Shannon M Monnat, Monica A F Lounsbery, Nicole J Smith
Correlates of state enactment of elementary school physical education laws
Preventive medicine
wearable device technology allows continuous monitoring biological markers thereby enables study timedependent relationships example paper interested impact daily energy expenditure period time subsequent progression toward obesity among children data devices appear either sparsely densely observed functional data methods functional regression often used statistical analyses study scalaronfunction regression model imprecisely measured values predictor function setting scalarvalued response functionvalued covariate collected single time period propose generalized method momentsbased approach estimation instrumental variable belonging time space imprecisely measured covariate used model identification additionally distributional assumptions regarding measurement errors assumed complex covariance structures allowed measurement errors implementation proposed methods demonstrate proposed estimator l2 consistent enjoys optimal rate convergence univariate nonparametric functions simulation study illustrate ignoring measurement error leads biased estimations functional coefficient simulation studies also confirm ability consistently estimate functionvalued coefficient compared approaches ignore potential measurement errors proposed methods applied motivating example assess impact baseline levels energy expenditure body mass index among elementary schoolaged children