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Multi-objective evaluation is a necessary aspect when managing complex systems, as the intrinsic complexity of a system is generally closely linked to the potential number of optimization objectives. However, an evaluation makes no sense…
We propose a new notion called `extremal depth' (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme `outlyingness'. ED has several…
The identification of influential observations is an important part of data analysis that can prevent erroneous conclusions drawn from biased estimators. However, in high dimensional data, this identification is challenging. Classical and…
We present a stochastic agent-based model for the distribution of personal incomes in a developing economy. We start with the assumption that incomes are determined both by individual labour and by stochastic effects of trading and…
In this study, we extend the research on the dynamic poverty indexes, namely the dynamic Headcount ratio, the dynamic income-gap ratio, the dynamic Gini and the dynamic Sen, proposed in D'Amico and Regnault (2018). The contribution is…
This paper introduces metrics for welfare analysis in dynamic models. We develop estimation and inference for these parameters even in the presence of a high-dimensional state space. Examples of welfare metrics include average welfare,…
We present a conceptual model to measure disparity--the target study--where social groups may be similarly situated (i.e., balanced) on allowable covariates. Our model, based on a sampling design, does not intervene to assign social group…
Is there a natural way to order data in dimension greater than one? The approach based on the notion of data depth, often associated with John Tukey, is among the most popular. Tukey's depth has found applications in robust statistics,…
Many variables of interest in clinical medicine, like disease severity, are recorded using discrete ordinal categories such as normal/mild/moderate/severe. These labels are used to train and evaluate disease severity prediction models.…
The intrinsic dimensionality refers to the ``true'' dimensionality of the data, as opposed to the dimensionality of the data representation. For example, when attributes are highly correlated, the intrinsic dimensionality can be much lower…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…
Recent studies show that paddings in convolutional neural networks encode absolute position information which can negatively affect the model performance for certain tasks. However, existing metrics for quantifying the strength of…
The distributionally robust Markov Decision Process (MDP) approach asks for a distributionally robust policy that achieves the maximal expected total reward under the most adversarial distribution of uncertain parameters. In this paper, we…
Depth-from-defocus (DFD), modeling the relationship between depth and defocus pattern in images, has demonstrated promising performance in depth estimation. Recently, several self-supervised works try to overcome the difficulties in…
For hypothesis testing of functional parameters, given a functional statistic $T_n$ and a functional depth $D$ with respect to the distribution $P_n$ of $T_n$, we propose the depth value $DT_n \equiv D(T_n;P_n)$ as a test statistic, which…
This paper addresses the problem of single image depth estimation (SIDE), focusing on improving the quality of deep neural network predictions. In a supervised learning scenario, the quality of predictions is intrinsically related to the…
We present canonical quantiles and depths for directional data following a distribution which is elliptically symmetric about a direction $\mu$ on the sphere $\mathcal{S}^{d-1}$. Our approach extends the concept of Ley et al. [1], which…
The article contains a methodology for social statistics assessing. The significance of minorities (groups that differ in their attributes from the majority) has grown substantially in the modern postindustrial economy and society. In the…
It is often desired that ordinal regression models yield unimodal predictions. However, in many recent works this characteristic is either absent, or implemented using soft targets, which do not guarantee unimodal outputs at inference. In…
We propose new ways to compare two latent distributions when only ordinal data are available and without imposing parametric assumptions on the underlying continuous distributions. First, we contribute identification results. We show how…