Second Order Approximations for Slightly Trimmed Sums

We investigate the second order asymptotic behavior of trimmed sums T_n=\frac 1n \sum_{i=\kn+1}^{n-\mn}\xin, where \kn, \mn are sequences of integers, 0\le \kn < n-\mn \le n, such that \min(\kn, \mn) \to \infty, as \nty, the \xin's denote the order statistics corresponding to a sample $X_1,...,X_n$ of $n$ i.i.d. random variables. In particular, we focus on the case of slightly trimmed sums with vanishing trimming percentages, i.e. we assume that \max(\kn,\mn)/n\to 0, as \nty, and heavy tailed distribution $F$, i.e. the common distribution of the observations $F$ is supposed to have an infinite variance. We derive optimal bounds of Berry -- Esseen type of the order $O\bigl(r_n^{-1/2}\bigr)$, r_n=\min(\kn,\mn), for the normal approximation to $T_n$ and, in addition, establish one-term expansions of the Edgeworth type for slightly trimmed sums and their studentized versions. Our results supplement previous work on first order approximations for slightly trimmed sums by Csorgo, Haeusler and Mason (1988) and on second order approximations for (Studentized) trimmed sums with fixed trimming percentages by Gribkova and Helmers (2006, 2007).Comment: 37 pages, to appear in Theory Probab. App

Using Technology and Collaboration to Support Reading Comprehension

The purpose of this action research study was to determine if there is a connection between using technology and collaboration to help increase reading comprehension skills. A combination of research-based instructional strategies infused with technology was used over a ten-week period. Quantitative data was collected through weekly assessment scores. Analysis of the data concluded that students who were involved in an intervention program infused with technology and collaboration would have better knowledge of the story. After further analysis of the data it is concluded that students who were involved in this action research study improved their academic scores

MEASURING SCOPE AND SCALE EFFICIENCY GAINS DUE TO SPECIALIZATION

Using the non-parametric linear programming approach, this study examines overall efficiency gains due to diversification between crop and livestock enterprises for a sample of Kansas farms. Overall efficiency gains were decomposed into scope efficiency gains and scale efficiency gains. Farms with both crops and livestock were found to be less efficient than farms with just crops or just livestock. Operator age, profit margin, and farm size were significantly related to overall efficiency.Farm Management,

On estimation of Poisson intensity functions

Under the presence of only one realization, we consider a computationally simple algorithm for estimating the intensity function of a Poisson process with exponential quadratic and cyclic of fixed frequency trends. We argue that the algorithm can successfully be used to estimate any Poisson intensity function provided that it has a parametric form

Strong laws for generalized absolute Lorenz curves when data are stationary and ergodic sequences

We consider generalized absolute Lorenz curves that include, as special cases, classical and generalized L - statistics as well as absolute or, in other words, generalized Lorenz curves. The curves are based on strictly stationary and ergodic sequences of random variables. Most of the previous results were obtained under the additional assumption that the sequences are weakly Bernoullian or, in other words, absolutely regular. We also argue that the latter assumption can be undesirable from the applications point of vie