Hasil untuk "math.ST"

A. Gelman

Discussion of ``Analysis of variance--why it is more important than ever'' by A. Gelman [math.ST/0504499]

Ji-Eun Choi, D. Shin

Bootstrapping tests are implemented for the tests U by Schmidt [Detecting changes in the trend function of heteroscedastic time series; 2021. Preprint: arXiv:2108.09206 [math.ST]] for mean break and Schmidt et al. [An asymptotic test for constancy of the variance under short-range dependence. Ann Stat. 2021;49:3460–3481.] for variance break based on U-statistics. The tests U have good powers against epidemic breaks that are common in practice. The test U for variance break is proved to have the nice property of consistency against a general class of alternatives. However, the tests U have non-ignorable finite sample size distortion under serial correlation and/or conditional heteroscedasticity. Our implementation based on autoregressive residual bootstrapping and moving block bootstrapping are shown to remedy the size distortion problems of U for mean break and for variance break, respectively, in a Monte-Carlo experiment. The experiment also demonstrates the power advantages of bootstrapping tests over the original tests and other standard break tests against epidemic breaks, which, however, are accompanied by disadvantages against simple single breaks. The proposed bootstrapping tests are well illustrated by break analyses of means and variances of the log-return and realized the volatility of the US S&P 500.

Y. Nefedova, I. Shevtsova

D. Pietrobon, A. Balbi, D. Marinucci

We cross correlate the new 3 year Wilkinson Microwave Anistropy Probe (WMAP) cosmic microwave background data with the NRAO VLA Sky Survey radio galaxy data and find further evidence of late integrated Sachs-Wolfe (ISW) effect taking place at late times in cosmic history. Our detection makes use of a novel statistical method (P. Baldi, G. Kerkyacharian, D. Marinucci, and D. Picard, math.ST/0606154 and P. Baldi, G. Kerkyacharian, D. Marinucci, D. Picard, math.ST/0606599) based on a new construction of spherical wavelets, called needlets. The null hypothesis (no ISW) is excluded at more than 99.7% confidence. When we compare the measured cross correlation with the theoretical predictions of standard, flat cosmological models with a generalized dark energy component parameterized by its density, {omega}{sub DE}, equation of state w and speed of sound c{sub s}{sup 2}, we find 0.3{<=}{omega}{sub DE}{<=}0.8 at 95% C.L., independently of c{sub s}{sup 2} and w. If dark energy is assumed to be a cosmological constant (w=-1), the bound on density shrinks to 0.41{<=}{omega}{sub DE}{<=}0.79. Models without dark energy are excluded at more than 4{sigma}. The bounds on w depend rather strongly on the assumed value of c{sub s}{sup 2}. We find that models with more negative equation ofmore » state (such as phantom models) are a worse fit to the data in the case c{sub s}{sup 2}=1 than in the case c{sub s}{sup 2}=0.« less

Victoria Zinde-Walsh

This is a companion note to Zinde-Walsh (2010), arXiv:1009.4217v1[MATH.ST], to clarify and extend results on identification in a number of problems that lead to a system of convolution equations. Examples include identification of the distribution of mismeasured variables, of a nonparametric regression function under Berkson type measurement error, some nonparametric panel data models, etc. The reason that identification in different problems can be considered in one approach is that they lead to the same system of convolution equations; moreover the solution can be given under more general assumptions than those usually considered, by examining these equations in spaces of generalized functions. An important issue that did not receive sufficient attention is that of well-posedness. This note gives conditions under which well-posedness obtains, an example that demonstrates that when well-posedness does not hold functions that are far apart can give rise to observable arbitrarily close functions and discusses misspecification and estimation from the stand-point of well-posedness.

S. Bityukov, N. Krasnikov, V. Smirnova et al.

In ref [math.ST/0411462] the notion of statistically dual distributions is introduced. The reconstruction of confidence density [AIP Conference Proceedings 803 (2005) 398] for the location parameter for several pairs of statistically dual distributions (Poisson and Gamma, normal and normal, Cauchy and Cauchy, Laplace and Laplace) in the case of single observation of the random variable is a unique. It allows to introduce the Transform between the space of observed values and the space of possible values of the parameter.

Bernard Ycart, Joel Ratsaby

Combinatorics

Ying Wei, Xuming He

Rejoinder: Conditional Growth Charts [math.ST/0702634]

Raymond J. Carroll, David Ruppert

Discussion of Conditional growth charts [math.ST/0702634]

Matias Salibian-Barrera, Ruben H. Zamar

Discussion of Conditional growth charts [math.ST/0702634]

Anneli Pere

Discussion of Conditional growth charts [math.ST/0702634]

Ming-Hui Chen, Sungduk Kim

Discussion of ``EQUI-energy sampler'' by Kou, Zhou and Wong [math.ST/0507080]

R. Holte

Comment: Elaboration on Two Points Raised in ``Classifier Technology and the Illusion of Progress'' [math.ST/0606441]

Ross W. Gayler

Comment on Classifier Technology and the Illusion of Progress--Credit Scoring [math.ST/0606441]

Yves F. Atchad'e, Jun S. Liu

We congratulate Samuel Kou, Qing Zhou and Wing Wong [math.ST/0507080] (referred to subsequently as KZW) for this beautifully written paper, which opens a new direction in Monte Carlo computation. This discussion has two parts. First, we describe a very closely related method, multicanonical sampling (MCS), and report a simulation example that compares the equi-energy (EE) sampler with MCS. Overall, we found the two algorithms to be of comparable efficiency for the simulation problem considered. In the second part, we develop some additional convergence results for the EE sampler.

Javier M. Moguerza, A. Muñoz

Rejoinder to ``Support Vector Machines with Applications'' [math.ST/0612817]

P. Minary, M. Levitt

Novel sampling algorithms can significantly impact open questions in computational biology, most notably the in silico protein folding problem. By using computational methods, protein folding aims to find the three-dimensional structure of a protein chain given the sequence of its amino acid building blocks. The complexity of the problem strongly depends on the protein representation and its energy function. The more detailed the model, the more complex its corresponding energy function and the more challenge it sets for sampling algorithms. Kou, Zhou and Wong [math.ST/0507080] have introduced a novel sampling method, which could contribute significantly to the field of structural prediction.

S. Kou, Qing Zhou, W. Wong

Rejoinder to ``Equi-energy sampler with applications in statistical inference and statistical mechanics'' by Kou, Zhou and Wong [math.ST/0507080]

S. Fienberg

Comment on Complex Causal Questions Require Careful Model Formulation: Discussion of Rubin on Experiments with ``Censoring'' Due to Death [math.ST/0612783]

Edward L. Korn

Comment on Causal Inference in the Medical Area [math.ST/0612783]