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This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions;…
Two frameworks for multivariate functional depth based on multivariate depths are introduced in this paper. The first framework is multivariate functional integrated depth, and the second framework involves multivariate functional extremal…
The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…
We consider nonparametric measurement error density deconvolution subject to heteroscedastic measurement errors as well as symmetry about zero and shape constraints, in particular unimodality. The problem is motivated by applications where…
Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based…
This paper proposes a nonparametric test for $m$th-degree inverse stochastic dominance which is a powerful tool for ranking distribution functions according to social welfare. We construct the test based on empirical process theory. The…
Graphs are very effective tools in visualizing information and are used in many fields including the medical field. In most developing countries primary care, graphs are used to monitor child growth. These measures are therefore often…
Depth estimation and 3D reconstruction have been extensively studied as core topics in computer vision. Starting from rigid objects with relatively simple geometric shapes, such as vehicles, the research has expanded to address general…
We measure the Out-of-domain uncertainty in the prediction of Neural Networks using a statistical notion called ``Lens Depth'' (LD) combined with Fermat Distance, which is able to capture precisely the ``depth'' of a point with respect to a…
Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…
Manual estimation of fetal Head Circumference (HC) from Ultrasound (US) is a key biometric for monitoring the healthy development of fetuses. Unfortunately, such measurements are subject to large inter-observer variability, resulting in low…
Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…
Deep neural network training often involves stochastic optimization, meaning each run will produce a different model. This implies that hyperparameters of the training process, such as the random seed itself, can potentially have…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…
In meta-analysis with continuous outcomes, the use of effect sizes based on the means is the most common. It is often found, however, that only the quantile summary measures are reported in some studies, and in certain scenarios, a…
The urban-rural consumption gap, as one of the important indicators in social development, directly reflects the imbalance in urban and rural economic and social development. Data elements, as an important component of New Quality…
Across many scientific disciplines, multiple observations are collected from the same experimental units, and in modern datasets these observations often arise as non-Euclidean random objects. In such settings, the incorporation of random…
In modern drug development, the broader availability of high-dimensional observational data provides opportunities for scientist to explore subgroup heterogeneity, especially when randomized clinical trials are unavailable due to cost and…
Difference-in-differences (DiD) is a cornerstone of causal inference, yet extending it to functional outcomes is not a routine scalar generalization; rather, it entails three fundamental challenges in identification, inference, and…
In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…