator for extreme conditional quantiles of time series data based on extreme…

ARMA–GARCH 模型中条件尾部风险度量的置信区间AI 解读

ARMA–GARCH models are widely used to model the conditional mean and conditional variance dynamics of returns on risky assets. Empirical results suggest heavy-tailed innovations with positive extreme value index for these models. Hence, one may use extreme value theory to estimate extreme quantiles of residuals. Using weak convergence of the weighted sequential tail empirical process of the residuals, we derive the limiting distribution of extreme conditional Value-at-Risk…

尖锐断点回归设计下分位数效应的一致推断AI 解读

This study develops methods for conducting uniform inference on quantile treatment effects for sharp regression discontinuity designs. We develop a score test for the treatment significance hypothesis and Wald-type tests for the hypotheses related to treatment significance, homogeneity, and unambiguity. The bias from the nonparametric estimation is studied in detail. In particular, we show that under some conditions, the asymptotic distribution of the score test is…

高维数据下的非可分模型AI 解读

This paper studies non-separable models with a continuous treatment when the dimension of the control variables is high and potentially larger than the effective sample size. We propose a three-step estimation procedure to estimate the average, quantile, and marginal treatment effects. In the first stage we estimate the conditional mean, distribution, and density objects by penalized local least squares, penalized local maximum likelihood estimation, and numerical…

删失最小绝对偏差估计量的精确计算AI 解读

We show that exact computation of the censored least absolute deviations (CLAD) estimator proposed by Powell (1984) may be achieved by formulating the estimator as a linear Mixed Integer Programming (MIP) problem with disjunctive constraints. We apply our approach to three previously studied datasets and find that widely used approximate optimization algorithms can lead to erroneous conclusions. Extensive simulations confirm that MIP-based computation using available solvers…

随机方差的已实现经验分布函数及其拟合优度检验AI 解读

We propose a nonparametric estimator of the empirical distribution function (EDF) of the latent spot variance of the log-price of a financial asset. We show that over a fixed time span our realized EDF (or REDF) – inferred from noisy high-frequency data – is consistent as the mesh of the observation grid goes to zero. In a double-asymptotic framework, with time also increasing to infinity, the REDF converges to the cumulative distribution function of volatility, if it…

存在无关协变量时条件分位数函数的非参数估计AI 解读

Allowing for the existence of irrelevant covariates, we study the problem of estimating a conditional quantile function nonparametrically with mixed discrete and continuous data. We estimate the conditional quantile regression function using the check-function-based kernel method and suggest a data-driven cross-validation (CV) approach to simultaneously determine the optimal smoothing parameters and remove the irrelevant covariates. When the number of covariates is large, we…

异质面板中个体球形性的检验AI 解读

Summary This manuscript considers locally best invariant tests for sphericity in heterogeneous panels. A new integral representation for the characteristic function of the test statistic under the null is presented, along with an algorithm for inverting it to obtain the distribution function. A saddlepoint approximation to the null distribution addresses the need to quickly compute approximate $p$-values in empirical work. The approximation shows substantial improvements…

重新审视面板数据分位数回归的简便方法AI 解读

Summary This note discusses two errors in the approach proposed in Canay (2011) for constructing a computationally simple two-step estimator in a quantile regression model with quantile-independent fixed effects. Firstly, we show that Canay’s assumption about n/Ts → 0 for some s > 1 is not strong enough and can entail severe bias or even the non-existence of the limiting distribution for the estimator of the vector of coefficients. The condition n/T → 0 appears to be closer…

基于分位数的平滑转换风险价值估计AI 解读

Summary Value at risk models are concerned with the estimation of conditional quantiles of a time series. Formally, these quantities are a function of conditional volatility and the respective quantile of the innovation distribution. The former is often subject to asymmetric dynamic behaviour, e.g., with respect to past shocks. In this paper, we propose a model in which conditional quantiles follow a generalised autoregressive process governed by two parameter regimes with…

引导式非参数拟合优度检验及其收入分布应用AI 解读

Summary We have developed a customizable goodness-of-fit test of a parametric density based on its distance to a consistently estimated density. This consistent estimate is obtained via a nonparametric density estimator with a parametric start, wherein the start is set to be the hypothesized parametric density. To cope with the influence of nonparametric estimation bias, nonparametric goodness-of-fit tests have resorted to remedies such as undersmoothing or convolution of…

网络分位数自回归AI 解读

The complex tail dependency structure in a dynamic network with a large number of nodes is an important object to study. We propose a network quantile autoregression model (NQAR), which characterizes the dynamic quantile behavior. Our NQAR model consists of a system of equations, of which we relate a response to its connected nodes and node specific characteristics in a quantile autoregression process. We show the estimation of the NQAR model and the asymptotic properties…

Lipschitz 损失正则化方法的估计界与尖锐预言不等式AI 解读

We obtain estimation error rates and sharp oracle inequalities for regularization procedures of the form \begin{equation*}\hat{f}\in\mathop{\operatorname{argmin}}_{f\in F}\Bigg(\frac{1}{N}\sum_{i=1}^{N}\ell_{f}(X_{i},Y_{i})+\lambda \Vert f\Vert \Bigg)\end{equation*} when $\Vert \cdot \Vert $ is any norm, $F$ is a convex class of functions and $\ell$ is a Lipschitz loss function satisfying a Bernstein condition over $F$. We explore both the bounded and sub-Gaussian stochastic…

超高维稀疏数据中基于条件严格凸损失的非参数筛选AI 解读

Sure screening technique has been considered as a powerful tool to handle the ultrahigh dimensional variable selection problems, where the dimensionality $p$ and the sample size $n$ can satisfy the NP dimensionality $\log p=O(n^{a})$ for some $a>0$ [J. R. Stat. Soc. Ser. B. Stat. Methodol. 70 (2008) 849–911]. The current paper aims to simultaneously tackle the “universality” and “effectiveness” of sure screening procedures. For the “universality,” we develop a general and…

回归不连续设计中分位数处理效应的稳健一致推断AI 解读

The practical importance of inference with robustness against large bandwidths for causal effects in regression discontinuity and kink designs is widely recognized. Existing robust methods cover many cases, but do not handle uniform inference for CDF and quantile processes in fuzzy designs. In this light, this paper extends the literature by developing a unified framework of inference with robustness against large bandwidths that applies to uniform inference for quantile…

不可观测异质性与内生支出下反事实需求的界限AI 解读

We propose a method to predict rational counterfactual demand responses from repeated cross-sections. We derive bounds on the distribution of counterfactual demands that are consistent with the Weak Axiom of Revealed Preferences, without putting any restriction on the preference heterogeneity across consumers. In contrast to existing methods, we also allow for endogeneity of total expenditures. In addition, the method can readily incorporate restrictions on the income…

预期短缺与风险价值的动态半参数模型AI 解读

Expected Shortfall (ES) is the average return on a risky asset conditional on the return being below some quantile of its distribution, namely its Value-at-Risk (VaR). The Basel III Accord, which will be implemented in the years leading up to 2019, places new attention on ES, but unlike VaR, there is little existing work on modeling ES. We use recent results from statistical decision theory to overcome the problem of “elicitability” for ES by jointly modeling ES and VaR, and…

删失分位数回归的适配损失函数AI 解读

In this article, we study a novel approach for the estimation of quantiles when facing potential right censoring of the responses. Contrary to the existing literature on the subject, the adopted strategy of this article is to tackle censoring at the very level of the loss function usually employed for the computation of quantiles, the so-called “check” function. For interpretation purposes, a simple comparison with the latter reveals how censoring is accounted for in the…

自适应控制检验尺寸的分位数回归推断AI 解读

Regression quantiles have asymptotic variances that depend on the conditional densities of the response variable given regressors. This article develops a new estimate of the asymptotic variance of regression quantiles that leads any resulting Wald-type test or confidence region to behave as well in large samples as its infeasible counterpart in which the true conditional response densities are embedded. We give explicit guidance on implementing the new variance estimator to…

Extremiles：非对称最小二乘的新视角AI 解读

Quantiles and expectiles of a distribution are found to be useful descriptors of its tail in the same way as the median and mean are related to its central behavior. This article considers a valuable alternative class to expectiles, called extremiles, which parallels the class of quantiles and includes the family of expected minima and expected maxima. The new class is motivated via several angles, which reveals its specific merits and strengths. Extremiles suggest better…