Search results for " normal distribution"
showing 10 items of 57 documents
Non-Gaussian Distribution for Var Calculation
2003
Publisher Summary This chapter compares different approaches to computing Value-at-Risk (VaR) for heavy tailed return series. Each model has been submitted to a backtest analysis. The most representative asset returns of the Italian stock market and the exchange rates for the major currencies are used. The results obtained confirm that when the percentiles are below 5%, the hypothesis of normality of the conditional return distribution determines intervals of confidence whose forecast ability is low. In fact, it is observed that the return distributions are asymmetric and leptokurtic and the hypothesis of normality is usually rejected when subject to statistical test. Among the alternative …
Two-stage adaptive designs with correlated test statistics.
2005
When performing a trial using an adaptive sequential design, it is usually assumed that the data for each stage come from different units; for example, patients. However, sometimes it is not possible to satisfy this condition or to check whether it is satisfied. In these cases, the test statistics and p-values of each stage may be dependent. In this paper we investigate the type I error of two-stage adaptive designs when the test statistics from the stages are assumed to be bivariate normal. Analytical considerations are performed under the restriction that the conditional error function is constant in the continuation region. We show that the decisions can become conservative as well as an…
Kullback-Leibler distance as a measure of the information filtered from multivariate data
2007
We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically determine the expected values of the Kullback-Leibler distance of a sample correlation matrix from a reference model and we show that the expected values are known also when the specific model is unknown. We propose to make use of the Kullback-Leibler distance to estimate the information extracted from a correlation matrix by correlation filtering procedures. We also show how to use this distance to measure the stability of filtering procedures with respect to s…
Toeplitz band matrices with small random perturbations
2021
We study the spectra of $N\times N$ Toeplitz band matrices perturbed by small complex Gaussian random matrices, in the regime $N\gg 1$. We prove a probabilistic Weyl law, which provides an precise asymptotic formula for the number of eigenvalues in certain domains, which may depend on $N$, with probability sub-exponentially (in $N$) close to $1$. We show that most eigenvalues of the perturbed Toeplitz matrix are at a distance of at most $\mathcal{O}(N^{-1+\varepsilon})$, for all $\varepsilon >0$, to the curve in the complex plane given by the symbol of the unperturbed Toeplitz matrix.
“Anti-Bayesian” flat and hierarchical clustering using symmetric quantiloids
2017
A myriad of works has been published for achieving data clustering based on the Bayesian paradigm, where the clustering sometimes resorts to Naive-Bayes decisions. Within the domain of clustering, the Bayesian principle corresponds to assigning the unlabelled samples to the cluster whose mean (or centroid) is the closest. Recently, Oommen and his co-authors have proposed a novel, counter-intuitive and pioneering PR scheme that is radically opposed to the Bayesian principle. The rational for this paradigm, referred to as the “Anti-Bayesian” (AB) paradigm, involves classification based on the non-central quantiles of the distributions. The first-reported work to achieve clustering using the A…
Statistical validation of simulation models of observable systems
2003
In this paper, for validating computer simulation models of real, observable systems, an uniformly most powerful invariant (UMPI) test is developed from the generalized maximum likelihood ratio (GMLR). This test can be considered as a result of a new approach to solving the Behrens‐Fisher problem when covariance matrices of two multivariate normal populations (compared with respect to their means) are different and unknown. The test is based on invariant statistic whose distribution, under the null hypothesis, does not depend on the unknown (nuisance) parameters. The sample size and threshold of the UMPI test are determined from minimization of the weighted sum of the model builder's risk a…
Discrete Time Portfolio Selection with Lévy Processes
2007
This paper analyzes discrete time portfolio selection models with Lévy processes. We first implement portfolio models under the hypotheses the vector of log-returns follow or a multivariate Variance Gamma model or a Multivariate Normal Inverse Gaussian model or a Brownian Motion. In particular, we propose an ex-ante and an ex-post empirical comparisons by the point of view of different investors. Thus, we compare portfolio strategies considering different term structure scenarios and different distributional assumptions when unlimited short sales are allowed.
The size of Simes’ global test for discrete test statistics
1999
Abstract To increase the power of the Bonferroni–Holm procedure several modified Bonferroni procedures have been proposed (for example, Hochberg, 1988. Biometrika 75, 800–802; Hommel, 1988. Biometrika 75, 383–386), which are based on Simes’ global test (Simes, 1986. Biometrika 73, 751–754). By several simulation studies which, in particular, considered multinormal test statistics, it has been suggested that the Simes test is a level α test. However, an exact proof exists for only few situations one of them assuming independence of test statistics. We studied the behaviour of Simes’ test for discrete test statistics. Due to discreteness one can expect more conservative decisions whereas depe…
Response models for mixed binary and quantitative variables
1992
SUMMARY A number of special representations are considered for the joint distribution of qualitative, mostly binary, and quantitative variables. In addition to the conditional Gaussian models and to conditional Gaussian regression chain models some emphasis is placed on models derived from an underlying multivariate normal distribution and on models in which discrete probabilities are specified linearly in terms of unknown parameters. The possibilities for choosing between the models empirically are examined, as well as the testing of independence and conditional independence and the estimation of parameters. Often the testing of independence is exactly or nearly the same for a number of di…
Una solucion bayesiana a la Paradoja de Stein
1982
If we are interested in making inferences about the square norm of the mean in a multivariate normal model, the usual uniform prior for the mean is not sound, as revealed by Stein in his 1959 work. This paper studies in what sense this prior must be modified by using the maximization of missing information procedure (Bernardo, 1979)