Functional limit laws for the increments of the quantile process; with applications

We establish a functional limit law of the logarithm for the increments of the normed quantile process based upon a random sample of size $n\to\infty$. We extend a limit law obtained by Deheuvels and Mason (12), showing that their results hold uniformly over the bandwidth $h$, restricted to vary in $[h'_n,h''_n]$, where $\{h'_n\}_{n\geq1}$ and $\{h''_n\}_{n\geq 1}$ are appropriate non-random sequences. We treat the case where the sample observations follow possibly non-uniform distributions. As a consequence of our theorems, we provide uniform limit laws for nearest-neighbor density estimators, in the spirit of those given by Deheuvels and Mason (13) for kernel-type estimators.Comment: Published in at http://dx.doi.org/10.1214/07-EJS099 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Formation of the Soil

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Excerpts from the Novel, Bear War-den

A woman park warden who works in Rocky Mountain National Park spends her time on such tasks as bear patrol, locating tourists who are lost or in other physical danger, and policing park rules. She has a particular affinity for grizzly bears, largely stemming from an experience she had in a Neolithic cave in Spain. During her work and her travels, she observes various ways in which bears are mistreated in parks, sometimes even by researchers with seemingly good intentions. While an out-of-control fire rages through the national park, the woman park warden, with two grizzly bear skulls in hand, begins a difficult and dream-like journey to the park boundary—where wild animals can seem like ghosts and trauma can strike as suddenly as lightning

The Influence of School Segregation on Students’ Educational Achievement

This literature review evaluates how race, geographical location, and socioeconomic status impacts a student’s educational achievement. These variables affect educational success, which is impacted by the history of housing and racial segregation in the United States. The discussion will include why schools are segregated and how this has an impact on a student’s education by looking at different studies and theories such as the Black Culture theory and the Acting White Hypothesis. Even in desegregated schools, “tracking” separates and further segregates races in the educational system. The literature review concludes with a summary of the findings, importance, and future research that can be done in this field including equal funding for public schools across Americ

Hadamard matrices modulo p and small modular Hadamard matrices

We use modular symmetric designs to study the existence of Hadamard matrices modulo certain primes. We solve the $7$-modular and $11$-modular versions of the Hadamard conjecture for all but a finite number of cases. In doing so, we state a conjecture for a sufficient condition for the existence of a $p$-modular Hadamard matrix for all but finitely many cases. When $2$ is a primitive root of a prime $p$, we conditionally solve this conjecture and therefore the $p$-modular version of the Hadamard conjecture for all but finitely many cases when $p \equiv 3 \pmod{4}$, and prove a weaker result for $p \equiv 1 \pmod{4}$. Finally, we look at constraints on the existence of $m$-modular Hadamard matrices when the size of the matrix is small compared to $m$.Comment: 14 pages; to appear in the Journal of Combinatorial Designs; proofs of Lemma 4.7 and Theorem 5.2 altered in response to referees' comment

The Formation of the Soil

PDF pages: 1