Bootstrap Approximation to the Distribution of M-estimates in a Linear Model

The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation,and prove that the approximation is valid in probability 1.A simulation is made to show the effects of bootstrap approximation,randomly weighted approximation and normal approximation.     

(Un)Conditional Sample Generation Based on Distribution Element Trees

Recently, distribution element trees (DETs) were introduced as an accurate and computationally efficient method for density estimation. In this work, we demonstrate that the DET formulation promotes an easy and inexpensive way to generate random samples similar to a smooth bootstrap. These samples can be generated unconditionally, but also, without further complications, conditionally using available information about certain probability-space components. This article is accompanied by the R codes that were used to produce all simulation results. Supplementary material for this article is available online.     

Optimal operation of hydrothermal systems with Hydrological Scenario Generation through Bootstrap and Periodic Autoregressive Models

In electrical power systems with strong hydro generation, the use of adequate techniques to generate synthetic hydrological scenarios is extremely important for the evaluation of the ways the system behaves in order to meet the forecast energy demand. This paper proposes a new model to generate natural inflow energy scenarios in the long-term operation planning of large-sized hydrothermal systems. This model is based on the Periodic Autoregressive Model, PAR (p), where the identification of the p orders is based on the significance of the Partial Autocorrelation Function (PACF) estimated via Bootstrap, an intensive computational technique. The scenarios generated through this new technique were applied to the operation planning of the Brazilian Electrical System (BES), using the previously developed methodology of Stochastic Dynamic Programming based on Convex Hull algorithm (SDP-CHull). The results show that identification via Bootstrap is considerably more parsimonious, leading to the identification of lower orders models in most cases which retains the statistical characteristics of the original series. Additionally it presents a closer total mean operation cost when compared to the cost obtained via historic series.     

双参数指数分布型元件并联系统的可靠性的广义置信下限

本文对于两个独立双参数指数分布元件组成的并联系统,基于两个元件的定数截尾数据,利用Weerahandi给出的广义枢轴量和广义置信区间的概念,建立了可靠性的广义置信下限,并从理论上研究了广义置信下限的频率性质.广义置信下限可以通过数值方法得到,计算方法是简单直接的.在小样本情形下,通过与Bootstrap置信下限的模拟研究,发现广义置信下限的覆盖率更令人满意.     

Estimation and test procedures for composite quantile regression with covariates missing at random

In this paper, we study the weighted composite quantile regression (WCQR) for general linear model with missing covariates. We propose the WCQR estimation and bootstrap test procedures for unknown parameters. Simulation studies and a real data analysis are conducted to examine the finite performance of our proposed methods.     

On the lifetime and one-year views of reserve risk,with application to IFRS 17 and Solvency II risk margins

This paper brings together analytic and simulation-based approaches to reserve risk in general (P&C) insurance, applied to the traditional actuarial view of risk over the lifetime of the liabilities and to the one-year view of Solvency II. It also connects the lifetime and one-year views of risk. The framework of the model in Mack (1993) is used throughout, although the results have wider applicability.The advantages of a simulation-based approach are highlighted, giving a full predictive distribution, which is used to estimate risk margins under Solvency II and risk adjustments under IFRS 17. We discuss methods for obtaining capital requirements in a cost-of-capital risk margin, and methods for estimating risk adjustments using risk measures applied to a simulated distribution of the outstanding liabilities over their lifetime.     

BOOTSTRAP MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETER IN SPECTRAL DENSITY OF STATIONARY PROCESSES

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稳态托卡马克堆中的自举电流

在稳态托卡马克堆的燃烧阶段,当感应电流下降后,新经典输运产生的自举电流便成为维持稳定电流的最好手段。本文根据α粒子新经典自举电流的最新结果,计算了感应电流消失阶段,稳态堆中α粒子、电子和离子的自举电流。     

Finite-size effects for some bootstrap percolation models

The consequences of Schonmann's new proof that the critical threshold is unity for certain bootstrap percolation models are explored. It is shown that this proof provides an upper bound for the finite-size scaling in these systems. Comparison with data for one case demonstrates that this scaling appears to give the correct asymptotics. We show that the threshold for a finite system of sizeL scales asO[ln(lnL)] for the isotropic model in three dimensions where sites that fail to have at least four neighbors are culled.Related systems have been studied in the context of cellular automata.⁽⁴⁾     

Bootstrap in Markov-sequences based on estimates of transition density

We develop a Bootstrap method in Markov-sequences. This method is based on kernel estimates of the transition density of the Markov-sequence. It is shown that the Bootstrap estimate of the variance of a statistic which is a function of means, is consistent. We also show that the Bootstrap distributions of mean-like statistics and von Mises differentiable statistics converge to appropriate normal distributions. A few simulation results are reported to illustrate the discussion.Most of this work was carried out when the author was at the Department of Statistics, Pennsylvania State University.