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We consider the problem of robustly detecting changepoints in the variability of a sequence of independent multivariate functions. We develop a novel changepoint procedure, called the functional Kruskal--Wallis for covariance (FKWC)…
This paper studies the problem of nonparametric testing for the effect of a random functional covariate on a real-valued error term. The covariate takes values in $L^2[0,1]$, the Hilbert space of the square-integrable real-valued functions…
We propose a kernel-based partial permutation test for checking the equality of functional relationship between response and covariates among different groups. The main idea, which is intuitive and easy to implement, is to keep the…
Functional depth is used for ranking functional observations from most outlying to most typical. The ranks produced by functional depth have been proposed as the basis for functional classifiers, rank tests, and data visualization…
The problem of estimating missing fragments of curves from a functional sample has been widely considered in the literature. However, a majority of the reconstruction methods rely on estimating the covariance matrix or the components of its…
We develop inference and testing procedures for conditional dispersion and skewness in a nonparametric regression setup based on statistical depth functions. The methods developed can be applied in situations, where the response is…
In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper…
Nonparametric tests for functional data are a challenging class of tests to work with because of the potentially high dimensional nature of the data. One of the main challenges for considering rank-based tests, like the Mann-Whitney or…
Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…
In this paper, we consider the problem of estimating the covariance kernel and its eigenvalues and eigenfunctions from sparse, irregularly observed, noise corrupted and (possibly) correlated functional data. We present a method based on…
For covariance test in functional data analysis, existing methods are developed only for fully observed curves, whereas in practice, trajectories are typically observed discretely and with noise. To bridge this gap, we employ a…
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…
Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation…
In nonparametric regression analysis, errors are possibly correlated in practice, and neglecting error correlation can undermine most bandwidth selection methods. When no prior knowledge or parametric form of the correlation structure is…
We propose a roughness regularization approach in making nonparametric inference for generalized functional linear models. In a reproducing kernel Hilbert space framework, we construct asymptotically valid confidence intervals for…
It is well known that nonparametric regression estimation and inference procedures are subject to the curse of dimensionality. Moreover, model interpretability usually decreases with the data dimension. Therefore, model-free variable…
Functional data often arise as sequential temporal observations over a continuous state-space. A set of functional data with a possible change in its structure may lead to a wrong conclusion if it is not taken in to account. So, sometimes,…
This paper focuses on the problem of testing the null hypothesis that the regression functions of several populations are equal under a general nonparametric homoscedastic regression model. It is well known that linear kernel regression…
How can we discern whether the covariance operator of a stochastic process is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for…
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…