Papers published on a yearly basis
Papers
Journal Article•
TL;DR: In this article, the authors proposed a wavelet shrinkage method that incorporates information on neighboring coe cients into the decision making, and investigated the asymptotic and numerical performances of two particular versions of the estimator.
Abstract: In standard wavelet methods, the empirical wavelet coe cients are thresholded term by term, on the basis of their individual magnitudes. Information on other coe cients has no in uence on the treatment of particular coe cients. We propose a wavelet shrinkage method that incorporates information on neighboring coe cients into the decision making. The coe cients are considered in overlapping blocks; the treatment of coe cients in the middle of each block depends on the data in the whole block. The asymptotic and numerical performances of two particular versions of the estimator are investigated. We show that, asymptotically, one version of the estimator achieves the exact optimal rates of convergence over a range of Besov classes for global estimation, and attains adaptive minimax rate for estimating functions at a point. In numerical comparisons with various methods, both versions of the estimator perform excellently.
388 citations
TL;DR: In this paper, it was shown that the Gamma distribution is a boundedly complete sufficient statistic, and that it is sufficient and sufficient to have the distribution of a statistic T 1 be independent of the sample variance s 2.
Abstract: If {Ρ θ}, θЄΩ, be a family of probability measures on an abstract sample space \(\mathcal {G}\) and Τ be a sufficient statistic for θ then for a statistic T 1 to be stochastically independent of Τ it is necessary that the probability distribution of T 1 be independent of θ. The condition is also sufficient if Τ be a boundedly complete sufficient statistic. Certain well-known results of distribution theory follow immediately from the above considerations. For instance, if x 1, x 2,. . . , x n , are independent Ν(μ, σ)’s then the sample mean \(\bar x\) and the sample variance s 2 are mutually independent and are jointly independent of any statistic f (real or vector valued) that is independent of change of scale and origin. It is also deduced that if x 1, x 2, . . ., x n are independent random variables such that their joint distribution involves an unknown location parameter θ then there can exist a linear boundedly complete sufficient statistic for θ only if the x’s are all normal. Similar characterizations for the Gamma distribution also are indicated.
250 citations
Journal Article•
144 citations
Journal Article•
TL;DR: The algorithm is a variant of the interior point algorithm described in Koenker and Portnoy (1997) for unconstrained quantile regression and is consequently quite efficient even for large problems, particularly when the inherent sparsity of the resulting linear algebra is exploited.
Abstract: . An algorithm for computing parametric linear quantile regression estimates subject to linear inequality constraints is described. The algorithm is a variant of the interior point algorithm described in Koenker and Portnoy (1997) for unconstrained quantile regression and is consequently quite efficient even for large problems, particularly when the inherent sparsity of the resulting linear algebra is exploited. Applications to qualitatively constrained nonparametric regression are described in the penultimate section. Implementations of the algorithm are available in MATLAB and R.
127 citations
Journal Article•
125 citations
Related Journals (5)
Journal of The Royal Statistical Society Series B-statistical Methodology
1.2K papers, 201K citations
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2018 | 4 |
| 2017 | 2 |
| 2016 | 3 |
| 2015 | 3 |
| 2014 | 6 |