Sequential fixed-width confidence bands for kernel regression estimation

We consider a random design model based on independent and identically distributed (iid) pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the unknown function m(x) when we have no precise information about the form of the true density, f(x) of X. We describe an estimation procedure of non-parametric regression model at a given point by some appropriately constructed fixed-width (2d) confidence interval with the confidence coefficient of at least 1−. Here, d(> 0) and 2 (0, 1) are two preassigned values. Fixed-width confidence intervals are developed using both Nadaraya-Watson and local linear kernel estimators of nonparametric regression with data-driven bandwidths.

The sample size was optimized using the purely and two-stage sequential procedure together with asymptotic properties of the Nadaraya-Watson and local linear estimators. A large scale simulation study was performed to compare their coverage accuracy. The numerical results indicate that the confidence bands based on the local linear estimator have the best performance than those constructed by using Nadaraya-Watson estimator. However both estimators are shown to have asymptotically correct coverage properties.

Sample size determination for kernel regression estimation using sequential fixed-width confidence bands

We consider a random design model based on independent and identically distributed pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the unknown function m(x) when we have no precise information about the form of the true density, f(x) of X. We describe an estimation procedure of non-parametric regression model at a given point by some appropriately constructed fixed-width (2d) confidence interval with the confidence coefficient of at least 1−. Here, d(> 0) and 2 (0, 1) are two preassigned values. Fixed-width confidence intervals are developed using both Nadaraya-Watson and local linear kernel estimators of nonparametric regression with data-driven bandwidths. The sample size was optimized using the purely and two-stage sequential procedures together with asymptotic properties of the Nadaraya-Watson and local linear estimators. A large scale simulation study was performed to compare their coverage accuracy. The numerical results indicate that the confi dence bands based on the local linear estimator have the better performance than those constructed by using Nadaraya-Watson estimator. However both estimators are shown to have asymptotically correct coverage properties.

Effect of moisture content on the physical properties of fibered flaxseed

The physical properties of fibered flaxseed were investigated within moisture content varying from 6.21 to 16.29%. The length, width, thickness and geometric mean diameter increased from 4.20 to 4.44mm, 1.99 to 2.13mm, 0.91 to 0.95mm, and 1.95 to 2.06mm, respectively in the moisture content range. One thousand seed weight increased linearly from 4.22 to 4.62g. The bulk density decreased from 726.783 to 611.872kg/m3, while the true density increased from 1165.265 to 1289.341kg/m3 in the moisture content range. The porosity values of flaxseed increased linearly from 37.67 to 52.54%. The highest static coefficient of friction was found on the plywood surface, while the lowest on the stainless steel surface. The static coefficient of friction increased from 0.467 to 0.972, 0.442 to 0.864, 0.492 to 0.927, and 0.490 to 0.845 for plywood, stainless steel, aluminum sheet and galvanized iron, respectively. The angle of repose increased linearly from 25.7° to 33.8° in the moisture content range. The results are necessary for design of equipment to handling, transportation, processing, and the storage of flaxseed.

Dingoes can help conserve wildlife and our methods can tell

Management of apex predators is among the most controversial wildlife management issues globally. In Australia, some ecologists have advocated using the dingo, Canis dingo, as a tool for conservation management, due to evidence that they suppress invasive mesopredators. Hayward & Marlow (Journal of Applied Ecology, 51, 2014 and 835) questioned the capacity of dingoes to provide benefits to native biodiversity due to their inability to eradicate foxes and cats. They also argued that indices of abundance commonly used in studies of mesopredator release by dingoes (namely, track-based indices) invalidate the conclusions of the studies. Hayward & Marlow caution conservation practitioners against incorporating dingoes into conservation programmes. Counter to their claims, we summarise research showing that the suppression of invasive mesopredators (cf. eradication) can enhance populations of native species and is therefore a meaningful conservation objective. We highlight literature supporting the hypothesis that dingoes suppress mesopredator abundance and activity, which in turn benefits native biodiversity. We show that Hayward & Marlow overlook many studies of carnivores that show track indices capture a large amount of the variation in the density of medium- and large-sized carnivores. Synthesis and applications. Practitioners cannot afford to wait to act given the perilous state of Australia's mammal species, and we argue that the evidence is sufficiently strong to justify managing dingoes for biodiversity conservation.

Energy density of foods and beverages in the Australian food supply: influence of macronutrients and comparison to dietary intake

Objectives: The energy density (ED) of the diet is considered an important determinant of total energy intake and thus energy balance and weight change. We aimed to compare relationships between ED and macronutrient content in individual food and beverage items as well as population diet in a typical Western country. Design: Nutrient data for 3673 food items and 247 beverage items came from the Australian Food and Nutrient database (AusNut). Food and beverage intake data came from the 1995 Australian National Nutrition Survey (a 24-h dietary recall survey in 13 858 people over the age of 2). Relationships between ED and macronutrient and water content were analysed by linear regression with 95% prediction bands. Results: For both individual food items and population food intake, there was a positive relationship between ED and percent energy as fat and negative relationships between ED and percent energy as carbohydrate and percent water by weight. In all cases, there was close agreement between the slopes of the regression lines between food items and dietary intake. There were no clear relationships between ED and macronutrient content for beverage items. Carbohydrate (mostly sucrose) contributed 91, 47, and 25% of total energy for sugar-based, fat-based, and alcohol-based beverages respectively. Conclusions: The relationship between ED and fat content of foods holds true across both population diets and individual food items available in the food supply in a typical Western country such as Australia. As high-fat diets are associated with a high BMI, population measures with an overall aim of reducing the ED of diets may be effective in mediating the growing problem of overweight and obesity.