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In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological data. In the present work, we exploit the asymptotic uncorrelation of random needlet coefficients at fixed angular distances to construct subsampling statistics evaluated on Voronoi cells on the sphere. We illustrate how such statistics can be used for isotropy tests and for bootstrap estimation of nuisance parameters, even when a single realization of the spherical random field is observed. The asymptotic theory is developed in detail in the high resolution sense.
Subsampling is a computationally effective approach to extract information from massive data sets when computing resources are limited. After a subsample is taken from the full data, most available methods use an inverse probability weighted objectiv
We provide sufficient conditions for the asymptotic normality of the generalized correlation coefficient $sum a_{ij}b_{ij}$ under the permutation null distribution when $a_{ij}$s are symmetric and $b_{ij}$s are symmetric.
The infinite-dimensional Hilbert sphere $S^infty$ has been widely employed to model density functions and shapes, extending the finite-dimensional counterpart. We consider the Frechet mean as an intrinsic summary of the central tendency of data lying
The lace expansion for the Ising two-point function was successfully derived in Sakai (Commun. Math. Phys., 272 (2007): 283--344). It is an identity that involves an alternating series of the lace-expansion coefficients. In the same paper, we claimed
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference of mean v