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# A Berry--Esseen theorem for weakly negatively dependent random variables and its applications

Acta Mathematica Hungarica
Authors: Jianfeng Wang and Lixin Zhang

## Summary

We provide uniform rates of convergence in the central limit theorem for linear negative quadrant dependent (LNQD) random variables. Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\{X_{n},\allowbreak n\ge1\}$ \end{document} be a LNQD sequence of random variables with \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $EX_{n}=0$ \end{document}, set \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $S_{n}=\sum_{j=1}^{n}X_{j}$ \end{document} and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $B_{n}^{2}=\text{Var}\, (S_{n})$ \end{document}. We show that \begin{gather*} \sup_{x} \left|P\left(\frac{S_{n}}{B_{n}}<x\right)-\Phi(x)\right|= O\bigg(n^{-\delta/(2+3\delta)}\vee \frac{n^{3\delta^{2}/(4+6\delta)}}{B^{2+\delta}_{n}} \sum_{i=1}^{n} E{|X_{i}|}^{2+\delta}\bigg) \end{gather*} under finite \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $(2+\delta)$ \end{document}th moment and a power decay rate of covariances. Moreover, by the truncation method, we obtain a Berry--Esseen type estimate for negatively associated (NA) random variables with only finite second moment. As applications, we obtain another convergence rate result in the central limit theorem and precise asymptotics in the law of the iterated logarithm for NA sequences, and also for LNQD sequences.

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# Prices and impact factors of interdisciplinary social science journals

Scientometrics
Author: A. Michalos

## Abstract

An examination of the relationships between journal impact factors and individual subscription prices of interdisciplinary social science journals revealed a very small and statistically nonsignificant negative association.

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# Spanish validation of the pathological buying screener in patients with eating disorder and gambling disorder

Authors: Fernando Fernández-Aranda, Roser Granero, Gemma Mestre-Bach, Trevor Steward, Astrid Müller, Matthias Brand, Teresa Mena-Moreno, Cristina Vintró-Alcaraz, Amparo del Pino-Gutiérrez, Laura Moragas, Núria Mallorquí-Bagué, Neus Aymamí, Mónica Gómez-Peña, María Lozano-Madrid, José M. Menchón, and Susana Jiménez-Murcia

sample, the factor loss of control / consequences obtained positive associations with all SCL-90-R scales and novelty seeking, and negative associations with self-directedness and cooperativeness. The factor excessive buying behavior only obtained

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# Exploring relationships between problem gambling, scratch card gambling, and individual differences in thinking style

Authors: Madison Stange, Alexander C. Walker, Derek J. Koehler, Jonathan A. Fugelsang, and Mike J. Dixon

. Discussion Across three studies, we observed a number of consistent relationships between various gambling-related and individual difference measures. These included twice-replicated negative associations between CRT and participants’ frequency of

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# The crucial role of recovery capital in individuals with a gambling disorder

Author: Belle Gavriel-Fried

resulting model was equivalent to the original model, its fit indices were the same as reported above. In this model, the paths from RC to the three dependent variables of GD severity, depression, and anxiety were significant (all p ’s < .001). Negative

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# An  Empirical Test of a Possible Solution to “the Central Theoretical Problem of Human Sociobiology”

Journal of Cultural and Evolutionary Psychology
Author: Satoshi Kanazawa

Kanazawa (2004) suggests that there is a negative association between social class and reproduction because lower-class individuals, who tend to have lower general intelligence, have greater difficulty employing evolutionarily-novel modern contraception. I derive three hypotheses from Kanazawa's theory: 1) There are no class differences in the numAber of desired children; 2) The effect of sexual activity on reproduction is weaker among the more intelligent; and 3) The interaction between sexual activity and intelligence is stronger among men. The analyses of the U.S. General Social Surveys support all three hypotheses.

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# Spatial regression analysis between air pollution and childhood leukaemia in Portugal

Journal of Radioanalytical and Nuclear Chemistry
Authors: M. Martinho and M. Freitas

## Abstract

This study aims to investigate whether known carcinogenic chemical elements in atmospheric deposition might be associated with child mortality due to leukemia in the Portuguese population. A Bayesian hierarchical model was used to explore the association between lichen biomonitoring measurements of four elements—As, Hg, Ni, Pb—and childhood leukemia death counts taken at small administrative units. This geographical epidemiological study found a non-significant positive association between the risk of childhood leukemia and levels of arsenic, mercury and lead, and a non-significant negative association between the disease and the level of nickel. Lead seems to show a weaker association with childhood leukemia than arsenic and mercury.

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# Environmental effects on associations among nitrogen use efficiency traits in wheat

Cereal Research Communications
Authors: B. Gorjanović, M. Kraljević-Balalić, and S. Janković

Nitrogen use efficiency parameters of twelve bread wheat cultivars were studied in nine environments comprised of three nitrogen applications tested over three years. An environment-by-trait association biplot and a trait-association by environment biplot were applied to understand environmental effects on these traits and relationships among them. The following trait associations were relatively stable across environments: negative associations of straw nitrogen content vs. nitrogen remobilization efficiency, straw nitrogen content vs. nitrogen harvest index and a positive association of nitrogen remobilization efficiency vs. nitrogen harvest index. The selection of genotypes with a high nitrogen harvest index and nitrogen remobilization efficiency could be used in the development of cultivars with desired nitrogen use efficiency. A low straw nitrogen content can also be used as a reliable and cost-effective indicator in the selection of genotypes with high nitrogen use efficiency.

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# Grain filling variation in winter wheat, barley and triticale in pannonian environments

Cereal Research Communications
Authors: M. Mirosavljević, V. Momčilović, P. Čanak, D. Trkulja, S. Mikić, B. Jocković, and N. Pržulj

Knowledge about the comparative development and grain filling of winter cereals under different environmental conditions is important for stable and high yielding crop production. The objective of this work was to compare patterns of grain filling in bread wheat, barley and triticale grown in the Pannonian region, as well as to investigate relationships among grain filling parameters, time to anthesis and grain yield. The trials with 12 winter cereal genotypes were carried out in four successive seasons at the location Novi Sad, Serbia. Results of this study showed that all studied grain filling parameters were significantly influenced by species, cultivar, growing season, and species by growing season interaction. Longer duration of grain filling period and period to maximum grain filling were observed in triticale and wheat cultivars compared with six and two-rowed barley. Two-rowed barley cultivars had a higher grain filling rate than other cultivars. Furthermore, a negative association between time to anthesis and grain yield indicates that cultivars with the long preanthesis period are not recommended for the agro-ecological conditions of the Pannonian plain. Generally, medium early cultivars of small grain cereals had the highest grain weight within species and spike type, suggesting that medium early cultivars have a balanced ratio of pre-anthesis and grain filling period. High values of final grain weight in different growing seasons indicate that weather conditions in the Pannonian plain are mainly suitable for grain growth.

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# Association between grain yield, grain quality and morpho-physiological traits along ten cycles of recurrent selection in bread wheat (Triticum aestivum L.)

Cereal Research Communications
Authors: R.H. Maich, M.E. Steffolani, J.A. Di Rienzo, and A.E. León

The objective of the present investigation was to examine the relationships between agronomical behavior and grain quality along ten cycles of a recurrent selection program performed under rainfed condition. Twenty-four lines, four for each one of the 0, 2, 4, 6, 8 and 10 cycles of recurrent selection, were evaluated for two consecutive years (2011 and 2012). The experimental lines were evaluated under conventional (CT) and no tillage (NT) systems. Grain yield and grain weight were determined and harvest index and grain number estimated. Flour protein content, sodium dodecyl sulphate sedimentation (IS-SDS) and lactic acid SRC (LASRC) were considered as end-use quality predictive tests. The Spearman correlation coefficient was used to measure the relationships among yield, its components and grain quality parameters. Within the context of CT, flour protein content was negatively associated with all the agronomic variables. The IS-SDS has a negative association with the grain weight; meanwhile, LASRC associated positively with all the agronomic variables. When wheat was grown in NT, the relationship between IS-SDS and harvest index, like LASRC with all agronomic traits, was positive. Confining the discussion to the CT results, after ten cycles of recurrent selection the highest grain yield achieved was accompanied by a decrease in protein percentage. However, the decrease in the percentage of protein in more advanced selection cycles was offset by an improvement of its quality.

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