Abstract
Considering the importance of science and mathematics achieve ments of young students, one of the most well known observed phenomenon is that the performance of U.S. students in mathematics and sciences is undesirable. In order to deal with the problem of declining mathematics and science scores of American high school students, many strategies have been implemented for several decades. In this paper, we give an in-depth longitudinal study of American youth using a double-kernel approach of non parametric quantile regression. Two of the advantages of this approach are: (1) it guarantees that a Nadaraya-Watson estimator of the conditional func tion is a distribution function while, in some cases, this kind of estimator being neither monotone nor taking values only between 0 and 1; (2) it guar antees that quantile curves which are based on Nadaraya-Watson estimator not absurdly cross each other. Previous work has focused only on mean re gression and parametric quantile regression. We obtained many interesting results in this study.
Highlights
More and more attention has been paid to the importance of science and mathematics achievements of young students as the pace of change in our lives is becoming faster and faster
Quantile regression methods have become increasingly popular in many applications in longitudinal studies because of its useful features: (1) given predictors, the models can show the character of the entire condition of a response variable; (2) both the recent advances in computing resources and the ready availability of linear programming algorithms make the estimation easy; (3) the resulting estimated coefficients are robust; (4) quantile regression estimators may be more efficient than those from least squared in the case that the error term is non-normal
The technique is based on the asymptotic mean square error (AMSE) together with the ‘plug-in’ rule to replace any unknown quantity in the AMSE
Summary
More and more attention has been paid to the importance of science and mathematics achievements of young students as the pace of change in our lives is becoming faster and faster. (For example, Ehrenberg and Brewer, 1994, 1995, and Hanushek, 1996) The findings of these studies conclude that improving school resource can hardly improve students’ performance on standardized achievement tests, which are run counter to the conventional view point. Several recent studies have modelled the performance of student on the standardized tests as a function of many factors such as the parents’ socio-economic status, the number of parents and siblings, class size, teacher qualifications, etc. About 60 seventh graders were randomly selected in each of the 52 schools and the total sample size was 3116 students These students were followed for six years from grade 7 to grade 12, writing mathematics and science achievement tests and completing student questionnaires annually. All available student achievement scores are used as dependent measures
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
