Estimation and inference in functional mixed-effects models

Antoniadis, Anestis; Sapatinas, Theofanis

doi:10.1016/j.csda.2006.09.038

Cited by 82 publications

(97 citation statements)

References 23 publications

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“…However, forming valid tests of various hypotheses about the functional regression parameters, with the control of the error rate, is not straightforward. One solution adopted in the literature is to develop global tests for the parameters of the model (Abramovich & Angelini, 2006;Antoniadis & Sapatinas, 2007;Cardot et al, 2007;Cuesta-Albertos & Febrero-Bande, 2010;Cuevas, Febrero, & Fraiman, 2004;Kayano, Matsui, Yamaguchi, Imoto, & Miyano, 2015;Schott, 2007;Staicu, Li, Crainiceanu, & Ruppert, 2014;Zhang & Liang, 2014). Such tests investigate if a covariate has a significant effect on the response but does not provide any domain selection.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric inference for functional‐on‐scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament

Abramowicz

Häger

Pini

et al. 2018

Scandinavian J Statistics

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Motivated by the analysis of the dependence of knee movement patterns during functional tasks on subject-specific covariates, we introduce a distribution-free procedure for testing a functional-on-scalar linear model with fixed effects. The procedure does not only test the global hypothesis on the entire domain but also selects the intervals where statistically significant effects are detected. We prove that the proposed tests are provided with an asymptotic control of the intervalwise error rate, that is, the probability of falsely rejecting any interval of true null hypotheses. The procedure is applied to one-leg hop data from a study on anterior cruciate ligament injury. We compare knee kinematics of three groups of individuals (two injured groups with different treatments and one group of healthy controls), taking individual-specific covariates into account.

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Section: Introductionmentioning

confidence: 99%

Nonparametric inference for functional‐on‐scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament

Abramowicz

Häger

Pini

et al. 2018

Scandinavian J Statistics

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show abstract

“…This could take the form of ANOVA except that in such experiments the parameter space will be of extremely high dimension, in 3D easily of size 2 20 -2 30 , so that we are dealing with essentially infinitedimensional function spaces. This leads to Functional ANOVA, designated FANOVA, a field that has recently attracted a good deal of attention; see, e.g., Antoniadis (2003).…”

Section: Estimation Using Group Cascadesmentioning

confidence: 99%

Untitled

2007

Quart. Appl. Math.

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“…In nonparametric regression approach, the estimation modelshape of the curve regression is determined based on the pattern of existing data. Some nonparametric regression approaches are: the kernel (Hardle, 1990), spline (Budiantara et al, 1997;Wahba, 1990) and wavelets (Antoniadis and Sapatinas, 2007). Spline estimator is one of the most commonly used estimator in nonparametric regression because it has a good visual interpretation, high flexibility and able to handle smooth function characters (Eubank, 1999).…”

Section: Introductionmentioning

confidence: 99%

Spline Estimator for Bi-Responses and Multi-Predictors Nonparametric Regression Model in Case of Longitudinal Data

Fernandes¹,

Budiantara²,

Otok³

et al. 2015

Journal of Mathematics and Statistics

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Nonparametric regression approach is used when the shape of the curve regression is unknown. The spline estimator approach for longitudinal data can accommodate the correlation between observations within the same subject, which is not found in the cross-section data, so that the autocorrelation assumption problem can be resolved. On the other hand, with bi-responses approach, it will accommodate any correlation between each response variables. The purposes of this study are (1) to obtain the function form of the nonparametric bi-responses and multipredictorsregression on longitudinal data, (2) to obtain the spline estimator in estimating the nonparametric bi-responses and multipredictorsregression curve on longitudinal data and (3) to apply the spline estimator in estimating the curve of nonparametric bi-responses and multi-predictorsregression on longitudinal data. Bi-responses and multipredictors nonparametric regression of the spline estimator on longitudinal data which meet the criteria of minimizing Penalized Weighted Least Square (PWLS). Application of data set (Patient in Pulmonary Tuberculosis) result shows that the spline estimator can be applied which gives the value of R 2 of 97.77%.

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Estimation and inference in functional mixed-effects models

Cited by 82 publications

References 23 publications

Nonparametric inference for functional‐on‐scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament

Nonparametric inference for functional‐on‐scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament

Untitled

Spline Estimator for Bi-Responses and Multi-Predictors Nonparametric Regression Model in Case of Longitudinal Data

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