Truncated Linear Models for Functional Data

Hall, Peter; Hooker, Giles

doi:10.1111/rssb.12125

Cited by 36 publications

(30 citation statements)

References 31 publications

(69 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Functional linear models have been extended to allow nonlinear responses (McLean et al . ), to include sparsity‐type penalties (James, Wang & Zhu ) and to allow data‐driven selection of how much past history to use (Hall & Hooker ). Machine learning methods rarely come with statistical measures of uncertainty, but confidence intervals and hypothesis tests for RF have very recently been developed (Mentch & Hooker 2014a, 2014b; Wager ).…”

Section: Discussionmentioning

confidence: 99%

Linking demography with drivers: climate and competition

et al. 2016

Self Cite

View full text Add to dashboard Cite

1. In observational demographic data, the number of measured factors that could potentially drive demography (such as daily weather records between two censuses) can easily exceed the number of independent observations. Thus, identifying the important drivers requires alternatives to standard model selection and variable selection methods.2. Spline methods that estimate smooth functions over continuous domains (such as space or time) have the potential to resolve high-dimensional problems in ecological systems. We consider two examples that are important for many plant populations: competition with neighbours that vary in size and distance from the focal individual and climate variables during a window of time before a response (growth, survival, etc.) is measured. 3. For competition covariates, we use a simulation study based on empirical data to show that a monotone spline estimate of competition kernels via approximate AIC returns very accurate estimates. We then apply the method to long-term, mapped quadrat data on the four dominant species in an Idaho (US) sagebrush steppe community. 4. For climate predictors and their temporal lags, we use simulated data sets to compare functional smoothing methods with competing linear (LASSO) or machine learning (random forests) methods. Given sufficient data, functional smoothing methods outperformed the other two methods. 5. Functional smoothing methods can advance data-driven population modelling by providing alternatives to specifying competition kernels a priori and to arbitrarily aggregating continuous environmental covariates. However, there are important open questions related to modelling of nonlinear climate responses and size 9 climate interactions.

show abstract

Section: Discussionmentioning

confidence: 99%

Linking demography with drivers: climate and competition

et al. 2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…For example, it is more reasonable to assume the accel-eration function influences particulate matter in a continuous and smooth manner. Moreover, in practice, predictor functions are often not very smooth, while our simulation study suggests that estimates of Hall and Hooker (2016) generally do not perform well in such case. Alternatively, we observe that model (1) is equivalent to a classic functional linear model with β(t) = 0 for all t ∈ [δ, T ].…”

Section: Introductionmentioning

confidence: 83%

“…Model (1) has been investigated by Hall and Hooker (2016) who proposed to estimate β(t) and δ by penalized least squares with a penalty on δ 2 . The resulting estimates for β(t) are discontinuous at t =δ whereδ stands for the estimated δ.…”

Section: Introductionmentioning

confidence: 99%

“…First, it is based on B-spline basis expansion and penalized least squares with a roughness penalty. Therefore, the resulting estimator of β(t) is continuous and smooth over the entire domain [0, T ], contrasting the discontinuous estimator of Hall and Hooker (2016). Second, it employs a new nested group bridge shrinkage method proposed in Section 2 to specifically shrink the estimated function on the tail region [T − δ, T ].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Estimating Truncated Functional Linear Models With a Nested Group Bridge Approach

Guan

Lin

Cao

2020

Journal of Computational and Graphical Statistics

View full text Add to dashboard Cite

We study a scalar-on-function historical linear regression model which assumes that the functional predictor does not influence the response when the time passes a certain cutoff point. We approach this problem from the perspective of locally sparse modeling, where a function is locally sparse if it is zero on a substantial portion of its defining domain. In the historical linear model, the slope function is exactly a locally sparse function that is zero beyond the cutoff time. A locally sparse estimate then gives rise to an estimate of the cutoff time. We propose a nested group bridge penalty that is able to specifically shrink the tail of a function. Combined with the B-spline basis expansion and penalized least squares, the nested group bridge approach can identify the cutoff time and produce a smooth estimate of the slope function simultaneously. The proposed locally sparse estimator is shown to be consistent, while its numerical performance is illustrated by simulation studies. The proposed method is demonstrated with an application of determining the effect of the past engine acceleration on the current particulate matter emission.

show abstract

“…If K is continuous and square integrable, we have the spectral decomposition from Mercer's theorem (Hsing and Eubank, 2015, pp 120): The operator K is of full rank in L 2 (I) (Hall and Hooker, 2016) in the sense that all λ j s = 0 and φ 1 , φ 2 , . .…”

Section: Population Least Squares7mentioning

confidence: 99%

Two-sample Functional Linear Models

Xu¹,

Zhang²,

Liang³

2019

STAT SINICA

View full text Add to dashboard Cite

In this paper we study two-sample functional linear regression with a scaling transformation of regression functions. We consider estimation of the intercept, the slope function and the scalar parameter based on the functional principal component analysis. We also establish the rates of convergence for the estimator of the slope function, which is shown to be optimal in a minimax sense under certain smoothness assumptions. We further investigate semiparametric efficiency for the estimation of the scalar parameter and hypothesis testing. We also extend the proposed method to sparsely and irregularly sampled functional data and establish the consistency for the estimators of the scalar and the slope function. We evaluate numerical performance of the proposed methods through simulation studies and illustrate their utility via analysis of an AIDS data set.

show abstract

Truncated Linear Models for Functional Data

Cited by 36 publications

References 31 publications

Linking demography with drivers: climate and competition

Linking demography with drivers: climate and competition

Estimating Truncated Functional Linear Models With a Nested Group Bridge Approach

Two-sample Functional Linear Models

Contact Info

Product

Resources

About