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Nonparametric estimations of non-negative random variables distributions

František Vávra, Pavel Nový, Hana Mašková, Michala Kotlíková, David Zmrhal (2003)

Kybernetika

The problem of estimation of distribution functions or fractiles of non- negative random variables often occurs in the tasks of risk evaluation. There are many parametric models, however sometimes we need to know also some information about the shape and the type of the distribution. Unfortunately, classical approaches based on kernel approximations with a symmetric kernel do not give any guarantee of non-negativity for the low number of observations. In this note a heuristic approach, based on...

Nonparametric inference for discretely sampled Lévy processes

Shota Gugushvili (2012)

Annales de l'I.H.P. Probabilités et statistiques

Given a sample from a discretely observed Lévy process X = (Xt)t≥0 of the finite jump activity, the problem of nonparametric estimation of the Lévy density ρ corresponding to the process X is studied. An estimator of ρ is proposed that is based on a suitable inversion of the Lévy–Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of ρ over suitable classes of Lévy triplets. The corresponding lower bounds are also discussed.

Nonparametric recursive aggregation process

Elena Tsiporkova, Veselka Boeva (2004)

Kybernetika

In this work we introduce a nonparametric recursive aggregation process called Multilayer Aggregation (MLA). The name refers to the fact that at each step the results from the previous one are aggregated and thus, before the final result is derived, the initial values are subjected to several layers of aggregation. Most of the conventional aggregation operators, as for instance weighted mean, combine numerical values according to a vector of weights (parameters). Alternatively, the MLA operators...

Nonparametric regression estimation based on spatially inhomogeneous data: minimax global convergence rates and adaptivity

Anestis Antoniadis, Marianna Pensky, Theofanis Sapatinas (2014)

ESAIM: Probability and Statistics

We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known density g with a finite number of well-separated zeros. In particular, we consider two different cases: when g has zeros of a polynomial order and when g has zeros of an exponential order. These two cases correspond to moderate and severe data losses, respectively. We obtain asymptotic (as the sample size increases)...

Normality assumption for the log-return of the stock prices

Pedro P. Mota (2012)

Discussiones Mathematicae Probability and Statistics

The normality of the log-returns for the price of the stocks is one of the most important assumptions in mathematical finance. Usually is assumed that the price dynamics of the stocks are driven by geometric Brownian motion and, in that case, the log-return of the prices are independent and normally distributed. For instance, for the Black-Scholes model and for the Black-Scholes pricing formula [4] this is one of the main assumptions. In this paper we will investigate if this assumption is verified...

Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality

Zofia Hanusz, Joanna Tarasińska (2015)

Biometrical Letters

Two very well-known tests for normality, the Kolmogorov-Smirnov and the Shapiro- Wilk tests, are considered. Both of them may be normalized using Johnson’s (1949) SB distribution. In this paper, functions for normalizing constants, dependent on the sample size, are given. These functions eliminate the need to use non-standard statistical tables with normalizing constants, and make it easy to obtain p-values for testing normality.

Normalizing constants for a statistic based on logarithms of disjoint m-spacings

Franciszek Czekała (1996)

Applicationes Mathematicae

The paper is concerned with the asymptotic normality of a certain statistic based on the logarithms of disjoint m-spacings. The exact and asymptotic mean and variance are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1].

Note on stability estimation in sequential hypothesis testing

E. Gordienko, J. Ruiz de Chávez, A. García (2013)

Applicationes Mathematicae

We introduce a quantitative measure Δ of stability in optimal sequential testing of two simple hypotheses about a density of observations: f=f₀ versus f=f₁. The index Δ represents an additional cost paid when a stopping rule optimal for the pair (f₀,f₁) is applied to test the hypothesis f=f₀ versus a "perturbed alternative" f=f̃₁. An upper bound for Δ is established in terms of the total variation distance between f₁(X)/f₀(X) and f̃₁(X)/f₀(X) with X∼f₀.

Note on universal algorithms for learning theory

Karol Dziedziul, Barbara Wolnik (2007)

Applicationes Mathematicae

We study the universal estimator for the regression problem in learning theory considered by Binev et al. This new approach allows us to improve their results.

Notes on the evolution of feature selection methodology

Petr Somol, Jana Novovičová, Pavel Pudil (2007)

Kybernetika

The paper gives an overview of feature selection techniques in statistical pattern recognition with particular emphasis on methods developed within the Institute of Information Theory and Automation research team throughout recent years. Besides discussing the advances in methodology since times of Perez’s pioneering work the paper attempts to put the methods into a taxonomical framework. The methods discussed include the latest variants of the optimal algorithms, enhanced sub-optimal techniques...

Nuevos modelos de distribuciones de extremos basados en aproximaciones en las ramas.

Enrique Castillo, Eladio Moreno, Jaime Puig-Pey (1983)

Trabajos de Estadística e Investigación Operativa

En este trabajo se presenta una metodología que permite clasificar funciones de distribución absolutamente continuas unidimensionales atendiendo a sus ramas. La idea básica es que, en las ramas la función de distribución difiere en un infinitésimo del valor uno o cero dependiendo de la rama de interés. La principal ventaja de esta clasificación es su aplicación a la teoría de distribuciones de extremos. En esta línea se obtienen nuevas familias de distribuciones de extremos. Entre ellas, las clásicas...

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