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Effective WLLN, SLLN and CLT in statistical models

Ryszard Zieliński (2004)

Applicationes Mathematicae

Weak laws of large numbers (WLLN), strong laws of large numbers (SLLN), and central limit theorems (CLT) in statistical models differ from those in probability theory in that they should hold uniformly in the family of distributions specified by the model. If a limit law states that for every ε > 0 there exists N such that for all n > N the inequalities |ξₙ| < ε are satisfied and N = N(ε) is explicitly given then we call the law effective. It is trivial to obtain an effective statistical...

Effet des erreurs de mesure sur l'évaluation de l'efficacité d'un traitement

Christian Heuchenne (1993)

Mathématiques et Sciences Humaines

L’effet d’un traitement T sur une compétence Y peut être exprimé par le coefficient de régression partiel β Y T avec contrôle de la compétence initiale X . Quand Y et X sont mesurées avec erreurs par y et x , cet effet se manifeste par le coefficient β y T dans la régression de y sur T et x . Le biais entre β Y T et β y T est explicité, discuté et montré systématique si X et T sont corrélés. L’importance de bien spécifier le modèle, dont une condition nécessaire et suffisante d’identification est donnée, est mise en...

Efficiency of cropping system designs via base contrast

U. Bronowicka-Mielniczuk, J. Mielniczuk, T. Przybysz (2000)

Applicationes Mathematicae

The present article is a continuation of previous papers by the same authors devoted to the efficiency of crop rotation experiments. We focus on plans distinguished by the cyclical pattern of the incidence matrix. For practical reasons, we slightly modify the efficiency coefficient. The relation between the resulting efficiency coefficients is examined. In addition, we provide a background material on crop rotation experiments.

Efficiency of some algorithms for prediction in finite stationary time series

Pavel Ranocha (2004)

Kybernetika

Important characteristics of any algorithm are its complexity and speed in real calculations. From this point of view, we analyze some algorithms for prediction in finite stationary time series. First, we review results developed by P. Bondon [1] and then, we derive the complexities of Levinson and a new algorithm. It is shown that the time needed for real calculations of predictions is proportional to the theoretical complexity of the algorithm. Some practical recommendations for the selection...

Efficiency rate and local deficiency of Huber's location estimators and of the α-estimators.

Asunción Rubio, Jan Amos Visek (1991)

Trabajos de Estadística

The paper studies the problem of selecting an estimator with (approximately) minimal asymptotic variance. For every fixed contamination level there is usually just one such estimator in the considered family. Using the first and the second derivative of the asymptotic variance with respect to the parameter which parametrizes the family of estimators the paper gives two examples of how to select the estimator and gives an approximation to a loss which we suffer when we use the estimator with approximately...

Efficient bootstrap simulation: an overview.

Alex Sánchez (1990)

Qüestiió

Two basic sources of error are associated to the use of bootstrap methods: one is derived from the fact that the true distribution is substituted by a suitable estimate, and the other is simulation errors. Some techniques to reduce or quantify these errors are discussed in this work. Some of them such as importance sampling or antithetic variates are adapted from classical Monte Carlo swindles, whereas others such as the centered and the balanced bootstrap, are more specific. The existence of common...

Efficient estimation of functionals of the spectral density of stationary Gaussian fields

Carenne Ludeña (2010)

ESAIM: Probability and Statistics

Minimax bounds for the risk function of estimators of functionals of the spectral density of Gaussian fields are obtained. This result is a generalization of a previous result of Khas'minskii and Ibragimov on Gaussian processes. Efficient estimators are then constructed for these functionals. In the case of linear functionals these estimators are given for all dimensions. For non-linear integral functionals, these estimators are constructed for the two and three dimensional problems.

Efficient online handwritten Chinese character recognition system using a two-dimensional functional relationship model

Yun Fah Chang, Jia Chii Lee, Omar Mohd Rijal, Syed Abdul Rahman Syed Abu Bakar (2010)

International Journal of Applied Mathematics and Computer Science

This paper presents novel feature extraction and classification methods for online handwritten Chinese character recognition (HCCR). The X-graph and Y-graph transformation is proposed for deriving a feature, which shows useful properties such as invariance to different writing styles. Central to the proposed method is the idea of capturing the geometrical and topological information from the trajectory of the handwritten character using the X-graph and the Y-graph. For feature size reduction, the...

Efficient robust estimation of time-series regression models

Pavel Čížek (2008)

Applications of Mathematics

The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior...

Efficient robust nonparametric estimation in a semimartingale regression model

Victor Konev, Serguei Pergamenshchikov (2012)

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

The paper considers the problem of robust estimating a periodic function in a continuous time regression model with the dependent disturbances given by a general square integrable semimartingale with an unknown distribution. An example of such a noise is a non-Gaussian Ornstein–Uhlenbeck process with jumps (see (J. R. Stat. Soc. Ser. B Stat. Methodol.63 (2001) 167–241), (Ann. Appl. Probab.18 (2008) 879–908)). An adaptive model selection procedure, based on the weighted least square estimates, is...

Eigenanalysis and metric multidimensional scaling on hierarchical structures.

Carles Maria Cuadras, Josep-Maria Oller (1987)

Qüestiió

The known hierarchical clustering scheme is equivalent to the concept of ultrametric distance. Every distance can be represented in a spatial model using multidimensional scaling. We relate both classes of representations of proximity data in an algebraic way, obtaining some results and relations on clusters and the eigenvalues of the inner product matrix for an ultrametric distance. Principal coordinate analysis on an ultrametric distance gives two classes of independent coordinates, describing...

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