Dependent generalized functional linear models

Abstract

Summary This paper considers testing for no effect of functional covariates on response variables in multivariate regression. We use generalized estimating equations to determine the underlying parameters and establish their joint asymptotic normality. This is then used to test the significance of the effect of predictors on the vector of response variables. Simulations demonstrate the importance of considering existing correlation structures in the data. To explore the effect of treating genetic data as a function, we perform a simulation study using gene sequencing data and find that the performance of our test is comparable to that of another popular method used in sequencing studies. We present simulations to explore the behaviour of our test under varying sample size, cluster size and dimension of the parameter to be estimated, and an application where we are able to confirm known associations between nicotine dependence and neuronal nicotinic acetylcholine receptor subunit genes.

A function‐based approach to model the measurement error in wearable devices

“…Similar form of test statistic can be found in References 21 and 29, though these works do not consider measurement error. We will show in the next section that asymptotically and under $$$ {H}_0 $$$, $$$ \hat{T} $$$ has a standard normal distribution and thus $$$ P $$$‐value for the test can be easily determined.…”

A Function-Based Approach to Model the Measurement Error in Wearable Devices

“…Similar form of test statistic can be found in ( 22) and (11), though these works do not consider measurement error. We will show in the next section that asymptotically and under H 0 , T has a standard normal distribution and thus p-value for the test can be easily determined.…”

“…In this section, we list results that establish the weak consistency of the suggested estimates, the asymptotic distribution of the test statistic in (11), and the necessary assumptions. The norm of…”

“…This also implies the consistency β(•). The following additional are assumptions similar to those in (11), are needed to prove that the asymptotic distribution of the statistic T in ( 11) is standard normal.…”

Bayesian surface regression versus spatial spectral nonparametric curve regression

“…Wang, Chiou and Müller [74] describe the usual FDA methodologies, including mean and covariance analysis, dimension reduction techniques, like Functional Principal Component Analysis, and recent advances in clustering/classification, nonlinear regression, and warping techniques for functional data. Finally, we refer to the contribution by Jadhav, Koul and Lu [40], in the multivariate functional regression context, where the effect of functional covariates on the response variable is analyzed.…”