Approximating many-server queues by means of single-server queues

Arjas, Elja; Lehtonen, Tapani

doi:10.1017/s0001867800030329

Cited by 13 publications

(14 citation statements)

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“…The above construction was known for a long time; see for example Rosenblatt (1952), Wiener (1958) and Arjas and Lehtonen (1978). It can be used to simulate multivariate distributions (see e.g.…”

Section: Representation Theory Of Stationary Processesmentioning

confidence: 99%

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Asymptotic theory for stationary processes

2011

Statistics and Its Interface

105

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We present a systematic asymptotic theory for statistics of stationary time series. In particular, we consider properties of sample means, sample covariance functions, covariance matrix estimates, periodograms, spectral density estimates, U -statistics, kernel density and regression estimates of linear and nonlinear processes. The asymptotic theory is built upon physical and predictive dependence measures, a new measure of dependence which is based on nonlinear system theory. Our dependence measures are particularly useful for dealing with complicated statistics of time series such as eigenvalues of sample covariance matrices and maximum deviations of nonparametric curve estimates.

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Section: Representation Theory Of Stationary Processesmentioning

confidence: 99%

“…It can be used to simulate multivariate distributions (see e.g. Deák (1990), chapter 5) and Arjas and Lehtonen (1978). For more background see Wu and Mielniczuk (2010).…”

Section: Representation Theory Of Stationary Processesmentioning

confidence: 99%

Asymptotic theory for stationary processes

2011

Statistics and Its Interface

105

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“…For other uses of the standard construction see e.g. Arjas and Lehtonen (1978) and Li et al (1996). If (X i ) is a Markov chain, then in view of definition of G i as a conditional quantile (12) …”

Section: Multivariate Dependencementioning

confidence: 99%

A new look at measuring dependence

Mielniczuk

2010

Lecture Notes in Statistics

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This paper revisits the concept of dependence. We view statistical dependence as the state of variables being influenced by others. Our viewpoint accords well with the daily understanding of the notion of dependence, while classical dependence measures such as Pearson's correlation coefficient, Kendall's τ and Spearman's ρ have different meanings. With this understanding of dependence, we introduce new dependence measures which are easy to work with and they are useful for developing an asymptotic theory for complicated stochastic systems. We also explore relations of the introduced dependence concept with nonlinear system theory, experimental design, information theory and risk management.

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“…In this respect, three alternative constructions have been used. They are (i) standard construction (e.g., Arjas and Lehtonen (1978)), (ii) dynamic construction (e.g., Shaked and Shanthikumar (1985b)), and (iii) total hazard construction (e.g., Norros (1984), Shaked and Shanthikumar (1985a) When X and Y are both n-dimensional (as will be assumed throughout the paper), then the standard and the total hazard constructions (to be described below in detail) require U and V to be n-dimensional. The dynamic construction requires U and V to be of (the same) dimension n?…”

Section: Introductionmentioning

confidence: 99%

The Total Hazard Construction, Antithetic Variates and Simulation of Stochastic Systems.

Shaked¹,

Shanthikumar²

1985

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Approximating many-server queues by means of single-server queues

Cited by 13 publications

References 0 publications

Asymptotic theory for stationary processes

Asymptotic theory for stationary processes

A new look at measuring dependence

The Total Hazard Construction, Antithetic Variates and Simulation of Stochastic Systems.

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