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1 – 10 of over 3000How to describe, reliably and effectively, the quality of a continuous stream is a problem facing many companies in the chemical industry. The average quality estimated from an…
Abstract
How to describe, reliably and effectively, the quality of a continuous stream is a problem facing many companies in the chemical industry. The average quality estimated from an average of individual test sample values is most useful if its distribution is known or can be estimated. A simple extension of the Central Limit Theorem is given that provides a means of estimating the distribution which, when coupled with the variogram method of variance estimation of Saunders et al., enables the calculation of probabilities of closeness of lot mean to the nominal value. The result “sits well” with the current emphasis being placed on the importance of “conformance to target”.
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By using the central limit theorem, it is possible to consider the Fourier’s transform of a stochastic process with independent increments as a Gaussian random variable of which…
Abstract
By using the central limit theorem, it is possible to consider the Fourier’s transform of a stochastic process with independent increments as a Gaussian random variable of which the mathematical expectation and the variance are respectively integrals of the mean and the variance of this process. One can then use this result to analyze the statistical properties of linear feedback systems in the frequency domain, that is to say in terms of transfer functions. The advantage of this approach is that one can deal with linear systems subject to squared white noises, in a very simple manner.
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Xiaohu Wang, Weilin Xiao and Jun Yu
This chapter derives asymptotic properties of the least squares (LS) estimator of the autoregressive (AR) parameter in local to unity processes with errors being fractional…
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This chapter derives asymptotic properties of the least squares (LS) estimator of the autoregressive (AR) parameter in local to unity processes with errors being fractional Gaussian noise (FGN) with the Hurst parameter
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Igor Vaynman and Brendan K. Beare
The variance targeting estimator (VTE) for generalized autoregressive conditionally heteroskedastic (GARCH) processes has been proposed as a computationally simpler and…
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The variance targeting estimator (VTE) for generalized autoregressive conditionally heteroskedastic (GARCH) processes has been proposed as a computationally simpler and misspecification-robust alternative to the quasi-maximum likelihood estimator (QMLE). In this paper we investigate the asymptotic behavior of the VTE when the stationary distribution of the GARCH process has infinite fourth moment. Existing studies of historical asset returns indicate that this may be a case of empirical relevance. Under suitable technical conditions, we establish a stable limit theory for the VTE, with the rate of convergence determined by the tails of the stationary distribution. This rate is slower than that achieved by the QMLE. The limit distribution of the VTE is nondegenerate but singular. We investigate the use of subsampling techniques for inference, but find that finite sample performance is poor in empirically relevant scenarios.
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In this paper, we consider a two color multi-drawing urn model. At each discrete time step, we draw uniformly at random a sample of
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In this paper, we consider a two color multi-drawing urn model. At each discrete time step, we draw uniformly at random a sample of
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Kohtaro Hitomi, Keiji Nagai, Yoshihiko Nishiyama and Junfan Tao
In this study, the authors investigate methods of sequential analysis to test prospectively for the existence of a unit root against stationary or explosive states in a p-th order…
Abstract
In this study, the authors investigate methods of sequential analysis to test prospectively for the existence of a unit root against stationary or explosive states in a p-th order autoregressive (AR) process monitored over time. Our sequential sampling schemes use stopping times based on the observed Fisher information of a local-to-unity parameter. In contrast to the Dickey–Fuller (DF) test statistic, the sequential test statistic has asymptotic normality. The authors derive the joint limit of the test statistic and the stopping time, which can be characterized using a 3/2-dimensional Bessel process driven by a time-changed Brownian motion. The authors obtain their limiting joint Laplace transform and density function under the null and local alternatives. In addition, simulations are conducted to show that the theoretical results are valid.
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The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency…
Abstract
The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter
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Joshua C. C. Chan, Chenghan Hou and Thomas Tao Yang
Importance sampling is a popular Monte Carlo method used in a variety of areas in econometrics. When the variance of the importance sampling estimator is infinite, the central…
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Importance sampling is a popular Monte Carlo method used in a variety of areas in econometrics. When the variance of the importance sampling estimator is infinite, the central limit theorem does not apply and estimates tend to be erratic even when the simulation size is large. The authors consider asymptotic trimming in such a setting. Specifically, the authors propose a bias-corrected tail-trimmed estimator such that it is consistent and has finite variance. The authors show that the proposed estimator is asymptotically normal, and has good finite-sample properties in a Monte Carlo study.
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The purpose of this paper is to investigate the fatigue crack growth (FCG) under random loading using analytical methods.
Abstract
Purpose
The purpose of this paper is to investigate the fatigue crack growth (FCG) under random loading using analytical methods.
Design/methodology/approach
For this purpose, two methods of cycle-by-cycle technique and central limit theorem (CLT) were used. The Walker equation was used to consider the stress ratio effect on the FCG rate. In order to validate the results in three random loading group with different loading levels and bandwidths, the results of the analysis, such as the mean lifetime of the specimen and the average crack length were compared with the test results in terms of the number of loading cycles.
Findings
The comparison indicated a good agreement between the results of the analysis and the test. Further, the diagrams of reliability and the probability of failure of the specimen were obtained for each loading group and were compared together.
Originality/value
Applying the cycle-by-cycle and CLT methods for the calculation of fatigue reliability of a CT specimen under random loading by the Walker equation and comparing their results with each other is not observed in other researches. Also in this study, the effect of the loading frequency bandwidth on lifetime was studied.
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Federico Echenique and Ivana Komunjer
In this article we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable implications…
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In this article we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable implications of the MCS prediction: that the extreme (high and low) conditiona l quantiles of the dependent variable increase monotonically with the explanatory variable. The main contribution of the article is to derive a likelihood-ratio test, which to the best of our knowledge is the first econometric test of MCS proposed in the literature. The test is an asymptotic “chi-bar squared” test for order restrictions on intermediate conditional quantiles. The key features of our approach are: (1) we do not need to estimate the underlying nonparametric model relating the dependent and explanatory variables to the latent disturbances; (2) we make few assumptions on the cardinality, location, or probabilities over equilibria. In particular, one can implement our test without assuming an equilibrium selection rule.
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