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非参数删失分位数回归的一致 Bahadur 表示：质量再分配方法AI 解读

Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of “redistribution-of-mass” in Efron (1967, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability , vol. 4, pp. 831–853, University of California Press) has better numerical performance than other available methods. In this paper, this idea is combined with the local…

工具变量分位数回归的平滑估计方程AI 解读

The moment conditions or estimating equations for instrumental variables quantile regression involve the discontinuous indicator function. We instead use smoothed estimating equations (SEE), with bandwidth h . We show that the mean squared error (MSE) of the vector of the SEE is minimized for some h > 0, leading to smaller asymptotic MSE of the estimating equations and associated parameter estimators. The same MSE-optimal h also minimizes the higher-order type I error of a…

长期依赖下含近单位根解释变量的非参数回归AI 解读

We study the nonparametric estimation of a regression function with nonstationary (integrated or nearly integrated) covariates and the error series of the regressor process following a fractional integrated autoregressive moving average model. A local linear estimation method is developed to estimate the unknown regression function. The asymptotic results of the resulting estimator at both interior points and boundaries are obtained. The asymptotic distribution is mixed…

基于时域数据的拉普拉斯反卷积及其动态对比增强成像应用AI 解读

Summary We consider the problem of Laplace deconvolution with noisy discrete non-equally spaced observations on a finite time interval. We propose a new method for Laplace deconvolution which is based on expansions of the convolution kernel, the unknown function and the observed signal over a Laguerre functions basis (which acts as a surrogate eigenfunction basis of the Laplace convolution operator) using a regression setting. The expansion results in a small system of…

部分识别半参数条件矩模型的统计推断AI 解读

This paper develops inference methods for conditional moment models in which the unknown parameter is possibly partially identified and may contain infinite-dimensional components. For a conjectured restriction on the parameter, we consider testing the hypothesis that the restriction is satisfied by at least one element of the identified set. We propose using the sieve minimum of a Kolmogorov–Smirnov type statistic as the test statistic, derive its asymptotic distribution,…

协整模型中平滑结构变化的估计AI 解读

This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time, and considers time-varying coefficient functions estimated by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional coefficients are multivariate. The reason for this breakdown is a kernel-induced degeneracy in the weighted signal matrix associated with the…

单调性约束下的非参数工具变量估计AI 解读

The ill-posedness of the inverse problem of recovering a regression function in a nonparametric instrumental variable (NPIV) model leads to estimators that may suffer from poor statistical performance.In this paper, we explore the possibility of imposing shape restrictions to improve the performance of the NPIV estimators.We assume that the regression function is monotone and consider sieve estimators that enforce the monotonicity constraint.We define a restricted measure of…

若干弱可识别有限混合模型的参数估计收敛速率AI 解读

We establish minimax lower bounds and maximum likelihood convergence rates of parameter estimation for mean-covariance multivariate Gaussian mixtures, shape-rate Gamma mixtures and some variants of finite mixture models, including the setting where the number of mixing components is bounded but unknown. These models belong to what we call “weakly identifiable” classes, which exhibit specific interactions among mixing parameters driven by the algebraic structures of the class…

利用局部线性生存密度进行样本内预测AI 解读

In this paper, in-sample forecasting is defined as forecasting a structured density to sets where it is unobserved. The structured density consists of one-dimensional in-sample components that identify the density on such sets. We focus on the multiplicative density structure, which has recently been seen as the underlying structure of non-life insurance forecasts. In non-life insurance, the in-sample area is defined as one triangle and the forecasting area as the triangle…

灵活的非参数条件独立检验AI 解读

This paper proposes a nonparametric test for conditional independence that is easy to implement, yet powerful in the sense that it is consistent and achieves n −1/2 local power. The test statistic is based on an estimator of the topological “distance” between restricted and unrestricted probability measures corresponding to conditional independence or its absence. The distance is evaluated using a family of Generically Comprehensively Revealing (GCR) functions, such as the…

具有非参数空间权重的函数系数空间自回归模型AI 解读

We apply local linear regression and sieve estimation technique to estimate functional coefficients and an unknown spatial weighting function, respectively, via a nonparametric GMM estimation method, where we allow both exogenous and endogenous spatial covariates. A consistency result is derived to support the method. Moreover, a two-step estimator is constructed for the functional coefficients, and under certain conditions, we show that this estimator can be oracle…

非线性Granger因果关系：多变量分析指南AI 解读

Summary We propose an extension of the bivariate nonparametric Diks–Panchenko Granger non‐causality test to multivariate settings. We first show that the asymptotic theory for the bivariate test fails to apply to the multivariate case, because the kernel density estimator bias and variance cannot both tend to zero at a sufficiently fast rate. To overcome this difficulty we propose to reduce the order of the bias by applying data sharpening prior to calculating the test…

一般平滑模型的平滑参数与模型选择AI 解读

This article discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be present. By construction the method is numerically stable and convergent, and enables smoothing parameter uncertainty to be quantified. The latter enables us to fix a well known problem with AIC for such models, thereby improving the range of…

温度风险的局部建模AI 解读

On the temperature derivative market, modeling temperature volatility is an important issue for pricing and hedging. To apply the pricing tools of financial mathematics, one needs to isolate a Gaussian risk factor. A conventional model for temperature dynamics is a stochastic model with seasonality and intertemporal autocorrelation. Empirical work based on seasonality and autocorrelation correction reveals that the obtained residuals are heteroscedastic with a periodic…

用局部近似加速计算密集模型的渐近精确 MCMCAI 解读

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis–Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into…

Peter Hall 对非参数函数估计与建模的贡献AI 解读

Peter Hall made wide-ranging and far-reaching contributions to nonparametric modeling. He was one of the leading figures in the developments of nonparametric techniques with over 300 published papers in the field alone. This article gives a selective overview on the contributions of Peter Hall to nonparametric function estimation and modeling. The focuses are on density estimation, nonparametric regression, bandwidth selection, boundary corrections, inference under shape…

Nonparametric estimation of mean and covariance functions is important in functional data analysis. We investigate the performance of local linear smoothers for both mean and covariance functions with a general weighing scheme, which includes two commonly used schemes, equal weight per observation (OBS), and equal weight per subject (SUBJ), as two special cases. We provide a comprehensive analysis of their asymptotic properties on a unified platform for all types of sampling…

纵向与聚类数据半变系数模型的有效估计AI 解读

In semivarying coefficient modeling of longitudinal/clustered data, of primary interest is usually the parametric component which involves unknown constant coefficients. First, we study semiparametric efficiency bound for estimation of the constant coefficients in a general setup. It can be achieved by spline regression using the true within-subject covariance matrices, which are often unavailable in reality. Thus, we propose an estimator when the covariance matrices are…

超大规模协方差矩阵的复合已实现核估计及投资组合选择应用AI 解读

We propose a composite realized kernel to estimate the ex-post covariation of asset prices. These measures can in turn be used to forecast the covariation of future asset returns. Composite realized kernels are a data-efficient method, where the covariance estimate is composed of univariate realized kernels to estimate variances and bivariate realized kernels to estimate correlations. We analyze the merits of our composite realized kernels in an ultra high-dimensional…

函数型时间序列的卷积自回归模型AI 解读

Functional data analysis has became an increasingly popular class of problems in statistical research. However, functional data observed over time with serial dependence remains a less studied area. Motivated by Bosq (2000), who first introduced the functional autoregressive models, we propose a convolutional functional autoregressive model, where the function at time t is a result of the sum of convolutions of the past functions and a set of convolution functions, plus a…

通过正则化核估计实现距离收缩与欧氏嵌入AI 解读

Summary Although recovering a Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based on the so-called regularized kernel estimate. We show that such an estimate can be characterized as simply applying a constant amount of shrinkage to all observed pairwise distances. This fact allows us to establish risk bounds for the…

局部线性风险率估计的双重单侧交叉验证AI 解读

Summary The paper brings together the theory and practice of local linear kernel hazard estimation. Bandwidth selection is fully analysed, including double one-sided cross-validation that is shown to have good practical and theoretical properties. Insight is provided into the choice of the weighting function in the local linear minimization and it is pointed out that classical weighting sometimes lacks stability. A new semiparametric hazard estimator transforming the…

基于k近邻估计的一致模型设定检验AI 解读

We propose a simple consistent test for a parametric regression functional form based on k-nearest-neighbor (k-nn) method. We derive the null distribution of the test statistic and show that the test achieves the minimax rate optimality against smooth alternatives. A wild bootstrap method is used to better approximate the null distribution of the test statistic. We also propose a k-nn statistic which tests for omitted variables nonparametrically. Simulations and an empirical…

Harris 常返马尔可夫过程的局部复合分位数回归平滑AI 解读

In this paper, we study the local polynomial composite quantile regression (CQR) smoothing method for the nonlinear and nonparametric models under the Harris recurrent Markov chain framework. The local polynomial CQR regression method is a robust alternative to the widely-used local polynomial method, and has been well studied in stationary time series. In this paper, we relax the stationarity restriction on the model, and allow that the regressors are generated by a general…