Multiplicative Bias Corrected Nonparametric Smoothers

Nonparametric estimation of the conditional distribution of the inter-jumping times for piecewise-deterministic Markov processes

This paper presents a nonparametric method for estimating the conditional density associated to the jump rate of a piecewise-deterministic Markov process. In our framework, the estimation needs only one observation of the process within a long time interval. Our method relies on a generalization of Aalen's multiplicative intensity model. We prove the uniform consistency of our estimator, under some reasonable assumptions related to the primitive characteristics of the process. A simulation example illustrates the behavior of our estimator.

On the nonparametric maximum likelihood estimator for Gaussian location mixture densities with application to Gaussian denoising

We study the Nonparametric Maximum Likelihood Estimator (NPMLE) for estimating Gaussian location mixture densities in $d$-dimensions from independent observations. Unlike usual likelihood-based methods for fitting mixtures, NPMLEs are based on convex optimization. We prove finite sample results on the Hellinger accuracy of every NPMLE. Our results imply, in particular, that every NPMLE achieves near parametric risk (up to logarithmic multiplicative factors) when the true density is a discrete Gaussian mixture without any prior information on the number of mixture components. NPMLEs can natural…

来自乘法测量误差观测的拟合检验

Goodness-of-fit testing from observations with multiplicative measurement error

本文提出了一种基于 Mellin 变换二次泛函的非参数拟合检验方法，用于处理乘法测量误差下的密度检验问题，并通过模拟研究验证了其有效性。

Nonparametric covariate-adjusted regression

We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that relies on restrictive assumptions usually made in the literature, to a sophisticated piecewise approach that involves reconstructing a smooth curve from an estimator of a constant multiple of its absolute value, and which can be applied in much more general scenarios. We show that, although our nonparametric estimators are constructed from predictors of the…

Semiparametric density estimation by local L_2-fitting

This article examines density estimation by combining a parametric approach with a nonparametric factor. The plug-in parametric estimator is seen as a crude estimator of the true density and is adjusted by a nonparametric factor. The nonparametric factor is derived by a criterion called local L_2-fitting. A class of estimators that have multiplicative adjustment is provided, including estimators proposed by several authors as special cases, and the asymptotic theories are developed. Theoretical comparison reveals that the estimators in this class are better than, or at least competitive with, …

Nonparametric Estimation and Testing on Discontinuity of Positive Supported Densities: A Kernel Truncation Approach

Discontinuity in density functions is of economic importance and interest. For instance, in studies on regression discontinuity designs, discontinuity in the density of a running variable suggests violation of the no-manipulation assumption. In this paper we develop estimation and testing procedures on discontinuity in densities with positive support. Our approach is built on splitting the gamma kernel (Chen, 2000) into two parts at a given (dis)continuity point and constructing two truncated kernels. The jump-size magnitude of the density at the point can be estimated nonparametrically by two…

乘性测量误差观测下的二次泛函估计

Quadratic functional estimation from observations with multiplicative measurement error

针对乘性误差干扰下的正随机变量密度二次泛函估计问题，提出结合Mellin变换估计与谱截断正则化反演的完全数据驱动插件估计器，采用Goldenshluger-Lepski方法选截断参数，证明其达对数衰减的神谕速率并通过模拟验证。

非参数回归的稳健经验似然及其在断点回归设计中的应用

On Robust Empirical Likelihood for Nonparametric Regression with Application to Regression Discontinuity Designs

本文提出稳健经验似然方法，解决非参数回归与断点回归设计中偏差校正经验似然推广的难题，该方法无需额外估计步骤，模拟与真实数据应用均验证其性能优于现有方法。

Large-sample study of the kernel density estimators under multiplicative censoring

The multiplicative censoring model introduced in Vardi [Biometrika 76 (1989) 751--761] is an incomplete data problem whereby two independent samples from the lifetime distribution $G$, $\mathcal{X}_m=(X_1,...,X_m)$ and $\mathcal{Z}_n=(Z_1,...,Z_n)$, are observed subject to a form of coarsening. Specifically, sample $\mathcal{X}_m$ is fully observed while $\mathcal{Y}_n=(Y_1,...,Y_n)$ is observed instead of $\mathcal{Z}_n$, where $Y_i=U_iZ_i$ and $(U_1,...,U_n)$ is an independent sample from the standard uniform distribution. Vardi [Biometrika 76 (1989) 751--761] showed that this model unifies …

Estimation of a semiparametric transformation model

This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or multiplicative separability. We give results for the estimation of the transformation when the rest of the model is estimated non- or semi-parametrically and fulfills some consistency conditions. We propose two methods for the estimation of the transformation parameter: maximizing a profile likelihood function or minimizing the mean squared distance from independenc…

绝对正则过程的广义加性条件分位数估计

Estimating Generalized Additive Conditional Quantiles for Absolutely Regular Processes

针对严格平稳绝对正则过程，提出带未知链接函数的广义加性条件分位数非参数估计方法，并证明各估计量的相合速率、二阶渐近展开与逐点渐近正态性。