Scrambled net variance for integrals of smooth functions

By Art B. Owen. 1997

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Citations in the corpus

On the asymptotic distribution of scrambled net quadrature (2003, methodology): “The following theorem, which is from Owen (1997b), gives the exact rate of convergence for σ 20,m,s .”
Applications of randomized low discrepancy sequences to the valuation of complex securities (2000, background): “For instance, Owen (1997b) shows that for a su$ciently smooth integrand f ; i.e., the mixed partial derivative g(x)"Lsf (x)/Lxs is Lipschitz continuous which means that Dg(x)!g(xH)D4BDDx!xHDDb for some B50, b3(0,1]s and DDzDD is the Euclidean norm of z, the variance of the randomized net is of…”
Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences (2003, methodology): “theorists have made significant advances in RQMC techniques ( Owen, 1997, 1998; Morohosi”
Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands (2010, unknown): “In this paper, we have extended the results of [16, 18], by introducing an algorithm and proving that this algorithm can take advantage of the smoothness of the integrand α, where α ∈ N can be arbitrarily large.”
Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model (2001, background): “Further, Owen (1997, 1998) has shown recently that some scrambled versions of QMC sequences have a convergence rate of the order of N -3 . is the even distribution (or maximal spread) of the points in the integration space.”
Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration (2010, methodology): “Owen [206] first showed that scrambling can yield a convergence of O(N−3/2+δ) for any δ > 0 (here N δ stands for logN to some power).”
Walsh Spaces Containing Smooth Functions and Quasi-Monte Carlo Rules of Arbitrary High Order (2008, unknown): “Slight improvements for smoother functions can be achieved using randomizations (see for example [3, 39]), but no systematic exploitation of stronger smoothness assumptions has been achieved for digital nets or sequences.”
A multi-level cross-classified model for discrete response variables (2000, background): “Further, Owen (1995, 1997, 1998) has shown that some scrambled versions of quasi-random sequences have a convergence rate of (lnR)d-1/R3.”
Best practices for differentiated products demand estimation with PyBLP (2020, background): “54 Owen (1997) shows that randomizing qMC sequences in a particular manner can give a O ( I −3/2 t · (log It)K2 ) rate for smooth integrands as in (23c).”
Explicit Constructions of Quasi-Monte Carlo Rules for the Numerical Integration of High-Dimensional Periodic Functions (2007, methodology): “Using a digital ( t, α, m, s )-net with a scrambling algorithm (see [24]) on the other hand does not improve the performance in non-periodic spaces compared to ( t, m, s )-nets.”
Discrepancy Theory and Quasi-Monte Carlo Integration (2014, methodology): “The main idea is to design randomisations such that Owen’s lemma [90, Lemma 2] still holds.”
Control variates for quasi-Monte Carlo (2005, methodology): “The coefficientsMu can be found in Owen (1997b).”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, methodology): “It turns out that if we make further assumptions on f , the convergence rate of the variance can be improved to O(n−3+ǫ) [330].”