Revisiting proportion estimators

Proportion estimators are quite frequently used in many application areas. The conventional proportion estimator (number of events divided by sample size) encounters a number of problems when the data are sparse as will be demonstrated in various settings. The problem of estimating its variance when sample sizes become small is rarely addressed in a satisfying framework. Specifically, we have in mind applications like the weighted risk difference in multicenter trials or stratifying risk ratio estimators (to adjust for potential confounders) in epidemiological studies. It is suggested to estimate p using the parametric family (see PDF for character) and p(1 - p) using (see PDF for character), where (see PDF for character). We investigate the estimation problem of choosing c 0 from various perspectives including minimizing the average mean squared error of (see PDF for character), average bias and average mean squared error of (see PDF for character). The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be independent of n and equals c = 1. The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be dependent of n with limiting value c = 0.833. This might justifiy to use a near-optimal value of c = 1 in practice which also turns out to be beneficial when constructing confidence intervals of the form (see PDF for character).

Effect of forage type and proportion of concentrate in the diet on milk fatty acid composition in cows given sunflower oil and fish oil

Based on the potential benefits of cis-9, trans- 11 conjugated linoleic acid (CLA) for human health there is a need to develop effective strategies for enhancing milk fat CLA concentrations. In this experiment, the effect of forage type and level of concentrate in the diet on milk fatty acid composition was examined in cows given a mixture of fish oil and sunflower oil. Four late lactation Holstein-British Friesian cows were used in a 4 x 4 Latin-square experiment with a 2 x 2 factorial arrangement of treatments and 21-day experimental periods. Treatments consisted of grass (G) or maize (M) silage supplemented with low (L) or high (H) levels of concentrates (65: 35 and 35: 65; forage: concentrate ratio, on a dry matter (DM) basis, respectively) offered as a total mixed ration at a restricted level of intake (20 kg DM per day). Lipid supplements (30 g/kg DM) containing fish oil and sunflower oil (2: 3 w/w) were offered during the last 14 days of each experimental period. Treatments had no effect on total DM intake, milk yield, milk constituent output or milk fat content, but milk protein concentrations were lower (P<0.05) for G than M diets (mean 43.0 and 47.3 g/kg, respectively). Compared with grass silage, milk fat contained higher (P<0.05) amounts Of C-12: 0, C-14: 0, trans C-18:1 and long chain >= C20 (n-3) polyunsaturated fatty acids (PUFA) and lower (P<0.05) levels Of C-18:0 and trans C-18:2 when maize silage was offered. Increases in the proportion of concentrate in the diet elevated (P<0.05) C-18:2 (n-6) and long chain >= C20 (n-3) PUFA content, but reduced (P<0.05) the amount Of C-18:3 (n-3). Concentrations of trans-11 C-18:1 in milk were independent of forage type, but tended (P<0.10) to be lower for high concentrate diets (mean 7.2 and 4.0 g/100 g fatty acids, for L and H respectively). Concentrations of trans-10 C-18:1 were higher (P<0.05) in milk from maize compared with grass silage (mean 10.3 and 4.1 g/100 g fatty acids, respectively) and increased in response to high levels of concentrates in the diet (mean 4.1 and 10.3 g/100 g fatty acids, for L and H, respectively). Forage type had no effect (P>0.05) on total milk conjugated linoleic acid (CLA) (2.7 and 2.8 g/100 g fatty acids, for M and G, respectively) or cis-9, trans-11 CLA content (2.2 and 2.4 g/100 g fatty acids). Feeding high concentrate diets tended (P<0.10) to decrease total CLA (3.3 and 2.2 g/100 g fatty acids, for L and H, respectively) and cis-9, trans-11 CLA (2.9 and 1/7 g/100 g fatty acids) concentrations and increase milk trans-9, cis-11 CLA and trans-10, cis-12 CLA content. In conclusion, the basal diet is an important determinant of milk fatty acid composition when a supplement of fish oil and sunflower oil is given.

The relationship between absolute and proportion scores of serial order memory: simulation predictions and empirical data

The capability of a feature model of immediate memory (Nairne, 1990; Neath, 2000) to predict and account for a relationship between absolute and proportion scoring of immediate serial recall when memory load is varied (the list-length effect, LLE) is examined. The model correctly predicts the novel finding of an LLE in immediate serial order memory similar to that observed with free recall and previously assumed to be attributable to the long-term memory component of that procedure (Glanzer, 1972). The usefulness of formal models as predictive tools and the continuity between short-term serial order and longer term item memory are considered.

Divine premotion

According to divine premotionism, God does not merely create and sustain the universe. He also moves all secondary causes to action as instruments without undermining their intrinsic causal efficacy. I explain and uphold the premotionist theory, which is the theory of St Thomas Aquinas and his most prominent exponents. I defend the premotionist interpretation of Aquinas in some textual detail, with particular reference to Suarez and to a recent paper by Louis Mancha. Critics, including Molinists and Suarezians, raise various objections to the view that premotion is compatible with genuine secondary causation. I rebut a number of these objections, in the course of which I respond to the central challenge that premotionism destroys free will. I also offer a number of positive reasons for embracing the premotionist theory.

The proportion of failures of the Hasse norm principle

For any number field we calculate the exact proportion of rational numbers which are everywhere locally a norm but not globally a norm from the number field.