In this paper a family of estimators for estimating mean, ratio and product of two means of a finite population has been suggested and studied under the two different situations of random non-response considered by Tracy and Osahan (1994), Singh and Joarder (1998) and Singh, Joarder and Tracy (2000). Asymptotic expressions of biases and mean squared errors of the proposed families have been der...

Outline drawings in a raised form were made by a blind woman, Tracy, who has been blind from very early in life. Highly practiced in drawing, she reports she is largely self-taught. To invoke matters of projection, she was asked to represent an object with faces slanting away from the observer, a fixed array from different vantage points, and sets of objects in depth. In particular, she drew a ...

The one-dimensional polynuclear growth model with external sources at edges is studied. The height fluctuation at the origin is known to be given by either the Gaussian, the GUE Tracy-Widom distribution, or certain distributions called GOE2 and F0, depending on the strength of the sources. We generalize these results and show that the scaling limit of the multi-point equal time height fluctuati...

We prove that the largest eigenvalues of the beta ensembles of random matrix theory converge in distribution to the low-lying eigenvalues of the random Schrödinger operator − d dx2 + x+ 2 √ β bx restricted to the positive half-line, where b ′ x is white noise. In doing so we extend the definition of the Tracy-Widom(β) distributions to all β > 0, and also analyze their tails. Last, in a parallel...

Selecting N random points in a unit square corresponds to selecting a random permutation. Placing symmetry restrictions on the points, we obtain special kinds of permutations : involutions, signed permutations and signed involutions. We are interested in the statistics of the length (in numbers of points) of the longest up/right path in each symmetry type as the number of points increases to in...

In this paper we compute some of the higher order terms in the asymptotic behavior of the two point function P(A2(0)≤ s1,A2(t)≤ s2), extending the previous work of Adler and van Moerbeke (arXiv:math.PR/0302329; Ann. Probab. 33, 1326–1361, 2005) and Widom (J. Stat. Phys. 115, 1129–1134, 2004). We prove that it is possible to represent any order asymptotic approximation as a polynomial and integr...

Let X be a n × p matrix and l1 the largest eigenvalue of the covariance matrix X∗X . The “null case” where Xi,j ∼ N (0, 1) is of particular interest for principal component analysis. For this model, when n, p → ∞ and n/p → γ ∈ R∗+, it was shown in Johnstone (2001) that l1, properly centered and scaled, converges to the Tracy-Widom law. We show that with the same centering and scaling, the resul...

Ashkelon 8: The Islamic and Crusader Periods, by Tracy Hoffman. Final Reports of the Leon Levy Expedition to 8. Eisenbrauns, 2019. 800 pp., 1110 color 191 BW illusttrations, index. Hb. $149.95. ISBN-13: 9781575067353.