In this paper, we propose a new regularization technique called "functional SCAD". We then combine with the smoothing spline method to develop smooth and locally sparse (i.e., zero on some sub-regions) estimator for coefficient function in functional linear regression. The SCAD has nice shrinkage property that enables our estimating procedure identify null subregions of without over shrinking non-zero values function. Additionally, smoothness estimated is regularized by roughness penalty...

The analysis of samples random objects that do not lie in a vector space is gaining increasing attention statistics. An important class such object data univariate probability measures defined on the real line. Adopting Wasserstein metric, we develop regression models for data, where distributions serve as predictors and responses are either also or scalars. To define this model, use geometry tangent bundles endowed with metric mapping to spaces. proposed distribution-to-distribution model...

Summary The ingenious approach of Chatterjee (2021) to estimate a measure dependence first proposed by Dette et al. (2013) based on simple rank statistics has quickly caught attention. This the appealing property being between 0 and 1, or 1 if only corresponding pair random variables is independent one measurable function other almost surely. However, more recent studies (Cao & Bickel 2020; Shi 2022b) showed that independence tests Chatterjee’s correlation are unfortunately rate...

Summary Functional principal component analysis (FPCA) is a popular approach to explore major sources of variation in sample random curves. These are represented by functional components (FPCs). The intervals where the values FPCs significant interpreted as curves have variations. However, these often hard for naïve users identify, because vague definition “significant values”. In this article, we develop novel penalty-based method derive that only nonzero precisely significant, whence...

In this work we develop a novel and foundational framework for analyzing general Riemannian functional data, in particular new development of tensor Hilbert spaces along curves on manifold. Such enable us to derive Karhunen–Loève expansion random processes. This also features an approach compare objects from different spaces, which paves the way asymptotic analysis data analysis. Built upon intrinsic geometric concepts such as vector field, Levi-Civita connection parallel transport...

We consider estimation of mean and covariance functions functional snippets, which are short segments possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval. Estimation function for snippets challenging since information far off-diagonal regions structure completely missing. address this difficulty by decomposing into a variance component correlation component. The can be effectively estimated nonparametrically, while part...

We present a new Riemannian metric, termed Log-Cholesky on the manifold of symmetric positive definite (SPD) matrices via Cholesky decomposition. first construct Lie group structure and bi-invariant metric space, collection lower triangular whose diagonal elements are all positive. Such then pushed forward to space SPD inverse decomposition that is bijective map between matrix space. This fully circumvent swelling effect, in sense determinant Fr\'echet average set under presented called...

Summary Two-sample hypothesis testing is a fundamental statistical problem for inference about two populations. In this paper, we construct novel test statistic to detect high-dimensional distributional differences based on the max-sliced Wasserstein distance mitigate curse of dimensionality. By exploiting an intriguing link between and suprema empirical processes, develop effective bootstrapping procedure approximate null distribution statistic. One distinctive feature proposed ability...

Posterior drift refers to changes in the relationship between responses and covariates while distributions of remain unchanged. In this work, we explore functional linear regression under posterior with transfer learning. Specifically, investigate when how auxiliary data can be leveraged improve estimation accuracy slope function target model occurs. We employ approximated least square method together a lasso penalty construct an estimator that transfers beneficial knowledge from source...

Abstract Iron metabolism plays an important role in maintaining cellular multiple biological functions. Dysfunction of iron homeostasis-maintaining systems was observed many diseases, including cancer. Ribosomal L1 domain-containing 1 (RSL1D1) is RNA-binding protein involved processes, senescence, proliferation and apoptosis. However, the regulatory mechanism RSL1D1 underlying senescence its process colorectal cancer (CRC) not clearly understood. Here, we report that expression downregulated...

Abstract Modern data collection often entails longitudinal repeated measurements that assume values on a Riemannian manifold. Analyzing such is challenging, because of both the sparsity observations and nonlinear manifold constraint. Addressing this challenge, we propose an intrinsic functional principal component analysis for data. Information pooled across subjects by estimating mean curve with local Fréchet regression smoothing covariance structure linearized tangent spaces around mean....

NERC requires considering the uncertainties in assessing total transmission capability (TTC) by calculating a term called reliability margin (TRM). As part of new BC Hydro TTC calculator, an improved 2m +1 point estimation based method (PEM) was developed to estimate standard deviation due system parameters including forecasted load, generation patterns, inter-tie schedules and change projected load dispatch conditions as result stress. The is used determine TRM. has now been accepted...

In recent years, bootstrap methods have drawn attention for their ability to approximate the laws of "max statistics" in high-dimensional problems. A leading example such a statistic is coordinatewise maximum sample average $n$ random vectors $\mathbb{R}^{p}$. Existing results this show that can work when $n\ll p$, and rates approximation (in Kolmogorov distance) been obtained with only logarithmic dependence $p$. Nevertheless, one challenging aspects setting established tend scale like...

Abstract Understanding causal relationships is one of the most important goals modern science. So far, inference literature has focused almost exclusively on outcomes coming from Euclidean space Rp. However, it increasingly common that complex datasets are best summarized as data points in nonlinear spaces. In this paper, we present a novel framework effects for Wasserstein cumulative distribution functions, which contrast to space, nonlinear. We develop doubly robust estimators and...

We study a scalar-on-function truncated linear regression model which assumes that the functional predictor does not influence response when time passes certain cutoff point. approach this problem from perspective of locally sparse modeling, where function is if it zero on substantial portion its defining domain. In model, slope exactly beyond time. A estimate then gives rise to an propose nested group bridge penalty able specifically shrink tail function. Combined with B-spline basis...

Summary We propose a new method for functional nonparametric regression with predictor that resides on finite-dimensional manifold, but is observable only in an infinite-dimensional space. Contamination of the due to discrete or noisy measurements also accounted for. By using local linear manifold smoothing, proposed estimator enjoys polynomial rate convergence adapts intrinsic dimension and contamination level. This contrast logarithmic literature regression. observe phase transition...

We propose a new approach to the problem of high-dimensional multivariate ANOVA via bootstrapping max statistics that involve differences sample mean vectors. The proposed method proceeds construction simultaneous confidence regions for population It is suited simultaneously test equality several pairs vectors potentially more than two populations. By exploiting variance decay property natural feature in relevant applications, we are able provide dimension-free and nearly parametric...

Summary We propose and investigate an additive regression model for symmetric positive-definite matrix-valued responses multiple scalar predictors. The exploits the Abelian group structure inherited from either of log-Cholesky log-Euclidean frameworks matrices naturally extends to general Lie groups. proposed is shown connect on a tangent space. This connection not only entails efficient algorithm estimate component functions, but also allows one generalize Riemannian manifolds. Optimal...

We introduce the concept of mixture inner product spaces associated with a given separable Hilbert space, which feature an infinite-dimensional finite-dimensional vector and are dense in underlying space. Any valued random element can be arbitrarily closely approximated by space elements. While this applied to data any case functional that elements $L^{2}$ square integrable functions is special interest. For data, provide new perspective, where each realization stochastic process falls into...

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption that there are enough domain interest to estimate both functions. We investigate estimation snippets which observations from subject available only an interval length strictly, often much, shorter than whole interest. For such sampling plan, no direct off-diagonal region function. tackle challenge via basis...