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Asymptotic inference using functional principal component regression (FPCR) has long been considered difficult, largely because, upon any scalar scaling, the FPCR estimator fails to satisfy a central limit theorem, leading to the prevailing…
Several methods of statistical analysis are proposed and analyzed in application for a specific task -- extraction of the structure functions from the cross sections of deep inelastic interactions of any type. We formulate the method based…
In many modern applications, a dependent functional response is observed for each subject over repeated time, leading to longitudinal functional data. In this paper, we propose a novel statistical procedure to test whether the mean function…
We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using kernels defined on function spaces. This…
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…
Student's $t$ statistic is finding applications today that were never envisaged when it was introduced more than a century ago. Many of these applications rely on properties, for example robustness against heavy tailed sampling…
This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…
In this paper, we propose a general method for testing inequality restrictions on nonparametric functions. Our framework includes many nonparametric testing problems in a unified framework, with a number of possible applications in auction…
Violation of the assumptions underlying classical (Gaussian) limit theory often yields unreliable statistical inference. This paper shows that the bootstrap can detect such violations by delivering simple and powerful diagnostic tests that…
Consider $M$-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found…
The derivation of the state of the art tensorial versions of Fundamental Measure Theory (a form of classical Density Functional Theory for hard spheres) are re-examined in the light of the recently introduced concept of global stability of…
We propose a computationally efficient inferential procedure for longitudinal function-on-function regression. The method follows a marginal three-step approach: (1) fit massive pointwise longitudinal scalar-on-function regression models,…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in…
In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed…
The wild bootstrap is a popular resampling method in the context of time-to-event data analyses. Previous works established the large sample properties of it for applications to different estimators and test statistics. It can be used to…
Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or…
Data depth has emerged as an invaluable nonparametric measure for the ranking of multivariate samples. The main contribution of depth-based two-sample comparisons is the introduction of the Q statistic (Liu and Singh, 1993), a quality…
Nonparametric cointegrating regression models have been extensively used in financial markets, stock prices, heavy traffic, climate data sets, and energy markets. Models with parametric regression functions can be more appealing in practice…
This paper proposes asymptotically distribution-free inference methods for comparing a broad range of welfare indices across dependent samples, including those employed in inequality, poverty, and risk analysis. Two distinct situations are…