Related papers: Interval Spacing
In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
Stochastic orders are binary relations defined on probability distributions which capture intuitive notions like being larger or being more variable. This paper introduces stochastic ordering of interference distributions in large-scale…
A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a super-position of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency…
Ordinal data analysis is an interesting direction in machine learning. It mainly deals with data for which only the relationships `$<$', `$=$', `$>$' between pairs of points are known. We do an attempt of formalizing structures behind…
A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…
In many statistical problems, several estimators are usually available for interval estimation of a parameter of interest, and hence, the selection of an appropriate estimator is important. The criterion for a good estimator is to have a…
Regression models are essential for a wide range of real-world applications. However, in practice, target values are not always precisely known; instead, they may be represented as intervals of acceptable values. This challenge has led to…
We propose here a number of approaches to implement constraint propagation for arithmetic constraints on integer intervals. To this end we introduce integer interval arithmetic. Each approach is explained using appropriate proof rules that…
Extensions of previous linear regression models for interval data are presented. A more flexible simple linear model is formalized. The new model may express cross-relationships between mid-points and spreads of the interval data in a…
Interval arithmetic is a simple way to compute a mathematical expression to an arbitrary accuracy, widely used for verifying floating-point computations. Yet this simplicity belies challenges. Some inputs violate preconditions or cause…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…
Time series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often…
Probability distributions can be read as simple expressions of information. Each continuous probability distribution describes how information changes with magnitude. Once one learns to read a probability distribution as a measurement scale…
We provide an analytical argument for understanding the likely nature of parameter shifts between those coming from an analysis of a dataset and from a subset of that dataset, assuming differences are down to noise and any intrinsic…
An interval matrix is a matrix whose entries are intervals in the set of real numbers. Let $p , q $ be nonzero natural numbers and let $\mu =( [m_{i,j}, M_{i,j}])_{i,j}$ be a $p \times q$ interval matrix; given a $p \times q$ matrix $A$…
We initiate the study of the Interval Selection problem in the (streaming) sliding window model of computation. In this problem, an algorithm receives a potentially infinite stream of intervals on the line, and the objective is to maintain…
We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…
Consider a string of $n$ positions, i.e. a discrete string of length $n$. Units of length $k$ are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring…