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基于指数平方损失的稳健变量选择AI 解读

Robust variable selection procedures through penalized regression have been gaining increased attention in the literature. They can be used to perform variable selection and are expected to yield robust estimates. However, to the best of our knowledge, the robustness of those penalized regression procedures has not been well characterized. In this paper, we propose a class of penalized robust regression estimators based on exponential squared loss. The motivation for this…

具有预言效率的广义可加模型两步估计AI 解读

The generalized additive model (GAM) is a multivariate nonparametric regression tool for non-Gaussian responses including binary and count data. We propose a spline-backfitted kernel (SBK) estimator for the component functions and the constant, which are oracally efficient under weak dependence. The SBK technique is both computationally expedient and theoretically reliable, thus usable for analyzing high-dimensional time series. Inference can be made on component functions…

混合数据的贝叶斯高斯 Copula 因子模型AI 解读

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the…

含单整协变量的半参数函数系数模型AI 解读

Abstract Cai, Li, and Park ( Journal of Econometrics , 2009) and Xiao ( Journal of Econometrics , 2009) developed asymptotic theories for estimators of semiparametric varying coefficient models when regressors are integrated processes but the smooth coefficients are functionals of stationary processes. Using a recent result from Phillips ( Econometric Theory , 2009), we extend this line of research by allowing for both the regressors and the covariates entering the smooth…

预测者偏好的可恢复性AI 解读

We study the problem of identifying a forecaster’s loss function from observations on forecasts, realizations, and the forecaster’s information set. Essentially different loss functions can lead to the same forecasts in all situations, though within the class of all continuous loss functions, this is strongly nongeneric. With the small set of exceptional cases ruled out, generic nonparametric preference recovery is theoretically possible, but identification depends…

Phillips–Perron 单位根检验的 fixed-b 视角AI 解读

In this paper we extend fixed- b asymptotic theory to the nonparametric Phillips–Perron (PP) unit root tests. We show that the fixed- b limits depend on nuisance parameters in a complicated way. These nonpivotal limits provide an alternative theoretical explanation for the well-known finite-sample problems of the PP tests. We also show that the fixed- b limits depend on whether deterministic trends are removed using one-step or two-step detrending approaches. This is in…

分类响应条件密度的平滑非参数检验AI 解读

We propose a consistent kernel-based specification test for conditional density models when the dependent variable is categorical/discrete. The method is applicable to popular parametric binary choice models such as the logit and probit specification and their multinomial and ordered counterparts, along with parametric count models, among others. The test is valid when the conditional density function contains both categorical and real-valued covariates. Theoretical support…

类别型半参数变系数模型AI 解读

SUMMARY Semiparametric varying‐coefficient models have become a common fixture in applied data analysis. Existing approaches, however, presume that those variables affecting the coefficients are continuous in nature (or that there exists at least one such continuous variable) which is often not the case. Furthermore, when all variables affecting the coefficients are categorical/discrete, theoretical underpinnings cannot be obtained as a special case of existing approaches…

上确界范数损失下的多元密度估计：Oracle 方法、自适应与独立结构AI 解读

This paper deals with the density estimation on $\mathbb{R}^{d}$ under sup-norm loss. We provide a fully data-driven estimation procedure and establish for it a so-called sup-norm oracle inequality. The proposed estimator allows us to take into account not only approximation properties of the underlying density, but eventual independence structure as well. Our results contain, as a particular case, the complete solution of the bandwidth selection problem in the multivariate…

可逆马尔可夫链的贝叶斯非参数分析AI 解读

We introduce a three-parameter random walk with reinforcement, called the $(\theta,\alpha,\beta)$ scheme, which generalizes the linearly edge reinforced random walk to uncountable spaces. The parameter $\beta$ smoothly tunes the $(\theta,\alpha,\beta)$ scheme between this edge reinforced random walk and the classical exchangeable two-parameter Hoppe urn scheme, while the parameters $\alpha$ and $\theta$ modulate how many states are typically visited. Resorting to de…

样本覆盖率非参数估计量的中偏差理论AI 解读

In this paper, we consider moderate deviations for Good’s coverage estimator. The moderate deviation principle and the self-normalized moderate deviation principle for Good’s coverage estimator are established. The results are also applied to the hypothesis testing problem and the confidence interval for the coverage.

图上光滑核的低秩估计AI 解读

Let $(V,A)$ be a weighted graph with a finite vertex set $V$, with a symmetric matrix of nonnegative weights $A$ and with Laplacian $\Delta$. Let $S_{\ast}: V\times V\mapsto{\mathbb{R}}$ be a symmetric kernel defined on the vertex set $V$. Consider $n$ i.i.d. observations $(X_{j},X_{j}',Y_{j})$, $j=1,\ldots,n$, where $X_{j}$, $X_{j}'$ are independent random vertices sampled from the uniform distribution in $V$ and $Y_{j}\in{\mathbb{R}}$ is a real valued response variable…

函数空间中平稳时间序列的傅里叶分析AI 解读

We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density operator, which generalises the notion of a spectral density matrix to the functional setting, and characterises the second-order dynamics of the process. Our main tool is the functional Discrete Fourier Transform (fDFT). We derive an…

We consider a multi-armed bandit problem in a setting where each arm produces a noisy reward realization which depends on an observable random covariate. As opposed to the traditional static multi-armed bandit problem, this setting allows for dynamically changing rewards that better describe applications where side information is available. We adopt a nonparametric model where the expected rewards are smooth functions of the covariate and where the hardness of the problem is…

层级阿基米德 Copula 的结构与估计AI 解读

In this paper we provide a method for estimating multivariate distributions defined through hierarchical Archimedean copulas. In general, the true structure of the hierarchy is unknown, but we develop a computationally efficient technique to determine it from the data. For this purpose we introduce a hierarchical estimation procedure for the parameters and provide an asymptotic analysis. We consider both parametric and nonparametric estimation of the marginal distributions.…

非对称信息的非参数检验AI 解读

Asymmetric information is an important phenomenon in many markets and in particular in insurance markets. Testing for asymmetric information has become a very important issue in the literature in the last two decades. Almost all testing procedures that are used in empirical studies are parametric, which may yield misleading conclusions in the case of misspecification of either functional or distributional relationships among the variables of interest. Motivated by the…

噪声与跳跃下二次变差的预平均估计：理论、实现与经验证据AI 解读

This article contributes to the theory for preaveraging estimators of the daily quadratic variation of asset prices and provides novel empirical evidence. We develop asymptotic theory for preaveraging estimators in the case of autocorrelated microstructure noise and propose an explicit test for serial dependence. Moreover, we extend the theory on preaveraging estimators for processes involving jumps. We discuss several jump-robust measures and derive feasible central limit…

函数系数工具变量模型的局部线性 GMM 估计及教育回报应用AI 解读

We consider the local linear generalized method of moment (GMM) estimation of functional coefficient models with a mix of discrete and continuous data and in the presence of endogenous regressors. We establish the asymptotic normality of the estimator and derive the optimal instrumental variable that minimizes the asymptotic variance-covariance matrix among the class of all local linear GMM estimators. Data-dependent bandwidth sequences are also allowed for. We propose a…

含二元内生变量的线性指数二元选择模型估计AI 解读

This paper presents computationally simple estimators for the index coefficients in a binary choice model with a binary endogenous regressor without relying on distributional assumptions or on large support conditions and yields root- n consistent and asymptotically normal estimators. We develop a multistep method for estimating the parameters in a triangular, linear index, threshold-crossing model with two equations. Such an econometric model might be used in testing for…

二元响应半参数结构模型：形状限制与部分识别AI 解读

I study the partial identifying power of structural single-equation threshold-crossing models for binary responses when explanatory variables may be endogenous. The sharp identified set of threshold functions is derived for the case in which explanatory variables are discrete, and I provide a constructive proof of sharpness. There is special attention to a widely employed semiparametric shape restriction, which requires the threshold-crossing function to be a monotone…

大规模数据的高效高斯过程回归AI 解读

Gaussian processes are widely used in nonparametric regression, classification and spatiotemporal modelling, facilitated in part by a rich literature on their theoretical properties. However, one of their practical limitations is expensive computation, typically on the order of n3 where n is the number of data points, in performing the necessary matrix inversions. For large datasets, storage and processing also lead to computational bottlenecks, and numerical stability of…

用于同时协方差估计的非参数先验AI 解读

In the modeling of longitudinal data from several groups, appropriate handling of the dependence structure is of central importance. Standard methods include specifying a single covariance matrix for all groups or independently estimating the covariance matrix for each group without regard to the others, but when these model assumptions are incorrect, these techniques can lead to biased mean effects or loss of efficiency, respectively. Thus, it is desirable to develop…

竞争风险当前状态数据的平滑非参数估计AI 解读

We study the nonparametric estimation of the cumulative incidence function and the cause-specific hazard function for current status data with competing risks via kernel smoothing. A smoothed naive nonparametric maximum likelihood estimator and a smoothed full nonparametric maximum likelihood estimator are shown to have pointwise asymptotic normality and faster convergence rates than the corresponding unsmoothed nonparametric likelihood estimators. Using the smoothed…

稀疏与密集纵向模型的统一推断AI 解读

In longitudinal data analysis, statistical inference for sparse data and dense data could be substantially different. For kernel smoothing estimate of the mean function, the convergence rates and limiting variance functions are different under the two scenarios. The latter phenomenon poses challenges for statistical inference as a subjective choice between the sparse and dense cases may lead to wrong conclusions. We develop self-normalization based methods that can adapt to…