Uniformity in weak convergence

Billingsley, Patrick; Topsøe, Flemming

doi:10.1007/bf00532093

Cited by 85 publications

(56 citation statements)

References 7 publications

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“…These metrics are defined as follows (of. [16,27] It is known that/3 metrizes the topology of weak convergence on ~( Z ) [16] and that a sequence (/x,) in ~( Z ) converges to/x ~ ~( Z ) in the sense of the (pseudo-) metric a~ if (/x,) converges weakly to/x and if Y3 is a/x-uniformity class ( [7] and Remark 5.2). For interrelations of/3 and ~ to other probability metrics on ~( Z ) we refer to the literature [16,27] and to Remark 5.10.…”

Section: Introductionmentioning

confidence: 99%

Distribution sensitivity in stochastic programming

Römisch

Schultz

1991

Mathematical Programming

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In this paper, stochastic programming problems are viewed as parametric programs with respect to the probability distributions of the random coefficients. General results on quantitative stability in parametric optimization are used to study distribution sensitivity of stochastic programs. For recourse and chance constrained models quantitative continuity results for optimal values and optimal solution sets are proved (with respect to suitable metrics on the space of probability distributions). The results are useful to study the effect of approximations and of incomplete information in stochastic programming.

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Section: Introductionmentioning

confidence: 99%

Distribution sensitivity in stochastic programming

Römisch

Schultz

1991

Mathematical Programming

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“…In Dehardt (1971) the proof of uniform convergence relies on the monotonicity of a family of functions under a fixed invariant distribution. Also, Billingsley and Topsoe (1967) prove various uniform convergence results for compact classes of functions. All these results fall short of what is generally required to substantiate con-sistency for simulation-based estimators in which the uniform convergence of the simulated statistics must hold over a continuum of invariant distributions.…”

Section: Introductionmentioning

confidence: 93%

Simulation-based estimation of dynamic models with continuous equilibrium solutions

Santos

2004

Journal of Mathematical Economics

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This paper presents several results on consistency properties of simulation-based estimators for a general class of dynamic models with continuous laws of motion. The consistency of these estimators follows from a uniform convergence property of the model's sample paths over the vector of parameters. This convergence property is established under either contractivity or monotonicity conditions on the dynamics of the system.

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“…The shortcoming of the test <I> at 9 is denoted by y(<j>,9) and defined by y(<j>, 9) This definition implies that y(<j>,9) ~ 0 for all 9 belonging to 8A and for all level a tests <j>. The maximum shortcoming of the test <I> when 9 ranges * over GA is denoted by y ($):…”

Section: Most Stringent and Everywhere Asymptotically Most Stringent mentioning

confidence: 99%