Multiscale testing of qualitative hypotheses

By Lutz Dümbgen, Vladimir Spokoiny. 2001

222 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/df89d7f3778592da08a2fc2fd798e3c8c5844ade

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Citations in the corpus

Wild binary segmentation for multiple change-point detection (2014, background): “See also D¨umbgen and Spokoiny (2001) and Frick, Munk and Sieling (2014) for related discussions.”
Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors (2012, background): “9, 30, 36] for the entire empirical process and have applications to inference in nonparametric problems such as construction of uniform conﬁdence bands and testing qualitative hypotheses (see, e.g., [21, 25] and [18]). 1.1. Organization of the paper. In Section 2, we give the results on Gaussian ap”
On the Bernstein–von Mises phenomenon for nonparametric Bayes procedures (2013, background): “inciple abstract and dictated by the applications we have in mind. They are, however, closely connected to the frequentist literature on nonparametric multiscale inference, as developed in the papers [11], [9], [12], [10], [29], where also many further references can be found. This connection gives ”
Adaptive test of conditional moment inequalities (2011, background): “Finally, an important related paper in the statistics literature is [16].”
Nonparametric covariate-adjusted regression (2016, methodology): “…sign of EX by a standard test of hypothesis for the mean applied to the data X̃1, . . . , X̃n, and then test the sign of the function ϕ0 = ϕ · EX at (2.4), using for example tests such as those in Dümbgen and Spokoiny (2001), Chetverikov (2012) and Lee et al. (2013), applied to the observed data.”
Testing Many Moment Inequalities (2013, methodology): “The last assertion follows from application of Lemma 6.2 in Dümbgen and Spokoiny (2001).”
Testing convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function (2005, methodology): “For r = 1 (resp.r = 2) ands = 1, Dümbgen and Spokoiny (2001) obtained the uniform separation rateρn,r for testing monotonicity (resp. convexity) in the Gaussian white noise model.”
Heterogeneous change point inference (2015, background): “This is optimal in the sense that no signal with a smaller rate can be detected asymptotically with probability 1 (see Dümbgen and Spokoiny (2001), Chan and Walther (2013) and Frick et al. (2014)) for the case of homogeneous observations, and note that this is a submodel of our model.”
Optimal Confidence Bands for Shape-Restricted Curves (2003, methodology): “similarly as in Dümbgen and Spokoiny (2001). It follows from Theorem 2.”
A MOSUM procedure for the estimation of multiple random change points (2018, methodology): “Multiscale tests have also been proposed by [15], which can be used to test the null hypothesis of stationarity versus possible change point alternatives.”
Nonparametric Shape-Restricted Regression (2017, background): “.g., deconvolution problems (see e.g., [65,77]) and the classical Wicksell’s corpuscle problem (see e.g., [58,124]). There are many applications that involve testing with shape constraints; see e.g., [44,123,140] and the references therein. imsart-generic ver. 2014/10/16 file: ShapeReg-Arxiv-II.tex ”
A Nonparametric Approach to Measuring and Testing Curvature (2005, methodology): “For the univariate case, we compare our approach with the testing alternatives proposed by Diack (2001) and Dümbgen and Spokoiny (2001).”
Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings (2015, unknown): “Finally, non-centered empirical processes are useful for multi-scale testing where one combines many statistics corresponding to different scales into one test using scale-dependent critical value for each statistic; see [13] where such tests were used for qualitative hypotheses testing.”