Boundary noncrossings of additive Wiener fields∗

Hashorva, Enkelejd; Mishura, Yuliya

doi:10.1007/s10986-014-9243-y

Cited by 8 publications

(13 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section other formulas for the upper and lower bounds of the power of KS and CvM tests involving thedimensional set-indexed Brownian sheet and pillow models are derived. Our results are obtained by generalizing the approach proposed in that studied in [18,19] who confined the investigation to one-dimensional Kolmogorov type boundary noncrossing probability involving the so-called univariate ordinary Brownian sheet and pillow.…”

Section: Alternative Approachesmentioning

confidence: 92%

“…As suggested in [14], p. 315, and [15], p. 423-424, studying the power function is of importance to be able to evaluate the performance of the test especially their rate of decay to . Therefore in this paper we investigate the upper and lower bounds for (6) by considering the result for the univariate Brownian sheet and Brownian pillow presented in Janssen [17] and Hashorva [18,19]. Upper and lower bound for the power function of goodness-of-fit test involving multiparameter Brownian process have been studied by Bass [20].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Accessing the Power of Tests Based on Set-Indexed Partial Sums of Multivariate Regression Residuals

Somayasa

2018

Journal of Applied Mathematics

View full text Add to dashboard Cite

The intention of the present paper is to establish an approximation method to the limiting power functions of tests conducted based on Kolmogorov-Smirnov and Cramér-von Mises functionals of set-indexed partial sums of multivariate regression residuals. The limiting powers appear as vectorial boundary crossing probabilities. Their upper and lower bounds are derived by extending some existing results for shifted univariate Gaussian process documented in the literatures. The application of multivariate Cameron-Martin translation formula on the space of high dimensional set-indexed continuous functions is demonstrated. The rate of decay of the power function to a presigned value α is also studied. Our consideration is mainly for the trend plus signal model including multivariate set-indexed Brownian sheet and pillow. The simulation shows that the approach is useful for analyzing the performance of the test.

show abstract

Section: Alternative Approachesmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Accessing the Power of Tests Based on Set-Indexed Partial Sums of Multivariate Regression Residuals

Somayasa

2018

Journal of Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…Assume that (D) holds and u is a lower semicontinuous function satisfying (U). Then for any γ ∈ M + (T 1 ) and f = Rγ the asymptotic expansion (14) holds withγ = γ.…”

Section: Sharp Asymptoticsmentioning

confidence: 98%

“…Let (D) and (P) hold, f ∈ H X and let u be a lower semicontinuous function satisfying (U). If furtherγ is the projection of 0 to the set C f , then(14) holds.…”

mentioning

confidence: 99%

Boundary Non-crossing Probabilities of Gaussian Processes: Sharp Bounds and Asymptotics

2020

Self Cite

View full text Add to dashboard Cite

We study boundary non-crossing probabilitiesfor continuous centered Gaussian process X indexed by some arbitrary compact separable metric space T. We obtain both upper and lower bounds for P f,u . The bounds are matching in the sense that they lead to precise logarithmic asymptotics for the large-drift case P cf,u , c → +∞, which are two-term approximations (up to o(c)). The asymptotics are formulated in terms of the solutionf to the constrained optimization problem h HX → min, h ∈ H X , h ≥ f in the reproducing kernel Hilbert space H X of X. Several applications of the results are further presented.2010 Mathematics Subject Classification. 60G15; 60G70; 60F10.

show abstract

“…Although an analytical formula for h ⇤ may not be available, it can always be computed by approximation (see Section 1.1 in de Berg et al, 2008). Such h ⇤ is referred to as the largest convex minorant of h, and it is the most cost-e cient path (in the sense of ||h 0 || 2 ; see Hashorva and Mishura, 2014) from (0, 0) to (1, 1) dominated by h.…”

Section: The Family Of Distortion Risk Measures Includes Commonly Usementioning

confidence: 99%

How Superadditive Can a Risk Measure Be?

2013

View full text Add to dashboard Cite

This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract In this paper, we study the extent to which any risk measure can lead to superadditive risk assessments, implying the potential for penalizing portfolio diversification. For this purpose we introduce the notion of extreme-aggregation risk measures. The extreme-aggregation measure characterizes the most superadditive behavior of a risk measure, by yielding the worst-possible diversification ratio across dependence structures. One of the main contributions is demonstrating that, for a wide range of risk measures, the extreme-aggregation measure corresponds to the smallest dominating coherent risk measure. In our main result, it is shown that the extremeaggregation measure induced by a distortion risk measure is a coherent distortion risk measure. In the case of convex risk measures, a general robust representation of coherent extreme-aggregation measures is provided. In particular, the extreme-aggregation measure induced by a convex shortfall risk measure is a coherent expectile. These results show that, in the presence of dependence uncertainty, quantification of a coherent risk measure is often necessary, an observation that lends further support to the use of coherent risk measures in portfolio risk management. Permanent repository link

show abstract

Boundary noncrossings of additive Wiener fields∗

Cited by 8 publications

References 29 publications

Accessing the Power of Tests Based on Set-Indexed Partial Sums of Multivariate Regression Residuals

Accessing the Power of Tests Based on Set-Indexed Partial Sums of Multivariate Regression Residuals

Boundary Non-crossing Probabilities of Gaussian Processes: Sharp Bounds and Asymptotics

How Superadditive Can a Risk Measure Be?

Contact Info

Product

Resources

About