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Remarks on a Multivariate Transformation

Murray Rosenblatt
- 01 Sep 1952 - 
- Vol. 23, Iss: 3, pp 470-472
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This article is published in Annals of Mathematical Statistics.The article was published on 1952-09-01 and is currently open access. It has received 2735 citations till now. The article focuses on the topics: Transformation (function).

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Environmental contours using copulas

TL;DR: In this work, some classes of bivariate copulas are considered for modeling the dependence structure of the environmental variables, and measures of association, rank-based methods for estimation of copula, goodness of fit tests for copulas, and copula selection criteria are examined and applied to metocean data from hindcasts of tropical storms and extra-tropical events in the Gulf of Mexico.
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Does crude oil price play an important role in explaining stock return behavior

TL;DR: In this article, the authors analyzed the impact of crude oil price shock on stock return dynamics using the MS-ARJI-GJR-GARCH-X model, in which the parameters for the jump process, the asymmetric GARCH effect and the impacts of oil price shocks are regime-dependent.
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An evaluation of tests of distributional forecasts

TL;DR: In this paper, the power of five statistics (including the Kolmogorov-Smirnov (KS) statistic) to reject uniformity of the pits in the presence of misspecification in the mean, variance, skewness or kurtosis of the forecast errors was investigated.
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Universal Residuals: A Multivariate Transformation.

TL;DR: This paper generalizes Rosenblatt's transformation so that it applies to arbitrary probability models, providing a tool for exploratory data analysis and formal goodness-of-fit testing for a very general class of probability models.
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Evaluating the Calibration of Multi-Step-Ahead Density Forecasts Using Raw Moments

TL;DR: In this paper, the authors proposed a new testing approach based on raw moments, which is extremely easy to implement, uses standard critical values, can include all moments regarded as important, and has correct asymptotic size.