14 results on '"Staicu, Ana-Maria"'
Search Results
2. Generalized Multilevel Functional Regression
- Author
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Crainiceanu, Ciprian M., Staicu, Ana-Maria, and Di, Chong-Zhi
- Published
- 2009
3. Functional Feature Construction for Individualized Treatment Regimes.
- Author
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Laber, Eric B. and Staicu, Ana-Maria
- Subjects
- *
REGRESSION analysis , *INDIVIDUALIZED medicine , *FUNCTIONAL analysis , *STOCHASTIC analysis , *OPTIMAL control theory - Abstract
Evidence-based personalized medicine formalizes treatment selection as an individualized treatment regime that maps up-to-date patient information into the space of possible treatments. Available patient information may include static features such race, gender, family history, genetic and genomic information, as well as longitudinal information including the emergence of comorbidities, waxing and waning of symptoms, side-effect burden, and adherence. Dynamic information measured at multiple time points before treatment assignment should be included as input to the treatment regime. However, subject longitudinal measurements are typically sparse, irregularly spaced, noisy, and vary in number across subjects. Existing estimators for treatment regimes require equal information be measured on each subject and thus standard practice is to summarize longitudinal subject information into a scalar, ad hoc summary during data preprocessing. This reduction of the longitudinal information to a scalar feature precedes estimation of a treatment regime and is therefore not informed by subject outcomes, treatments, or covariates. Furthermore, we show that this reduction requires more stringent causal assumptions for consistent estimation than are necessary. We propose a data-driven method for constructing maximally prescriptive yet interpretable features that can be used with standard methods for estimating optimal treatment regimes. In our proposed framework, we treat the subject longitudinal information as a realization of a stochastic process observed with error at discrete time points. Functionals of this latent process are then combined with outcome models to estimate an optimal treatment regime. The proposed methodology requires weaker causal assumptions than Q-learning with an ad hoc scalar summary and is consistent for the optimal treatment regime. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
4. Scalar-on-image regression via the soft-thresholded Gaussian process.
- Author
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Kang, Jian, Reich, Brian J, and Staicu, Ana-Maria
- Subjects
SCALAR field theory ,REGRESSION analysis ,GAUSSIAN processes ,BAYESIAN analysis ,NONPARAMETRIC estimation - Abstract
Thiswork concerns spatial variable selection for scalar-on-image regression.We propose a new class of Bayesian nonparametric models and develop an efficient posterior computational algorithm. The proposed soft-thresholded Gaussian process provides large prior support over the class of piecewise-smooth, sparse, and continuous spatially varying regression coefficient functions. In addition, under some mild regularity conditions the soft-thresholded Gaussian process prior leads to the posterior consistency for parameter estimation and variable selection for scalar-on-image regression, even when the number of predictors is larger than the sample size. The proposed method is compared to alternatives via simulation and applied to an electroencephalography study of alcoholism. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
5. Additive Function-on-Function Regression.
- Author
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Kim, Janet S., Staicu, Ana-Maria, Maity, Arnab, Carroll, Raymond J., and Ruppert, David
- Subjects
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ADDITIVE functions , *REGRESSION analysis , *COMPUTATIONAL complexity , *PARAMETER estimation , *LOGICAL prediction - Abstract
We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself, as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. We discuss prediction of a new response trajectory, propose an inference procedure that accounts for total variability in the predicted response curves, and construct pointwise prediction intervals. The estimation/inferential procedure accommodates realistic scenarios, such as correlated error structure as well as sparse and/or irregular designs. We investigate our methodology in finite sample size through simulations and two real data applications. Supplementary material for this article is available online. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
6. Classical testing in functional linear models.
- Author
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Kong, Dehan, Staicu, Ana-Maria, and Maity, Arnab
- Subjects
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CLASSICAL test theory , *LINEAR statistical models , *REGRESSION analysis , *STATISTICAL hypothesis testing , *PRINCIPAL components analysis , *LIKELIHOOD ratio tests - Abstract
We extend four tests common in classical regression – Wald, score, likelihood ratio andFtests – to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
7. Testing for additivity in non-parametric regression.
- Author
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Zhang, Yichi, Staicu, Ana‐Maria, and Maity, Arnab
- Subjects
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REGRESSION analysis , *LIKELIHOOD ratio tests , *MATHEMATICAL decomposition , *COMPUTER algorithms , *DISEASES , *MATHEMATICAL models - Abstract
This article discusses a novel approach for testing for additivity in non-parametric regression. We represent the model using a linear mixed model framework and equivalently rewrite the original testing problem as testing for a subset of zero variance components. We propose two testing procedures: the restricted likelihood ratio test and the generalized F test. We develop the finite sample null distribution of the restricted likelihood ratio test and generalized F test using the spectral decomposition of the restricted likelihood ratio and the residual sum of squares, respectively. The null distribution is non-standard and we provide a fast algorithm to simulate from the null distribution of the tests. We show, through numerical investigation, that the proposed testing procedures outperform the available alternatives and apply the methods to a diabetes data set. The Canadian Journal of Statistics 44: 445-462; 2016 © 2016 Statistical Society of Canada [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
8. Interactive graphics for functional data analyses.
- Author
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Wrobel, Julia, Park, So Young, Staicu, Ana Maria, and Goldsmith, Jeff
- Subjects
DATA analysis ,DATA visualization ,EXPLORATORY factor analysis ,REGRESSION analysis ,DIFFUSION tensor imaging - Abstract
Although there are established graphics that accompany the most common functional data analyses, generating these graphics for each dataset and analysis can be cumbersome and time-consuming. Often, the barriers to visualization inhibit useful exploratory data analyses and prevent the development of intuition for a method and its application to a particular dataset. The refund.shiny package was developed to address these issues for several of the most common functional data analyses. After conducting an analysis, the plot_shiny() function is used to generate an interactive visualization environment that contains several distinct graphics, many of which are updated in response to user input. These visualizations reduce the burden of exploratory analyses and can serve as a useful tool for the communication of results to non-statisticians. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
9. Marginal Functional Regression Models for Analyzing the Feeding Behavior of Pigs.
- Author
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Gertheiss, Jan, Maier, Verena, Hessel, Engel, and Staicu, Ana-Maria
- Subjects
REGRESSION analysis ,MULTIVARIATE analysis ,BINARY number system ,BINARY sequences ,RADIO frequency measurement - Abstract
We observe a group of pigs over a period of about 100 days. Using high frequency radio frequency identification, it is recorded when each pig is feeding, leading to very dense binary functional data for each pig and day. One aim of the data analysis is to find pig-specific feeding profiles showing us the typical feeding pattern of each pig. For modeling the data, we use a marginal functional logistic regression approach, allowing us to model the densely observed binary measurements by assuming an underlying smooth subject-specific profile. The method also allows to incorporate additional covariates such as temperature and humidity that may influence the pigs' behavior. To account for correlation of measurements, we use robust standard errors and corresponding pointwise confidence intervals. Before analyzing the feeding behavior of pigs, the method employed is evaluated in simulation studies. As our approach is rather general, it may also be applied to other types of generalized functional data with similar characteristics as the pig data. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
10. Penalized function-on-function regression.
- Author
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Ivanescu, Andrada, Staicu, Ana-Maria, Scheipl, Fabian, and Greven, Sonja
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REGRESSION analysis , *SPLINES , *DIFFUSION tensor imaging , *EIGENFUNCTIONS , *DEMYELINATION - Abstract
A general framework for smooth regression of a functional response on one or multiple functional predictors is proposed. Using the mixed model representation of penalized regression expands the scope of function-on-function regression to many realistic scenarios. In particular, the approach can accommodate a densely or sparsely sampled functional response as well as multiple functional predictors that are observed on the same or different domains than the functional response, on a dense or sparse grid, and with or without noise. It also allows for seamless integration of continuous or categorical covariates and provides approximate confidence intervals as a by-product of the mixed model inference. The proposed methods are accompanied by easy to use and robust software implemented in the pffr function of the R package refund. Methodological developments are general, but were inspired by and applied to a diffusion tensor imaging brain tractography dataset. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
11. Glacier Terminus Estimation from Landsat Image Intensity Profiles.
- Author
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Usset, Joseph, Maity, Arnab, Staicu, Ana-Maria, and Schwartzman, Armin
- Subjects
LANDSAT satellites ,ARTIFICIAL satellites ,REGRESSION analysis ,MULTIVARIATE analysis ,SPLINES - Abstract
Mountain glacier retreat is an important problem related to temperature increase caused by global climate change. The retreat of mountain glaciers has been studied from the ground, but there exists a need for automated methods to catalog glacial change with a wider scope. A viable approach is to extract intensity profiles from Landsat images along the glacial flowline and follow the terminus location over time. We propose a new robust and accurate statistical algorithm to estimate the movement of glacial termini over time from these extracted image intensity profiles. The method we propose first uses regression splines to smooth the image intensity profiles. For each profile, the glacial terminus location is assumed to lie near a point of high negative change in the smoothed profiles. An approximate path of termini locations over time is obtained by an algorithm that seeks to minimize the cumulative first derivative value across the profiles. Spline smoothing is applied to this pilot path for estimation of long-term terminus movement. The predictions from the method are evaluated on simulated data and compared to available ground measurements for the Nigardsbreen, Gorner, Rhone, and Franz Josef glaciers. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
12. Functional Additive Mixed Models.
- Author
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Scheipl, Fabian, Staicu, Ana-Maria, and Greven, Sonja
- Subjects
- *
ADDITIVES , *REGRESSION analysis , *STATISTICAL correlation , *SPATIOTEMPORAL processes , *LONGITUDINAL method , *DATA analysis - Abstract
We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, for example, spatial, temporal, or longitudinal functional data. Additionally, our framework includes linear and nonlinear effects of functional and scalar covariates that may vary smoothly over the index of the functional response. It accommodates densely or sparsely observed functional responses and predictors which may be observed with additional error and includes both spline-based and functional principal component-based terms. Estimation and inference in this framework is based on standard additive mixed models, allowing us to take advantage of established methods and robust, flexible algorithms. We provide easy-to-use open source software in the pffr() function for the R package refund. Simulations show that the proposed method recovers relevant effects reliably, handles small sample sizes well, and also scales to larger datasets. Applications with spatially and longitudinally observed functional data demonstrate the flexibility in modeling and interpretability of results of our approach. [ABSTRACT FROM PUBLISHER]
- Published
- 2015
- Full Text
- View/download PDF
13. Interaction models for functional regression.
- Author
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Usset, Joseph, Staicu, Ana-Maria, and Maity, Arnab
- Subjects
- *
REGRESSION analysis , *DATA analysis , *COMPUTER software , *HYPOTHESIS , *TENSOR algebra - Abstract
A functional regression model with a scalar response and multiple functional predictors is proposed that accommodates two-way interactions in addition to their main effects. The proposed estimation procedure models the main effects using penalized regression splines, and the interaction effect by a tensor product basis. Extensions to generalized linear models and data observed on sparse grids or with measurement error are presented. A hypothesis testing procedure for the functional interaction effect is described. The proposed method can be easily implemented through existing software. Numerical studies show that fitting an additive model in the presence of interaction leads to both poor estimation performance and lost prediction power, while fitting an interaction model where there is in fact no interaction leads to negligible losses. The methodology is illustrated on the AneuRisk65 study data. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
14. Inference in functional linear quantile regression.
- Author
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Li, Meng, Wang, Kehui, Maity, Arnab, and Staicu, Ana-Maria
- Subjects
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QUANTILE regression , *REGRESSION analysis , *INFERENTIAL statistics , *PRINCIPAL components analysis , *ASYMPTOTIC distribution - Abstract
In this paper, we study statistical inference in functional quantile regression for scalar response and a functional covariate. Specifically, we consider a functional linear quantile regression model where the effect of the covariate on the quantile of the response is modeled through the inner product between the functional covariate and an unknown smooth regression parameter function that varies with the level of quantile. The objective is to test that the regression parameter is constant across several quantile levels of interest. The parameter function is estimated by combining ideas from functional principal component analysis and quantile regression. An adjusted Wald testing procedure is proposed for this hypothesis of interest, and its chi-square asymptotic null distribution is derived. The testing procedure is investigated numerically in simulations involving sparse and noisy functional covariates and in a capital bike share data application. The proposed approach is easy to implement and the R code is published online at https://github.com/xylimeng/fQR-testing. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
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