Asymptotic normality of convergent estimates of conditional quantiles

By Alain F. Berlinet, Ali Gannoun, Eric Atzner-løber. 2001

54 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/30dc8746f399c900a5166e5750eed35ff8c88ebb

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Citations in the corpus

Kernel estimators of extreme level curves (2011, background): “Many authors are interested in this type of estimator for fixed α ∈ (0, 1): weak and strong consistency are proved respectively in [40] and [16], asymptotic normality being established in [41, 38, 4].”
On kernel smoothing for extremal quantile regression (2012, unknown): “Many papers are dedicated to the asymptotic properties of this type of estimator for fixed α ∈ (0,1): weak and strong consistency are proved, respectively, in [30] and [13], asymptotic normality being established in [3,28,31].”
Functional kernel estimators of large conditional quantiles (2011, background): “This result coincides with [3], Theorem 6.”
On Additive Conditional Quantiles With High-Dimensional Covariates (2003, background): “0 in probability (see, e.g., Berlinet, Gannoun, and Matzner-Løber 2001; De Gooijer et al. 2002 for a similar proof).”
Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models (2006, background): “Here also, as far as we know, the literature on (conditional and/or unconditional) quantile estimation is quite important when the explanatory variable X is real (see for instance Samanta [29], for previous results and Berlinet et al. [ 3 ], for recent advances and references).”
Nonparametric prediction by conditional median and quantiles (2003, methodology): “Under the conditions of Theorem 3 and by using Theorem 1 and Lemma 3 of Berlinet et al. (1998), we have that fn( 1; n(x) | x) converges to f( (x) | x), and gn(x) converges to g(x), in probability.”
Modelling beyond regression functions: an application of multimodal regression to speed–flow data (2006, unknown): “As observed by Berlinet et al. (1998, 2001) in the context of nonparametric regression, and Hyndman (1995) and MatznerLøber et al. (1998) in the context of nonparametric forecasting, the conditional mode has clear advantages when the conditional distributions and the forecast densities respectively…”
Asymptotic Results of a Nonparametric Conditional Quantile Estimator for Functional Time Series (2008, methodology): “…simple algebra show that: al = axl = d ∫ 1 0 Kl u ud−1du = 1 C d ∫ u ≤1 Kl u du for, l = 1 2 and a2 a21 = ∫ d K2 u du therefore 2 x p x = p 1− p g x f 2 p x x ∫ d K2 u du Note that this is the very expression of variance obtained by Berlinet et al. (2001) in their Theorem 6.4 in finite dimension.”