Related papers: Distribution and Symmetric Distribution Regression…
Histogram-valued variables are a particular kind of variables studied in Symbolic Data Analysis where to each entity under analysis corresponds a distribution that may be represented by a histogram or by a quantile function. Linear…
A Distributional (Single) Index Model (DIM) is a semi-parametric model for distributional regression, that is, estimation of conditional distributions given covariates. The method is a combination of classical single index models for the…
Symbolic regression (SR) aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, is a powerful paradigm for scientific discovery. Recent advances have expanded SR to describe related phenomena using a…
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…
This paper presents a factor analysis model for symbolic data, focusing on the particular case of interval-valued variables. The proposed method describes the correlation structure among the measured interval-valued variables in terms of a…
We address classification of distributional data, where units are described by histogram or interval-valued variables. The proposed approach uses a linear discriminant function where distributions or intervals are represented by quantile…
Symbolic data analysis (SDA) is an emerging area of statistics concerned with understanding and modelling data that takes distributional form (i.e. symbols), such as random lists, intervals and histograms. It was developed under the premise…
Symbolic Data Analysis (SDA) is a relatively new field of statistics that extends conventional data analysis by taking into account intrinsic data variability and structure. Unlike conventional data analysis, in SDA the features…
Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the…
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
A statistical model is a mathematical representation of an often simplified or idealised data-generating process. In this paper, we focus on a particular type of statistical model, called linear mixed models (LMMs), that is widely used in…
In this paper we present a linear regression model for modal symbolic data. The observed variables are histogram variables according to the definition given in the framework of Symbolic Data Analysis and the parameters of the model are…
Symbolic regression is a nonlinear regression method which is commonly performed by an evolutionary computation method such as genetic programming. Quantification of uncertainty of regression models is important for the interpretation of…
This paper deals with the state estimation of linear time-invariant systems using distributed observers with local sampled-data measurement and aperiodic communication. Each observer agent perceives partial information of the system to be…
Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods…
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…
Logistic regression models are a popular and effective method to predict the probability of categorical response data. However inference for these models can become computationally prohibitive for large datasets. Here we adapt ideas from…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
A standard approach for assessing the performance of partition models is to create synthetic data sets with a prespecified clustering structure, and assess how well the model reveals this structure. A common format is that subjects are…