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样条估计量的统一框架AI 解读

This article develops a unified framework to study the asymptotic properties of all periodic spline-based estimators, that is, of regression, penalized and smoothing splines. The explicit form of the periodic Demmler–Reinsch basis in terms of exponential splines allows the derivation of an expression for the asymptotic equivalent kernel on the real line for all spline estimators simultaneously. The corresponding bandwidth, which drives the asymptotic behaviour of spline…

经验贝叶斯反卷积估计AI 解读

An unknown prior density $g(\\theta )$ has yielded realizations $\\Theta _1,\\ldots ,\\Theta _N$ . They are unobservable, but each $\\Theta _i$ produces an observable value $X_i$ according to a known probability mechanism, such as $X_i\\sim {\\rm Po}(\\Theta _i)$ . We wish to estimate $g(\\theta )$ from the observed sample $X_1,\\ldots ,X_N$ . Traditional asymptotic calculations are discouraging, indicating very slow nonparametric rates of convergence. In this article we…

二维流形上的空间回归模型AI 解读

We propose a regression model for data spatially distributed over general two-dimensional Riemannian manifolds. This is a generalized additive model with a roughness penalty term involving a differential operator computed over the non-planar domain. By virtue of a semiparametric framework, the model allows inclusion of space-varying covariate information. Estimation can be performed by conformally parameterizing the non-planar domain and then generalizing existing models for…

基于非参数经验贝叶斯与极大似然推断的高维分类AI 解读

We propose new nonparametric empirical Bayes methods for high-dimensional classification. Our classifiers are designed to approximate the Bayes classifier in a hypothesized hierarchical model, where the prior distributions for the model parameters are estimated nonparametrically from the training data. As is common with nonparametric empirical Bayes, the proposed classifiers are effective in high-dimensional settings even when the underlying model parameters are in fact…

含检测限协变量的回归半参数方法AI 解读

We consider generalized linear regression with a covariate left-censored at a lower detection limit. Complete-case analysis, where observations with values below the limit are eliminated, yields valid estimates for regression coefficients but loses efficiency, ad hoc substitution methods are biased, and parametric maximum likelihood estimation relies on parametric models for the unobservable tail probability distribution and may suffer from model misspecification. To obtain…

条件独立性的非参数贝叶斯推断AI 解读

In many application areas, a primary focus is on assessing evidence in the data refuting the assumption of independence of |$Y$| and |$X$| conditionally on |$Z$|⁠, with |$Y$| response variables, |$X$| predictors of interest, and |$Z$| covariates. Ideally, one would have methods available that avoid parametric assumptions, allow |$Y, X, Z$| to be random variables on arbitrary spaces with arbitrary dimension, and accommodate rapid consideration of different candidate…

识别消费变动的独立来源AI 解读

Summary By representing a system of budget shares as an approximate factor model we determine its rank, i.e. the number of common functional forms or factors, and we estimate a base of the factor space by means of approximate principal components. We assume that the extracted factors span the same space of basic Engel curves representing the fundamental forces driving consumers' behaviour. We identify these curves by imposing statistical independence and by studying their…

定价核单调性的实证检验AI 解读

Summary A large class of asset pricing models predicts that securities which have high payoffs when market returns are low tend to be more valuable than those with high payoffs when market returns are high. More generally, we expect the projection of the stochastic discount factor on the market portfolio—that is, the discounted pricing kernel evaluated at the market portfolio—to be a monotonically decreasing function of the market portfolio. Numerous recent empirical studies…

有界回归变量博弈模型的经验内容AI 解读

This paper develops a strategy for identification and estimation of complete information games that does not require a regressor that has large support or a parametric specification for the distribution of the unobservables. The identification result uses a nonstandard but plausible condition on the unobservables: the assumption that the joint density of the unobservables of all agents is unimodal in the sense of achieving the global maximum at a unique point. Also, a…

超高维部分线性可加分位数回归AI 解读

We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete picture of the conditional distribution of a response variable given high dimensional covariates. (2) The sparsity level is allowed to be different at different quantile levels. (3) The partially linear additive structure accommodates…

因子模型中的投影主成分分析AI 解读

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employees principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to high-dimensional factor analysis, the projection removes noise components. We show that the unobserved latent factors can be more accurately estimated than the conventional PCA if the projection is genuine, or more precisely, when the factor…

低密度区域的自适应估计及其支撑恢复应用AI 解读

A scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a Hölder continuous density, this locally minimax-optimal bandwidth is shown to be smaller than the usual rate, even in case of homogeneous smoothness. Some new type of risk bound with respect to a density-dependent standardized loss of this…

广义误差独立性的非参数自助检验AI 解读

In this paper, we develop a general method of testing for independence when unobservable generalized errors are involved. Our method can be applied to testing for serial independence of generalized errors, and testing for independence between the generalized errors and observable covariates. The former can serve as a unified approach to testing the adequacy of time series models, as model adequacy often implies that the generalized errors obtained after a suitable…

极值估计量拟似然比检验的非参数自助法渐近改进AI 解读

We study the asymptotic refinements of nonparametric bootstrap for quasi‐likelihood ratio type tests of nonlinear restrictions. The bootstrap method applies to extremum estimators, such as quasi‐maximum likelihood and generalized method of moments estimators, among others. Unlike existing parametric bootstrap procedures for quasi‐likelihood ratio type tests, this bootstrap approach does not require any specific parametric assumption on the data distribution, and constructs…

效率前沿的非参数工具变量估计AI 解读

The paper investigates endogeneity issues in nonparametric frontier models. It considers a nonseparable model for a cost function C=φ(Y,U) where C and Y are the cost and the output, U is uniform in [0,1] and φ is increasing with respect to U. The cost frontier corresponds to U=0 and U can be interpreted as a normalized level of inefficiency. The endogeneity issue arises when Y is dependent of U. For identification and estimation, we use a nonparametric instrumental variables…

非参数前沿估计中的不可观测异质性与内生性AI 解读

In production theory, firm efficiencies are measured by their distances to a production frontier. In the presence of heterogeneous conditions (like environmental factors) that may influence the shape and the position of the frontier, traditional measures of efficiency obtained in the space of inputs/outputs are difficult to interpret, since they mix managerial inefficiency and shift of the frontier. This can be corrected by using nonparametric conditional efficiencies. In…

存在内生选择与固定效应的变系数面板模型AI 解读

This paper considers a flexible panel data sample selection model in which (i) the outcome equation is permitted to take a semiparametric, varying coefficient form to capture potential parameter heterogeneity in the relationship of interest, (ii) both the outcome and (parametric) selection equations contain unobserved fixed effects and (iii) selection is generalized to a polychotomous case. We propose a two-stage estimator. Given consistent parameter estimates from the…

空间依赖稳健非参数协方差矩阵估计的 fixed-b 渐近理论AI 解读

This paper develops a method for performing inference using spatially dependent data. We consider test statistics formed using nonparametric covariance matrix estimators that account for heteroskedasticity and spatial correlation (spatial HAC). We provide distributions of commonly used test statistics under “fixed- b ” asymptotics, in which HAC smoothing parameters are proportional to the sample size. Under this sequence, spatial HAC estimators are not consistent but…

尾部风险度量的无模型推断AI 解读

Understanding uncertainty in estimating risk measures is important in modern financial risk management. In this paper we consider a nonparametric framework that incorporates auxiliary information available in covariates and propose a family of inferential methods for the value at risk, expected shortfall, and related risk measures. A two-step generalized empirical likelihood test statistic is constructed and is shown to be asymptotically pivotal without requiring variance…

非平稳数据的非参数变换回归AI 解读

We examine a kernel regression estimator for time series that takes account of the error correlation structure as proposed by Xiao et al. (2003, Journal of the American Statistical Association 98, 980–992). We show that this method continues to improve estimation in the case where the regressor is a unit root or a near unit root process.

利用外部大数据汇总信息校准模型的约束最大似然估计AI 解读

Information from various public and private data sources of extremely large sample sizes are now increasingly available for research purposes. Statistical methods are needed for utilizing information from such big data sources while analyzing data from individual studies that may collect more detailed information required for addressing specific hypotheses of interest. In this article, we consider the problem of building regression models based on individual-level data from…

动态神经影像数据反卷积的函数型方法AI 解读

Positron emission tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are currently analyzed based on the assumption that linear first-order kinetics can be used to adequately describe the system under observation. However, there has recently been strong evidence that this is not the case. To provide an analysis of PET data which…

多个二元密度函数的联合估计及其在蛋白质环建模中的应用AI 解读

This article develops a method for simultaneous estimation of density functions for a collection of populations of protein backbone angle pairs using a data-driven, shared basis that is constructed by bivariate spline functions defined on a triangulation of the bivariate domain. The circular nature of angular data is taken into account by imposing appropriate smoothness constraints across boundaries of the triangles. Maximum penalized likelihood is used to fit the model and…

分位数回归中变系数的估计与检验AI 解读

In this article, we establish a novel connection between the null hypothesis H0 on the coefficients and a rank-reducible form of the varying coefficient model in quantile regression. We use B-splines to approximate the varying coefficients in the rank-reducible model, and make use of the fact that the null hypothesis H0 implies a unidimensional structure of a transformed coefficient matrix for the B-spline basis functions. By evaluating the unidimensional structure, we…