We propose a new class of trans-Gaussian random fields named Tukey g-and-h (TGH) random fields to model non-Gaussian spatial data. The proposed TGH random fields have extremely flexible marginal distributions, possibly skewed and/or heavy-tailed, and, therefore, have a wide range of applications. The special formulation of the TGH random field enables an automatic search for the most suitable t...

We present a new algorithm for Tukey (halfspace) depth level sets and its implementation. Given d-dimensional data set for any d ≥ 2, the algorithm is based on representation of level sets as intersections of balls in R, and can be easily adapted to related depths (Type D, Zuo and Serfling (Ann. Stat. 28 (2000), 461–482)). The algorithm complexity is O(dn + n log n) where n is the data set size...

This is a survey of recent work on the structure of Tukey reductions among analytic σ-ideals of compact subsets of compact metric spaces and analytic P-ideals of sets of natural numbers. An attempt is made to organize the results into a unified whole. This organization makes it possible to identify natural unresolved problems. Some new joint results with Stevo Todorcevic are announced. This pap...

5. LAUSBERG, T. 1935. Quantitative Untersuchungen uber die kutikulare Exkretion der Laubblatter. Jahrb. Wiss. Botan. 81: 769-806. 6. SCHOCH, K. 1955. Erfassung der kutikularen Rekretion von K and Ca. Ber. Schweiz. Botan. Ges. 65: 205-50. 7. TUKEY, H. B., JR. AND J. V. MORGAN. 1964. The occurrence of leaching from above-ground plant parts and the nature of the materials leached. Proc. XVI Intern...

The deliberate introduction of controlled intersymbol interference (ISI) in Tukey signalling enables the recovery signal amplitude and (in part) phase under direct detection, giving rise to significant data rate improvements compared intensity modulation with detection (IMDD). use an integrate-and-dump detector makes precise waveform shaping unnecessary, thereby equipping scheme a high degree r...

We investigate the asymptotic behavior of two types of Tukey depth-based multivariate trimmed means. Sufficient conditions for asymptotic normality of these location estimators are given. Two approaches to trimming are distinguished and central limit theorems are derived for each one. Asymptotic normality is proved using Hadamard differentiability of the location functionals. In the one-dimensi...

In 1965 J. Cooley and J. Tukey published an article detailing an efficient algorithm to compute the Discrete Fourier Transform, necessary for processing the newly available reams of digital time series produced by recently invented analog-to-digital converters. Since then, the Cooley– Tukey Fast Fourier Transform and its variants has been a staple of digital signal processing. Among the many ca...

The publication by Cooley and Tukey [5] in 1965 of an e cient algorithm for the calculation of the DFT was a major turning point in the development of digital signal processing. During the ve or so years that followed, various extensions and modi cations were made to the original algorithm [6]. By the early 1970's the practical programs were basically in the form used today. The standard develo...

Motivated by a question of Isbell, we show that ♦ implies there is a non-P-point U ∈ βω \ ω such that neither 〈U ,⊇〉 nor 〈U ,⊇∗〉 is Tukey equivalent to 〈[c],⊆〉. We also show that 〈U ,⊇∗〉 ≡T 〈[c] ,⊆〉 for some U ∈ βω \ ω, assuming cf(κ) = κ ≤ p = c. We also prove two negative ZFC results about the possible Tukey classes of ultrafilters on ω.