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反卷积密度估计中的参数辅助非参数方法AI 解读

Nonparametric estimation of a density from contaminated data is a difficult problem, for which convergence rates are notoriously slow. We introduce parametrically assisted nonparametric estimators which can dramatically improve on the performance of standard nonparametric estimators when the assumed model is close to the true density, without degrading much the quality of purely nonparametric estimators in other cases. We establish optimal convergence rates for our problem…

高斯过程混合模型的核平滑估计AI 解读

When the functional data are not homogeneous, e.g., there exist multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this paper, we propose a new estimation procedure for the Mixture of Gaussian Processes, to incorporate both functional and inhomogeneous properties of the data. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed…

一种半参数空间动态模型AI 解读

Stimulated by the Boston house price data, in this paper, we propose a semiparametric spatial dynamic model, which extends the ordinary spatial autoregressive models to accommodate the effects of some covariates associated with the house price. A profile likelihood based estimation procedure is proposed. The asymptotic normality of the proposed estimators are derived. We also investigate how to identify the parametric/nonparametric components in the proposed semiparametric…

自回归误差分布的预言效率估计与同时置信带AI 解读

We propose kernel estimator for the distribution function of unobserved errors in autoregressive time series, based on residuals computed by estimating the autoregressive coefficients with the Yule–Walker method. Under mild assumptions, we establish oracle efficiency of the proposed estimator, that is, it is asymptotically as efficient as the kernel estimator of the distribution function based on the unobserved error sequence itself. Applying the result of Wang, Cheng and…

协变量维数增长时相关数据的广义可加部分线性模型估计与选择AI 解读

We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases statistical power for correlated data through incorporating the correlation information. A unique feature of the proposed method is its capability of handling model selection in cases where it is difficult to specify the likelihood…

非参数回归中基于平方根 Lasso 的枢轴估计AI 解读

We propose a self-tuning $\sqrt{\mathrm {Lasso}} $ method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic) non-Gaussianity of the noise. In addition, our analysis allows for badly behaved designs, for example, perfectly collinear regressors, and generates sharp bounds even in extreme cases, such as the infinite variance case and the noiseless case, in…

利用显示偏好不等式界定分位数需求函数AI 解读

This paper develops a new approach to the estimation of consumer demand models with unobserved heterogeneity subject to revealed preference inequality restrictions. Particular attention is given to nonseparable heterogeneity. The inequality restrictions are used to identify bounds on counterfactual demand. A nonparametric estimator for these bounds is developed and asymptotic properties are derived. An empirical application using data from the UK Family Expenditure Survey…

参数与半参数模型的快速重抽样方法AI 解读

We propose a fast resample method for two step nonlinear parametric and semiparametric models, which does not require recomputation of the second stage estimator during each resample iteration. The fast resample method directly exploits the score function representations computed on each bootstrap sample, thereby reducing computational time considerably. This method is used to approximate the limit distribution of parametric and semiparametric estimators, possibly simulation…

固定效应面板似不相关部分线性回归的渐近理论AI 解读

This paper deals with statistical inference for the fixed effects panel data seemingly unrelated partially linear regression model. The model naturally extends the traditional fixed effects panel data regression model to allow for semiparametric effects. Multiple regression equations are permitted, and the model includes the aggregated partially linear model as a special case. A weighted profile least squares estimator for the parametric components is proposed and shown to…

GMM 的渐近效率AI 解读

The efficiency of the generalized method of moment (GMM) estimator is addressed by using a characterization of its variance as an inner product in a reproducing kernel Hilbert space. We show that the GMM estimator is asymptotically as efficient as the maximum likelihood estimator if and only if the true score belongs to the closure of the linear space spanned by the moment conditions. This result generalizes former ones to autocorrelated moments and possibly infinite number…

基于联合加性模型的图估计AI 解读

In recent years, there has been considerable interest in estimating conditional independence graphs in high dimensions. Most previous work has assumed that the variables are multivariate Gaussian, or that the conditional means of the variables are linear; in fact, these two assumptions are nearly equivalent. Unfortunately, if these assumptions are violated, the resulting conditional independence estimates can be inaccurate. We propose a semi-parametric method, graph…

预调整的条件分布函数非参数估计AI 解读

Summary The paper deals with non-parametric estimation of a conditional distribution function. We suggest a method of preadjusting the original observations non-parametrically through location and scale, to reduce the bias of the estimator. We derive the asymptotic properties of the estimator proposed. A simulation study investigating the finite sample performances of the estimators discussed is provided and reveals the gain that can be achieved. It is also shown how the…

随机时变系数模型的统计推断AI 解读

Recently, there has been considerable work on stochastic time-varying coefficient models as vehicles for modelling structural change in the macroeconomy with a focus on the estimation of the unobserved paths of random coefficient processes. The dominant estimation methods, in this context, are based on various filters, such as the Kalman filter, that are applicable when the models are cast in state space representations. This paper introduces a new class of autoregressive…

基于条件矩不等式的非参数推断AI 解读

This paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and/or equalities. The parameters need not be identified. Confidence sets and tests are introduced. The correct uniform asymptotic size of these procedures is established. The false coverage probabilities and power of the CS’s and tests are established for fixed alternatives and some local alternatives. Finite-sample simulation results are given…

存在平滑趋势时周期序列的非参数估计AI 解读

We investigate a nonparametric regression model including a periodic component, a smooth trend function, and a stochastic error term. We propose a procedure to estimate the unknown period and the function values of the periodic component as well as the nonparametric trend function. The theoretical part of the paper establishes the asymptotic properties of our estimators. In particular, we show that our estimator of the period is consistent. In addition, we derive the…

SUMMARY crs is a library for R written by Jeffrey S. Racine (Maintainer) and Zhenghua Nie. This add‐on package provides a collection of functions for spline‐based nonparametric estimation of regression functions with both continuous and categorical regressors. Currently, the crs package integrates data‐driven methods for selecting the spline degree, the number of knots and the necessary bandwidths for nonparametric conditional mean, IV and quantile regression. A function for…

互补性与同类匹配的总体影响：非参数分析AI 解读

This paper presents econometric methods for measuring the average output effect of reallocating an indivisible input across production units. A distinctive feature of reallocations is that, by definition, they involve no augmentation of resources and, as such, leave the marginal distribution of the reallocated input unchanged. Nevertheless, if the production technology is nonseparable, they may alter average output. An example is the reallocation of teachers across…

针对目标统计泛函的有效降维AI 解读

We introduce a new sufficient dimension reduction framework that targets a statistical functional of interest, and propose an efficient estimator for the semiparametric estimation problems of this type. The statistical functional covers a wide range of applications, such as conditional mean, conditional variance and conditional quantile. We derive the general forms of the efficient score and efficient information as well as their specific forms for three important…

利用多带宽 Gaussian 过程估计各向异性函数AI 解读

In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on defining a Bayesian procedure that leads to the minimax optimal rate of posterior contraction (up to a log factor) adapting to the unknown dimension and anisotropic smoothness of the true surface. We propose such an approach based on a…

通过趋势滤波进行自适应分段多项式估计AI 解读

We study trend filtering, a recently proposed tool of Kim et al. [SIAM Rev. 51 (2009) 339–360] for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the penalty term sums the absolute $k$th order discrete derivatives over the input points. Perhaps not surprisingly, trend filtering estimates appear to have the structure of $k$th degree spline functions, with adaptively chosen knot points (we say…

非平稳时间序列加权V统计量的推断及应用AI 解读

We investigate the behavior of Fourier transforms for a wide class of nonstationary nonlinear processes. Asymptotic central and noncentral limit theorems are established for a class of nondegenerate and degenerate weighted $V$-statistics through the angle of Fourier analysis. The established theory for $V$-statistics provides a unified treatment for many important time and spectral domain problems in the analysis of nonstationary time series, ranging from nonparametric…

分别可交换网络数据的协同聚类AI 解读

This article establishes the performance of stochastic blockmodels in addressing the co-clustering problem of partitioning a binary array into subsets, assuming only that the data are generated by a nonparametric process satisfying the condition of separate exchangeability. We provide oracle inequalities with rate of convergence $\mathcal{O}_{P}(n^{-1/4})$ corresponding to profile likelihood maximization and mean-square error minimization, and show that the blockmodel can be…

单指标约束回归模型中的自适应估计AI 解读

The problem of adaptive multivariate function estimation in the single-index regression model with random design and weak assumptions on the noise is investigated. A novel estimation procedure that adapts simultaneously to the unknown index vector and the smoothness of the link function by selecting from a family of specific kernel estimators is proposed. We establish a pointwise oracle inequality which, in its turn, is used to judge the quality of estimating the entire…

This paper is concerned with parameter estimation and inference in a cointegrating regression, where as usual endogenous regressors as well as serially correlated errors are considered. We propose a simple, new estimation method based on an augmented partial sum (integration) transformation of the regression model. The new estimator is labeled integrated modified ordinary least squares (IM-OLS). IM-OLS is similar in spirit to the fully modified OLS approach of Phillips and…