Local Linear Functional Regression Based on Weighted Distance-based Regression

Val, Eva Boj del; Delicado, Pedro; Fortiana, Josep

doi:10.1007/978-3-7908-2062-1_10

Cited by 6 publications

(14 citation statements)

References 17 publications

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“…2.1 Distance-based linear model: definition and results DB-LM was introduced by Cuadras (1989) and has been developed in Cuadras and Arenas (1990), Cuadras et al (1996), , Esteve et al (2009) and Boj et al (2010). Here we recall its main concepts, as given in these articles, where the reader is referred to for more details and proofs.…”

Section: Review Of Db-lm and Glmmentioning

confidence: 99%

“…The following Theorem (proved in Boj et al 2010) states that DB-LM does not depend on a specific X w , since the final quantities are obtained directly from the distances. Usually such a configuration needs not be made explicit, and neither doβ or x n+1 .…”

Section: Review Of Db-lm and Glmmentioning

confidence: 99%

“…The idea is to translate to the DB-GLM context the principles of local likelihood, as stated in Loader (1999, Chapter 4) (see also Section 3.4 in Bowman and Azzalini 1997, Section 6.5 in Hastie et al 2009, Section 5.10 in Wasserman 2006, or the book of Wood 2006). Our approach parallels that used in Boj et al (2010), where local DB-LM was defined.…”

Section: Local Distance-based Generalized Linear Modelmentioning

confidence: 99%

“…Both roles are unrelated and in fact it is possible to work with two different distance functions involved in the local DB-GLM: one of them, say δ 1 , used in equation (14), and the other, say δ 2 , in equations (15) and (16). In the context of local DB-LM, Boj et al (2010) show that using two distance functions provides more flexibility than using only one (δ 1 = δ 2 ). For instance, in the case of univariate explanatory variable, x i , a local cubic polynomial fitting can be implemented using the local DB-LM with…”

Section: Local Distance-based Generalized Linear Modelmentioning

confidence: 99%

“…In this line, Boj et al (2010) introduced local DB-LM, a nonparametric prediction technique extending (weighted) DB-LM. In the present paper we introduce two further extensions: the distance-based generalized linear models (DB-GLM) and their nonparametric version (the local DB-GLM) via local likelihood.…”

Section: Introductionmentioning

confidence: 99%

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Global and local distance-based generalized linear models

Val

Mestres²,

Delicado

et al. 2015

TEST

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This paper introduces local distance-based generalized linear models. These models extend (weighted) distance-based linear models firstly to the generalized linear model framework. Then a nonparametric version of these models is proposed by means of local fitting. Distances between individuals are the only predictor information needed to fit these models. Therefore they are applicable, among others, to mixed (qualitative and quantitative) explanatory variables or when the regressor is of functional type. An implementation is provided by the R package dbstats, which also implements other distancebased prediction methods. Supplementary material for this article is available online, which reproduces all the results of this article.

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Section: Review Of Db-lm and Glmmentioning

confidence: 99%

Section: Review Of Db-lm and Glmmentioning

confidence: 99%

Section: Local Distance-based Generalized Linear Modelmentioning

confidence: 99%

Section: Local Distance-based Generalized Linear Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Global and local distance-based generalized linear models

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et al. 2015

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Nonparametric estimation for a functional-circular regression model

2023

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Changes on temperature patterns, on a local scale, are perceived by individuals as the most direct indicators of global warming and climate change. As a specific example, for an Atlantic climate location, spring and fall seasons should present a mild transition between winter and summer, and summer and winter, respectively. By observing daily temperature curves along time, being each curve attached to a certain calendar day, a regression model for these variables (temperature curve as covariate and calendar day as response) would be useful for modeling their relation for a certain period. In addition, temperature changes could be assessed by prediction and observation comparisons in the long run. Such a model is presented and studied in this work, considering a nonparametric Nadaraya–Watson-type estimator for functional covariate and circular response. The asymptotic bias and variance of this estimator, as well as its asymptotic distribution are derived. Its finite sample performance is evaluated in a simulation study and the proposal is applied to investigate a real-data set concerning temperature curves.

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A microbial perspective on balancing trade-offs in ecosystem functions in a constructed stormwater wetland

Bledsoe

Bean

Austin

et al. 2020

Ecological Engineering

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Green stormwater infrastructure, such as constructed wetlands (CWs), is a type of stormwater control measure that can decrease nutrient and pollutant loads from urban stormwater runoff. Wetland soil microorganisms provide nutrient and pollutant removal benefits which can also result in ecosystem disservices such as greenhouse gas (GHG) emissions and can inadvertently exacerbate climate change. Microbial respiration by facultative anaerobes in anoxic conditions is the primary pathway for nitrogen removal (benefit). Similar anoxic conditions that support denitrifying microorganisms can also support obligate anaerobes that produce methane (CH 4 ) via methanogenesis (disservice). We examined nitrogen removal potential, GHG production, and microbial community structure within permanently flooded and shallow land or temporarily-flooded areas of a stormwater CW to identify zones for CW design optimization.Results indicate that permanently flooded zones compared to shallow land zones are greater sources of CH 4 emissions (80.80 ± 118.31, 2.32 ± 9.33 mg CH 4 -C m -2 hr -1 , respectively) and emit more carbon to the atmosphere (7161.27 kg CO 2 , 93.20 kg CO 2 equivalents, respectively). However, nitrogen removal potential rates were similar across both flooded and shallow land zones (24.45 ± 20.18, 20.29 ± 15.14 ng N 2 O-N hr -1 g -1 dry soil, respectively). At this particular CW, reduction of permanently flooded zones within the wetland could decrease GHG emissions (disservice) without limiting nitrogen removal (benefit) potential of the wetland. Holistic development and design of stormwater control measures, which account for microbial activity, provides the opportunity to maximize benefits (i.e., nutrient and pollutant removal) and reduce disservices (i.e., GHG emissions) of green stormwater infrastructure.

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Local Linear Functional Regression Based on Weighted Distance-based Regression

Cited by 6 publications

References 17 publications

Global and local distance-based generalized linear models

Global and local distance-based generalized linear models

Nonparametric estimation for a functional-circular regression model

A microbial perspective on balancing trade-offs in ecosystem functions in a constructed stormwater wetland

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