Let $\{X_{n,j},1\le j\le m\left(n\right),n\ge 1\}$ be an array of rowwise pairwise negative quadrant dependent mean 0 random variables and let $0<b_n\to \infty$. Conditions are given for ${\sum }_{j=1}^{m\left(n\right)}{X}_{n,j}/b_n\to 0$ completely and for ${max}_{1\le k\le m\left(n\right)}\left|{\sum }_{j=1}^k{X}_{n,j}\right|/b_n\to 0$ completely. As an application of these results, we obtain a complete convergence theorem for the row sums ${\sum }_{j=1}^{m\left(n\right)}{X}_{n,j}^{*}$ of the dependent bootstrap samples $\{\{X_{n,j}^{*},1\le j\le m\left(n\right)\},n\ge 1\}$ arising from a sequence of i.i.d. random variables $\{X_n,n\ge 1\}$.

Complete $f$-moment convergence is much more general than complete convergence and complete moment convergence. In this work, we mainly investigate the complete $f$-moment convergence for weighted sums of widely orthant dependent (WOD, for short) arrays. A general result on Complete $f$-moment convergence is obtained under some suitable conditions, which generalizes the corresponding one in the literature. As an application, we establish the complete consistency for the weighted linear estimator in nonparametric...

Se define en este artículo el concepto de proceso suficiente para un proceso de control, así como el de control basado en un proceso suficiente. Se demuestra a continuación que el conjunto de controles basados en un proceso suficiente forma una clase esencialmente completa; por consiguiente, dado un control, existe un control basado en el proceso suficiente que tiene el mismo coste esperado que el anterior.

We assume that the result of a football game depends upon the difference of the strengths of the teams, home-field advantage, random factors and also other components. We describe the goal outcome per game by independent Poisson random variables; we concentrate on expected values. The least squares estimators of the parameters are obtained. The study is illustrated by examples from the Italian and Polish leagues.

The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the $L^{\infty }$-measure of non-exchangeability for copulas belonging to this class.

En este trabajo se analiza el comportamiento de los tests de raíces unitarias cuando se utilizan los componentes ciclo-tendencia obtenidos a partir de procedimientos de extracción de señales en lugar de utilizar las series originales. Adicionalmente se intenta detectar las causas finales de los efectos perniciosos observados. Los procedimientos de extracción de señales analizados son el basado en modelos ARIMA y el filtro de líneas aéreas modificado. Un ejercicio de simulación nos permite concluir...

2000 Mathematics Subject Classification: 60K10, 62P05.The compound Poisson risk models are widely used in practice. In this paper the counting process in the insurance risk model is a compound Poisson process. The model is called Compound Compound Poisson Risk Model. Some basic properties and ruin probability are given. We analyze the model under the proportional reinsurance. The optimal retention level and the corresponding adjustment coefficient are obtained. The particular case of the Pólya-Aeppli...

Many lifetime distributions are motivated only by mathematical interest. Here, eight new families of distributions are introduced. These distributions are motivated as models for the stress of a system consisting of components working in parallel/series and each component has a fixed number of sub-components working in parallel/series. Mathematical properties and estimation procedures are derived for one of the families of distributions. A real data application shows superior performance of a three-parameter...

To obtain a robust version of exponential and Holt-Winters smoothing the idea of $M$-estimation can be used. The difficulty is the formulation of an easy-to-use recursive formula for its computation. A first attempt was made by Cipra (Robust exponential smoothing, J. Forecast. 11 (1992), 57–69). The recursive formulation presented there, however, is unstable. In this paper, a new recursive computing scheme is proposed. A simulation study illustrates that the new recursions result in smaller forecast...

One of the main goals in times series analysis is to forecast future values. Many forecasting methods have been developed and the most successful are based on the concept of exponential smoothing, based on the principle of obtaining forecasts as weighted combinations of past observations. Classical procedures to obtain forecast intervals assume a known distribution for the error process, what is not true in many situations. A bootstrap methodology can be used to compute distribution free forecast...