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## On the Geometric Brownian Motion assumption for financial time series

### Functional Statistics and Related Fields (2017-01-01): 59-65 , January 01, 2017

The Geometric Brownian Motion type process is commonly used to describe stock price movements and is basic for many option pricing models. In this paper a new methodology for recognizing Brownian functionals is applied to financial datasets in order to evaluate the compatibility between real financial data and the above modeling assumption. The method rests on using the volumetric term which appears in the factorization of the small–ball probability of a random curve.

## Monitoring process variability using auxiliary information

### Computational Statistics (2008-04-01) 23: 253-276 , April 01, 2008

In this study a Shewhart type control chart namely *V*_{r} chart is proposed for improved monitoring of process variability (targeting large shifts) of a quality characteristic of interest *Y*. The proposed control chart is based on regression type estimator of variance using a single auxiliary variable *X*. It is assumed that (*Y, X*) follow a bivariate normal distribution. The design structure of *V*_{r} chart is developed and its comparison is made with the well-known Shewhart control chart namely *S*^{2} chart used for the same purpose. Using power curves as a performance measure it is observed that *V*_{r} chart outperforms the *S*^{2} chart for detecting moderate to large shifts, which is main target of Shewhart type control charts, in process variability under certain conditions on ρ_{yx}. These efficiency conditions on ρ_{yx} are also obtained for *V*_{r} chart in this study.

## A New Independence Test for VaR Violations

### Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications (2013-01-01) , January 01, 2013

Interval forecasts evaluation can be reduced to examining the unconditional coverage and independence properties of the hit sequence. In this work we propose a definition for tendency to clustering of violations and an exact independence test for the hit sequence. This test is suitable to detect models with a tendency to generate clusters of violations and is based on an exact distribution that does not depend on any unknown parameter. Moreover, we provide evidence through a simulation study that the suggested test performs better than other tests presented in the literature.

## Free Knot Splines for Supervised Classification

### Journal of Classification (2007-09-01) 24: 221-234 , September 01, 2007

Data in many different fields come to practitioners through a process naturally described as functional. We propose a classification procedure of oxidation curves. Our algorithm is based on two stages: fitting the functional data by linear splines with free knots and classifying the estimated knots which estimate useful oxidation parameters. A real data set on 57 oxidation curves is used to illustrate our approach.

## Procrustes Procedures

### Modern Multidimensional Scaling (1997-01-01): 339-355 , January 01, 1997

The Procrustes problem is concerned with fitting a configuration (testee) to another (target) as closely as possible. In the simplest case, both configurations have the same dimensionality and the same number of points, which can be brought into a 1-1 correspondence by substantive considerations. Under orthogonal transformations, the testee can be rotated and reflected arbitrarily in an effort to fit it to the target. In addition to such rigid motions, one may also allow for dilations and for shifts. In the oblique case, the testee can also be distorted linearly. Further generalizations include an incompletely specified target configuration, different dimensionalities of the configurations, and different numbers of points in both configurations.

## New Advances in Statistical Modeling and Applications

### New Advances in Statistical Modeling and Applications (2014-01-01) , January 01, 2014

## Scan Statistics in Genome-Wide Scan for Complex Trait Loci

### Scan Statistics (2009-01-01): 195-202 , January 01, 2009

In genome-wide genetic scans for disease susceptibility loci, true peaks have been shown to be wider than false peaks. We describe scan statistics to make use of this extra information, which is not generally taken into account otherwise. Our methods are applied to four disease datasets.

## Conditional tests in a competing risks model

### Lifetime Data Analysis (2008-06-01) 14: 154-166 , June 01, 2008

Testing for equality of competing risks based on their cumulative incidence functions (CIFs) or their cause specific hazard rates (CSHRs) has been considered by many authors. The finite sample distributions of the existing test statistics are in general complicated and the use of their asymptotic distributions can lead to conservative tests. In this paper we show how to perform some of these tests using the conditional distributions of their corresponding test statistics instead (conditional on the observed data). The resulting *conditional* tests are initially developed for the case of *k* = 2 and are then extended to *k* > 2 by performing a sequence of two sample tests and by combining several risks into one. A simulation study to compare the powers of several tests based on their conditional and asymptotic distributions shows that using conditional tests leads to a gain in power. A real life example is also discussed to show how to implement such conditional tests.

## Causal Inference Through Principal Stratification: A Special Type of Latent Class Modelling

### Classification and Multivariate Analysis for Complex Data Structures (2011-01-01): 265-270 , January 01, 2011

Principal stratification is an increasingly adopted framework for drawing counterfactual causal inferences in complex situations. After outlining the framework, with special emphasis on the case of truncation by death, I describe an application of the methodology where the analysis is based on a parametric model with latent classes. Then, I discuss the special features of latent class models derived within the principal strata framework. I argue that the concept of principal stratification gives latent class models a solid theoretical basis and helps to solve some specification and fitting issues.

## On a measure of multivariate skewness and a test for multivariate normality

### Annals of the Institute of Statistical Mathematics (1982-12-01) 34: 531-541 , December 01, 1982

### Summary

We consider an extension of Pearson measure of skewness to a multivariate case and apply the proposed measure to a test of multivariate normality.