Tailor-made tests for goodness of fit to semiparametric hypotheses

Adaptive semiparametric wavelet estimator and goodness-of-fit test for long memory linear processes

This paper is first devoted to study an adaptive wavelet based estimator of the long memory parameter for linear processes in a general semi-parametric frame. This is an extension of Bardet {\it et al.} (2008) which only concerned Gaussian processes. Moreover, the definition of the long memory parameter estimator is modified and asymptotic results are improved even in the Gaussian case. Finally an adaptive goodness-of-fit test is also built and easy to be employed: it is a chi-square type test. Simulations confirm the interesting properties of consistency and robustness of the adaptive estimat…

Adaptive estimator of the memory parameter and goodness-of-fit test using a multidimensional increment ratio statistic

The increment ratio (IR) statistic was first defined and studied in Surgailis {\it et al.} (2007) for estimating the memory parameter either of a stationary or an increment stationary Gaussian process. Here three extensions are proposed in the case of stationary processes. Firstly, a multidimensional central limit theorem is established for a vector composed by several IR statistics. Secondly, a goodness-of-fit $χ^2$-type test can be deduced from this theorem. Finally, this theorem allows to construct adaptive versions of the estimator and test which are studied in a general semiparametric fra…

Tests for validity of the semiparametric heteroskedastic transformation model

There exist a number of tests for assessing the nonparametric heteroscedastic location-scale assumption. Here we consider a goodness-of-fit test for the more general hypothesis of the validity of this model under a parametric functional transformation on the response variable. Specifically we consider testing for independence between the regressors and the errors in a model where the transformed response is just a location/scale shift of the error. Our criteria use the familiar factorization property of the joint characteristic function of the covariates under independence. The difficulty is t…

具有尺寸依赖核的高维$U$-统计量的高斯近似

Gaussian Approximation for High-Dimensional $U$-statistics with Size-Dependent Kernels

本文为核依赖于样本量的高维固定阶$U$-统计量建立了高斯近似结果，允许Hoeffding分解主导分量缺失或未知，误差界精确到几乎能恢复固定维设置的最弱带宽条件，并应用于半参数估计、拟合优度检验及高维密度加权平均导数同时推断。

高维计数在 sup 范数下的局部尖锐拟合优度检验

Locally sharp goodness-of-fit testing in sup norm for high-dimensional counts

该研究针对高维计数数据的sup范数拟合优度检验，证明局部极小极大分离速率由类别速率的精细衰减行为决定，通过样本最大值检验获上界、简化原假设获下界，并确定特定渐近设定下的尖锐常数。

半参数加速失效时间模型的一般模型检验程序

A general model-checking procedure for semiparametric accelerated failure time models

提出一组半参数加速失效时间模型拟合优度检验，基于多参数累积和过程与扰动版本，通过模拟和原发性胆汁性肝硬化数据验证有效性，并实现于R包afttest。