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非参数回归、置信区域与正则化AI 解读

In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and nonasymptotic confidence region $\mathcal{A}_{n}$ which is defined by a set of linear inequalities involving the values of the functions at the design points. Interest will typically center on certain simplest functions in $\mathcal{A}_{n}$ where simplicity can be defined in terms of shape (number of local extremes, intervals of…

Copula 的改进核估计：弱收敛与拟合优度检验AI 解读

We reconsider the existing kernel estimators for a copula function, as proposed in Gijbels and Mielniczuk [Comm. Statist. Theory Methods 19 (1990) 445–464], Fermanian, Radulovič and Wegkamp [Bernoulli 10 (2004) 847–860] and Chen and Huang [Canad. J. Statist. 35 (2007) 265–282]. All of these estimators have as a drawback that they can suffer from a corner bias problem. A way to deal with this is to impose rather stringent conditions on the copula, outruling as such many…

聚类数据的半参数模型AI 解读

In the analysis of cluster data the regression coefficients are frequently assumed to be the same across all clusters. This hampers the ability to study the varying impacts of factors on each cluster. In this paper, a semiparametric model is introduced to account for varying impacts of factors over clusters by using cluster-level covariates. It achieves the parsimony of parametrization and allows the explorations of nonlinear interactions. The random effect in the…

样本覆盖度非参数估计量的渐近正态性AI 解读

This paper establishes a necessary and sufficient condition for the asymptotic normality of the nonparametric estimator of sample coverage proposed by Good [Biometrica 40 (1953) 237–264]. This new necessary and sufficient condition extends the validity of the asymptotic normality beyond the previously proven cases.

含缺失数据的半参数加速失效时间模型渐近理论AI 解读

We consider a class of doubly weighted rank-based estimating methods for the transformation (or accelerated failure time) model with missing data as arise, for example, in case-cohort studies. The weights considered may not be predictable as required in a martingale stochastic process formulation. We treat the general problem as a semiparametric estimating equation problem and provide proofs of asymptotic properties for the weighted estimators, with either true weights or…

通过凸规划进行非参数估计AI 解读

The problem we concentrate on is as follows: given (1) a convex compact set X in ℝn, an affine mapping x↦A(x), a parametric family {pμ(⋅)} of probability densities and (2) N i.i.d. observations of the random variable ω, distributed with the density pA(x)(⋅) for some (unknown) x∈X, estimate the value gTx of a given linear form at x. For several families {pμ(⋅)} with no additional assumptions on X and A, we develop computationally efficient estimation routines which are…

误差分布未知时的反卷积AI 解读

We consider the problem of estimating a density fX using a sample Y1, …, Yn from fY=fX⋆fε, where fε is an unknown density. We assume that an additional sample ε1, …, εm from fε is observed. Estimators of fX and its derivatives are constructed by using nonparametric estimators of fY and fε and by applying a spectral cut-off in the Fourier domain. We derive the rate of convergence of the estimators in case of a known and unknown error density fε, where it is assumed that fX…

平面变形各向同性高斯随机场的一致估计AI 解读

This paper proves fixed domain asymptotic results for estimating a smooth invertible transformation f: ℝ2→ℝ2 when observing the deformed random field Z○f on a dense grid in a bounded, simply connected domain Ω, where Z is assumed to be an isotropic Gaussian random field on ℝ2. The estimate f̂ is constructed on a simply connected domain U, such that U̅⊂Ω and is defined using kernel smoothed quadratic variations, Bergman projections and results from quasiconformal theory. We…

半参数模型失去可识别性时的渐近最优检验AI 解读

We consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models, where regularity conditions for profile likelihood theory fail. Exponential average tests based on integrated profile likelihood are constructed and shown to be asymptotically optimal under a weighted average power criterion with respect to a prior on the nonidentifiable aspect of the model. These results extend existing results for parametric models, which…

混合分布递归估计的一致性AI 解读

Mixture models have received considerable attention recently and Newton [Sankhyā Ser. A 64 (2002) 306–322] proposed a fast recursive algorithm for estimating a mixing distribution. We prove almost sure consistency of this recursive estimate in the weak topology under mild conditions on the family of densities being mixed. This recursive estimate depends on the data ordering and a permutation-invariant modification is proposed, which is an average of the original over…

利用条件矩不等式对内生删失回归模型进行推断AI 解读

Under a quantile restriction, randomly censored regression models can be written in terms of conditional moment inequalities. We study the identified features of these moment inequalities with respect to the regression parameters where we allow for covariate dependent censoring, endogenous censoring and endogenous regressors. These inequalities restrict the parameters to a set. We show regular point identification can be achieved under a set of interpretable sufficient…

函数系数协整模型AI 解读

This paper studies estimation and inference of functional coefficient cointegration models. The proposed model offers a more flexible structure of cointegration where the value of cointegrating coefficients may be affected by informative covariates and thus may vary over time. The model may be viewed as a stochastic cointegration model and includes the conventional cointegration model as a special case. The proposed new model provides a useful complement to the conventional…

含内生解释变量的参数分位数回归模型检验AI 解读

This paper is concerned with inference about a function g that is identified by a conditional quantile restriction involving instrumental variables. The paper presents a test of the hypothesis that g belongs to a finite-dimensional parametric family against a nonparametric alternative. The test is not subject to the ill-posed inverse problem of nonparametric instrumental variable estimation. Under mild conditions, the test is consistent against any alternative model. In…

分位数、期望分位数与样条AI 解读

A time-varying quantile can be fitted by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. It is shown that such quantiles satisfy the defining property of fixed quantiles in having the appropriate number of observations above and below. Like quantiles, time-varying expectiles can be estimated by a state space signal extraction algorithm and they satisfy properties…

第一价格拍卖中的进入与竞争效应：采购拍卖的理论和证据AI 解读

Motivated by several interesting features of the highway mowing auction data from the Texas Department of Transportation (TDoT), we study three competing procurement auction models with endogenous entry. Our entry and bidding models provide several interesting implications. For the first time, we show that even within an independent private value paradigm, as the number of potential bidders increases, bidders' equilibrium bidding behaviour can become less aggressive, and the…

异质依赖数据下核估计量的一致收敛速度AI 解读

The main uniform convergence results of Hansen (2008, Econometric Theory 24, 726–748) are generalized in two directions: Data are allowed to (a) be heterogeneously dependent and (b) depend on a (possibly unbounded) parameter. These results are useful in semiparametric estimation problems involving time-inhomogeneous models and/or sampling of continuous-time processes. The usefulness of these results is demonstrated by two applications: kernel regression estimation of a…

高效半参数似不相关分位数回归估计AI 解读

We propose an efficient semiparametric estimator for the coefficients of a multivariate linear regression model—with a conditional quantile restriction for each equation—in which the conditional distributions of errors given regressors are unknown. The procedure can be used to estimate multiple conditional quantiles of the same regression relationship. The proposed estimator is asymptotically as efficient as if the true optimal instruments were known. Simulation results…

生产前沿的偏差修正非参数包络估计量AI 解读

In efficiency analysis, the production frontier is defined as the set of the most efficient alternatives among all possible combinations in the input-output space. The nonparametric envelopment estimators rely on the assumption that all the observations fall on the same side of the frontier. The free disposal hull (FDH) estimator of the attainable set is the smallest free disposal set covering all the observations. By construction, the FDH estimator is an inward-biased…

泛函在双样本调查线性化与复合估计中的应用AI 解读

An important problem associated with two-sample surveys is the estimation of nonlinear functions of finite population totals such as ratios, correlation coefficients or measures of income inequality. Computation and estimation of the variance of such complex statistics are made more difficult by the existence of overlapping units. In one-sample surveys, the linearization method based on the influence function approach is a powerful tool for variance estimation. We introduce…

惩罚样条估计量的渐近性质AI 解读

We study the class of penalized spline estimators, which enjoy similarities to both regression splines, without penalty and with fewer knots than data points, and smoothing splines, with knots equal to the data points and a penalty controlling the roughness of the fit. Depending on the number of knots, sample size and penalty, we show that the theoretical properties of penalized regression spline estimators are either similar to those of regression splines or to those of…

半参数变换模型中的加权 Breslow 型估计与最大似然估计AI 解读

A semiparametric transformation model comprises a parametric component for covariate effects and a nonparametric component for the baseline hazard/intensity. The Breslow-type estimator has been proposed for estimating the nonparametric component in some inefficient estimation procedures. We show that introducing weights into this estimator leads to nonparametric maximum likelihood estimation, with the weights depending on the martingale residuals. The weighted Breslow-type…

加性风险回归模型的经验贝叶斯估计AI 解读

We develop a novel empirical Bayesian framework for the semiparametric additive hazards regression model. The integrated likelihood, obtained by integration over the unknown prior of the nonparametric baseline cumulative hazard, can be maximized using standard statistical software. Unlike the corresponding full Bayes method, our empirical Bayes estimators of regression parameters, survival curves and their corresponding standard errors have easily computed closed-form…

半参数加速失效时间模型的诱导平滑：渐近理论与聚类数据扩展AI 解读

This paper extends the induced smoothing procedure of Brown & Wang (2006) for the semiparametric accelerated failure time model to the case of clustered failure time data. The resulting procedure permits fast and accurate computation of regression parameter estimates and standard errors using simple and widely available numerical methods, such as the Newton-Raphson algorithm. The regression parameter estimates are shown to be strongly consistent and asymptotically normal; in…

分布性及一般处理效应的半参数估计与推断AI 解读

Summary There is a large literature on methods of analysis for randomized trials with noncompliance which focuses on the effect of treatment on the average outcome. The paper considers evaluating the effect of treatment on the entire distribution and general functions of this effect. For distributional treatment effects, fully non-parametric and fully parametric approaches have been proposed. The fully non-parametric approach could be inefficient but the fully parametric…