2 resultados para Kronecker product and Kronecker sum

em DigitalCommons@The Texas Medical Center


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The purpose of this research was development of a method of estimating nutrient availability in populations as approximated by supermarket purchase records. Demographic information describing 12,516 panel households was obtained from a marketing and advertising program operated by H. E. Butt Grocery Company of San Antonio, Texas. A non-probability sample of 2,161 households meeting expenditure criteria was selected and all purchases of dairy products for this sample of households were organized into a database constructed to facilitate the retrieval, aggregation, and analysis of dairy product purchases and their nutrient contents. Two hypotheses were tested: (1) no difference would be found between Hispanic and non-Hispanic purchases of dairy product categories during the study period and (2) no difference would be found between Hispanic and non-Hispanic purchases of nutrients contained in those dairy products during the thirteen-week study period.^ Food purchase records were used to estimate nutrient exposure on a weekly, per capita basis for Hispanic and non-Hispanic households by linking some 40,000 dairy purchase Universal Product code (UPC) numbers with food composition values contained in USDA Handbook 8-1. Results of this study suggest Hispanic sample households consistently purchased fewer dairy products than did non-Hispanic sample households and consequently had fewer nutrients available from dairy purchases. While weekly expenditures for dairy products among the sample households remained relatively constant during the study period, shifts in the types of dairy products purchased were observed. The effect of ethnicity on dairy product and nutrient purchases was significant over the thirteen-week period. A database consisting of customer, household, and purchase information can be developed to successfully associate food item UPC numbers with a standard reference of food composition to estimate nutrient availability in a population over extended periods of time. ^

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In the biomedical studies, the general data structures have been the matched (paired) and unmatched designs. Recently, many researchers are interested in Meta-Analysis to obtain a better understanding from several clinical data of a medical treatment. The hybrid design, which is combined two data structures, may create the fundamental question for statistical methods and the challenges for statistical inferences. The applied methods are depending on the underlying distribution. If the outcomes are normally distributed, we would use the classic paired and two independent sample T-tests on the matched and unmatched cases. If not, we can apply Wilcoxon signed rank and rank sum test on each case. ^ To assess an overall treatment effect on a hybrid design, we can apply the inverse variance weight method used in Meta-Analysis. On the nonparametric case, we can use a test statistic which is combined on two Wilcoxon test statistics. However, these two test statistics are not in same scale. We propose the Hybrid Test Statistic based on the Hodges-Lehmann estimates of the treatment effects, which are medians in the same scale.^ To compare the proposed method, we use the classic meta-analysis T-test statistic on the combined the estimates of the treatment effects from two T-test statistics. Theoretically, the efficiency of two unbiased estimators of a parameter is the ratio of their variances. With the concept of Asymptotic Relative Efficiency (ARE) developed by Pitman, we show ARE of the hybrid test statistic relative to classic meta-analysis T-test statistic using the Hodges-Lemann estimators associated with two test statistics.^ From several simulation studies, we calculate the empirical type I error rate and power of the test statistics. The proposed statistic would provide effective tool to evaluate and understand the treatment effect in various public health studies as well as clinical trials.^