Confidence sets for optimal factor levels of a response surface

Confidence sets for a level set in linear regression

Regression modeling is the workhorse of statistics and there is a vast literature on estimation of the regression function. It has been realized in recent years that in regression analysis the ultimate aim may be the estimation of a level set of the regression function, ie, the set of covariate values for which the regression function exceeds a predefined level, instead of the estimation of the regression function itself. The published work on estimation of the level set has thus far focused mainly on nonparametric regression, especially on point estimation. In this article, the construction of confidence sets for the level set of linear regression is considered. In particular,1 - α $$ 1-\alpha $$ level upper, lower and two-sided confidence sets are constructed for the normal-error linear regression. It is shown that these confidence sets can be easily constructed from the corresponding1 - α $$ 1-\alpha $$ level simultaneous confidence bands. It is also pointed out that the construction method is readily applicable to other parametric regression models where the mean response depends on a linear predictor through a monotonic link function, which include generalized linear models, linear mixed models and generalized linear mixed models. Therefore, the method proposed in this article is widely applicable. Simulation studies with both linear and generalized linear models are conducted to assess the method and real examples are used to illustrate the method.

Effects of Extraction Technique on the Content and Antioxidant Activity of Flavonoids from Gossypium Hirsutum linn. Flowers

Cotton is one of the Uyghur medical materials in China and is rich in flavonoids. Flavonoids have important pharmacological effects. The yield of flavonoids in traditional extraction methods is low, which affects the development of flavonoids. Therefore, it is urgent to optimize the extraction techniques. The yield of flavonoids in cotton flowers was effectively improved by response surface methodology, and the highest yield of flavonoids reached 5.66%, and the optimal extraction process conditions were obtained. The DPPH free radical scavenging rate, hydroxyl free radical scavenging rate, superoxide anion free radical scavenging rate, and reducing ability were tested to reflect the antioxidant capacity of flavonoids. The flavonoids had an excellent antioxidant effect. Cell experiments suggested that the flavonoids had the effect of protecting glutamate-induced damage to HT-22 cells. The results of this study provide a theoretical basis for the extraction of cotton flowers flavonoids and the comprehensive evaluation of antioxidant products, as well as the extraction of other plant flavonoids.

Confidence Sets for Statistical Classification

Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences among others. In statistical terms, classification is inference about the unknown parameters, i.e., the true classes of future objects. Hence, various standard statistical approaches can be used, such as point estimators, confidence sets and decision theoretic approaches. For example, a classifier that classifies a future object as belonging to only one of several known classes is a point estimator. The purpose of this paper is to propose a confidence-set-based classifier that classifies a future object into a single class only when there is enough evidence to warrant this, and into several classes otherwise. By allowing classification of an object into possibly more than one class, this classifier guarantees a pre-specified proportion of correct classification among all future objects. An example is provided to illustrate the method, and a simulation study is included to highlight the desirable feature of the method.