Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Low, Mark G."'
Autor:
Low, Mark G., Ma, Zongming
Publikováno v:
Annals of Statistics 2015, Vol. 43, No. 4, 1448-1454
Discussion of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].
Comment: Published at http://dx.doi.org/10.1214/15-AOS1270D in the Annals of Statistics (http://w
Comment: Published at http://dx.doi.org/10.1214/15-AOS1270D in the Annals of Statistics (http://w
Externí odkaz:
http://arxiv.org/abs/1509.01904
Publikováno v:
Annals of Statistics 2013, Vol. 41, No. 2, 722-750
Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in terms of a
Externí odkaz:
http://arxiv.org/abs/1305.5673
Autor:
Cai, T. Tony, Low, Mark G.
Publikováno v:
Annals of Statistics 2011, Vol. 39, No. 2, 1012-1041
A general lower bound is developed for the minimax risk when estimating an arbitrary functional. The bound is based on testing two composite hypotheses and is shown to be effective in estimating the nonsmooth functional ${\frac{1}{n}}\sum|\theta_i|$
Externí odkaz:
http://arxiv.org/abs/1105.3039
Autor:
Low, Mark G., Zhou, Harrison H.
Publikováno v:
Annals of Statistics 2007, Vol. 35, No. 3, 1146-1165
This paper examines asymptotic equivalence in the sense of Le Cam between density estimation experiments and the accompanying Poisson experiments. The significance of asymptotic equivalence is that all asymptotically optimal statistical procedures ca
Externí odkaz:
http://arxiv.org/abs/0708.2233
Autor:
Cai, T. Tony, Low, Mark G.
Publikováno v:
Annals of Statistics 2006, Vol. 34, No. 5, 2298-2325
Adaptive estimation of a quadratic functional over both Besov and $L_p$ balls is considered. A collection of nonquadratic estimators are developed which have useful bias and variance properties over individual Besov and $L_p$ balls. An adaptive proce
Externí odkaz:
http://arxiv.org/abs/math/0702682
Publikováno v:
Annals of Statistics 2007, Vol. 35, No. 6, 2421-2449
For high dimensional statistical models, researchers have begun to focus on situations which can be described as having relatively few moderately large coefficients. Such situations lead to some very subtle statistical problems. In particular, Ingste
Externí odkaz:
http://arxiv.org/abs/math/0612623
Autor:
Cai, T. Tony, Low, Mark G.
Publikováno v:
Annals of Statistics 2006, Vol. 34, No. 1, 202-228
Adaptive confidence balls are constructed for individual resolution levels as well as the entire mean vector in a multiresolution framework. Finite sample lower bounds are given for the minimum expected squared radius for confidence balls with a pres
Externí odkaz:
http://arxiv.org/abs/math/0605462
Autor:
Cai, T. Tony, Low, Mark G.
Publikováno v:
Annals of Statistics 2005, Vol. 33, No. 6, 2930-2956
Estimation of a quadratic functional over parameter spaces that are not quadratically convex is considered. It is shown, in contrast to the theory for quadratically convex parameter spaces, that optimal quadratic rules are often rate suboptimal. In s
Externí odkaz:
http://arxiv.org/abs/math/0603134
Autor:
Cai, T. Tony, Low, Mark G.
Publikováno v:
Annals of Statistics 2005, Vol. 33, No. 5, 2311-2343
Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two parameter sp
Externí odkaz:
http://arxiv.org/abs/math/0602299
Autor:
Cai, T. Tony, Low, Mark G.
Publikováno v:
Annals of Statistics 2005, Vol. 33, No. 1, 184-213
A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for the evaluati
Externí odkaz:
http://arxiv.org/abs/math/0504508