2,424 research outputs found
Multivariate risks and depth-trimmed regions
No full textAcceptance set, Cone, Depth-trimmed region, Multivariate risk, Risk measure, 91B30, 91B82, 60D05, 62H99, C60, C61,
THE EXPECTED CONVEX HULL TRIMMED REGIONS OF A SAMPLE
No full textGiven a data set in the multivariate Euclidean space, we study regions of central points built by averaging all their subsets with a fixed number of elements. The averaging of these sets is performed by appropriately scaling the Minkowski or elementwise summation of their convex hulls. The volume of such central regions is proposed as a multivariate scatter estimate and a circular sequence algorithm to compute the central regions of a bivariate data set is described.
The expected convex hull trimmed regions of a sample
No full textGiven a data set in the multivariate Euclidean space, we study regions of central points built by averaging all their subsets with a fixed number of elements. The averaging of these sets is performed by appropriately scaling the Minkowski or elementwise summation of their convex hulls. The volume of such central regions is proposed as a multivariate scatter estimate and a circular sequence algorithm to compute the central regions of a bivariate data set is described
The zonoid region parameter depth
No full textSpanish Ministry of Science and Innovation [grants
PID2021-123592OB-I00 and TED2021-129316B-I00]; the Principality of Asturias/FEDER [grants GRUPIN-IDI2018-000132 and SV-PA-21-AYUD/2021/50897]; the Spanish Ministry of Science and Innovation [grants PID2019-104486GB-I00 and MTM2015-63971-P
Los estadísticos dan guerra
No full textAudiovisuales. Concurso Stat Wars. Disponible en http://www.youtube.com/watch?v=1a6J9KXyoQo .El pasado 13 de noviembre, en el marco de la Semana de la Ciencia, el departamento organizó la competición Stats Wars, una batalla estadística que congregó a mil asistentes, casi todos estudiantes de secundaria y bachillerato, en el auditorio de Leganés. El día 29, la universidad acogerá la jornada de Estadística de Leganés, que contará con otro concurso, Stats&Google, para estudiantes de grado.Contiene: ¿Es el año de la Estadística? Probablemente, sí (p.6) .-- Ser estadístico importa / Rosa Lillo (p.7) .-- Stat Wars,: que empiece el espectáculo (pp. .8-9) .-- La importancia de la estadística en lo cotidiano / Ignacio Cascos (p.9)
Statistical process control and the joint monitoring of multivariate through the zonoid region parameter depth
No full textA new concept of depth for central regions is introduced. The proposed depth notion assesses how well an interval fits a given univariate distribution
as its zonoid region of level 1/2, and it is extended to the multivariate setting by means of a projection argument. Since central regions capture
information about location, scatter, and dependency among several variables, the new depth evaluated on an empirical zonoid region quantifies the
degree of similarity (in terms of the features captured by central regions) of the corresponding sample with respect to some reference distribution.
Statistical process control and the joint monitoring of multivariate and interval-valued data in terms of location and scale are proposed by exploiting
the above-mentioned depth notio
Depth functions based on a number of observations of a random vector
No full textWe present two statistical depth functions given in terms of the random variable defined as the
minimum number of observations of a random vector that are needed to include a fixed given
point in their convex hull. This random variable measures the degree of outlyingness of a point
with respect to a probability distribution. We take advantage of this in order to define the new
depth functions. Further, a technique to compute the probability that a point is included in the
convex hull of a given number of i.i.d. random vectors is presented.
Consider the sequence of random sets whose n-th element is the convex hull of
independent copies of a random vector. Their sequence of selection expectations is nested and
we derive a depth function from it. The relation of this depth function with the linear convex
stochastic order is investigated and a multivariate extension of the Gini mean difference is
defined in terms of the selection expectation of the convex hull of two independent copies of a
random vector
MULTIVARIATE RISKS AND DEPTH-TRIMMED REGIONS
No full textWe describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk measures are described in this axiomatic framework. It is shown that the concept of depth-trimmed (or central) regions from the multivariate statistics is closely related to the definition of risk measures. In particular, the halfspace trimming corresponds to the Value-at-Risk, while the zonoid trimming yields the expected shortfall. In the abstract framework, it is shown how to establish a both-ways correspondence between risk measures and depth-trimmed regions. It is also demonstrated how the lattice structure of the space of risk values influences this relationship.
Choosing a random distribution with prescribed risks
No full textWe describe several simulation algorithms that yield random probability distributions with given values of risk measures. In case of vanilla risk measures, the algorithms involve combining and transforming random cumulative distribution functions or random Lorenz curves obtained by simulating rather general random probability distributions on the unit interval. A new algorithm based on the simulation of a weighted barycentres array is suggested to generate random probability distributions with a given value of the spectral risk measure
Depth functions based on a number of observations of a random vector
No full textWe present two statistical depth functions given in terms of the random variable defined as the minimum number of observations of a random vector that are needed to include a fixed given point in their convex hull. This random variable measures the degree of outlyingness of a point with respect to a probability distribution. We take advantage of this in order to define the new depth functions. Further, a technique to compute the probability that a point is included in the convex hull of a given number of i.i.d. random vectors is presented. Consider the sequence of random sets whose n-th element is the convex hull of independent copies of a random vector. Their sequence of selection expectations is nested and we derive a depth function from it. The relation of this depth function with the linear convex stochastic order is investigated and a multivariate extension of the Gini mean difference is defined in terms of the selection expectation of the convex hull of two independent copies of a random vector.
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