Related papers: Bootstrap independence test for functional linear …
Functional linear models are one of the most fundamental tools to assess the relation between two random variables of a functional or scalar nature. This contribution proposes a goodness-of-fit test for the functional linear model with…
For testing hypothesis on the covariance operator of functional time series, we suggest to use the full functional information and to avoid dimension reduction techniques. The limit distribution follows from the central limit theorem of the…
In this paper we consider a heteroscedastic transformation model, where the transformation belongs to a parametric family of monotone transformations, the regression and variance function are modelled nonparametrically and the error is…
Let $X_1,X_2, \ldots$ be independent and identically distributed random elements taking values in a separable Hilbert space $\mathbb{H}$. With applications for functional data in mind, $\mathbb{H}$ may be regarded as a space of…
A consistent goodness-of-fit test for distributional regression is introduced. The test statistic is based on a process that traces the difference between a nonparametric and a semi-parametric estimate of the marginal distribution function…
We propose a bootstrap testing framework for a general class of hypothesis tests, which allows resampling under the null hypothesis as well as other forms of bootstrapping. We identify combinations of resampling schemes and bootstrap…
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…
Heteroskedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroskedasticity for the nonparametric regression model with multiple covariates. It is based on a suitable…
Measuring and testing the dependency between multiple random functions is often an important task in functional data analysis. In the literature, a model-based method relies on a model which is subject to the risk of model misspecification,…
We investigate asymptotic inference in a linear regression model where both response and regressors are functions, using an estimator based on functional principal components analysis. Although this approach is widely used in functional…
A conventional linear model for functional data involves expressing a response variable $Y$ in terms of the explanatory function $X(t)$, via the model: $Y=a+\int_I b(t)X(t)dt+\hbox{error}$, where $a$ is a scalar, $b$ is an unknown function…
The problem of comparing the entire second order structure of two functional processes is considered and a $L^2$-type statistic for testing equality of the corresponding spectral density operators is investigated. The test statistic…
Regression models with a response variable taking values in a Hilbert space and hybrid covariates are considered. This means two sets of regressors are allowed, one of finite dimension and a second one functional with values in a Hilbert…
We consider the problem of testing for long-range dependence in time-varying coefficient regression models, where the covariates and errors are locally stationary, allowing complex temporal dynamics and heteroscedasticity. We develop KPSS,…
Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…
We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which…
Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…
Consider a random vector $(X,Y)$ and let $m(x)=E(Y|X=x)$. We are interested in testing $H_0:m\in {\cal M}_{\Theta,{\cal G}}=\{\gamma(\cdot,\theta,g):\theta \in \Theta,g\in {\cal G}\}$ for some known function $\gamma$, some compact set…
We develop methodology for testing hypotheses regarding the slope function in functional linear regression for time series via a reproducing kernel Hilbert space approach. In contrast to most of the literature, which considers tests for the…
Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly…