Testing model assumptions in functional regression models

Bücher, Axel; Dette, Holger; Wieczorek, Gabriele

doi:10.1016/j.jmva.2011.05.014

Cited by 11 publications

(5 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A simple example that satisfies (2.7) is the uniform design with p(z) ≡ 1, z ∈ [0, 1] and z ij = [(k − 1)n 0 + j]/(kn 0 ). See, for example, [27].…”

Section: Semiparametric Least Squares Estimationmentioning

confidence: 99%

Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors

You

Zhou

Zhou³

2010

Journal of Multivariate Analysis

View full text Add to dashboard Cite

a b s t r a c tWe consider a panel data semiparametric partially linear regression model with an unknown parameter vector for the linear parametric component, an unknown nonparametric function for the nonlinear component, and a one-way error component structure which allows unequal error variances (referred to as heteroscedasticity). We develop procedures to detect heteroscedasticity and one-way error component structure, and propose a weighted semiparametric least squares estimator (WSLSE) of the parametric component in the presence of heteroscedasticity and/or one-way error component structure. This WSLSE is asymptotically more efficient than the usual semiparametric least squares estimator considered in the literature. The asymptotic properties of the WSLSE are derived. The nonparametric component of the model is estimated by the local polynomial method. Some simulations are conducted to demonstrate the finite sample performances of the proposed testing and estimation procedures. An example of application on a set of panel data of medical expenditures in Australia is also illustrated.

show abstract

“…A simple example that satisfies (2.7) is the uniform design with p(z) ≡ 1, z ∈ [0, 1] and z ij = [(k − 1)n 0 + j]/(kn 0 ). See, for example, [27].…”

Section: Semiparametric Least Squares Estimationmentioning

confidence: 99%

Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors

You

Zhou

Zhou³

2010

Journal of Multivariate Analysis

View full text Add to dashboard Cite

show abstract

“…In addition to the GoF proposals for the FLMSR discussed above, Delsol, Ferraty, and Vieu (2011) formulated a kernel-based test for model assumptions, whereas Bücher, Dette, and Wieczorek (2011) introduced testing procedures well adapted for the time-variation of directional profiles. Generalized likelihood ratio tests were suggested in McLean, Hooker, and Ruppert (2015) to test the linearity of functional generalized additive models.…”

Section: Introductionmentioning

confidence: 99%

A goodness‐of‐fit test for the functional linear model with functional response

García‐Portugués

Álvarez-Liébana

Álvarez‐Pérez

et al. 2020

Scandinavian J Statistics

View full text Add to dashboard Cite

The functional linear model with functional response (FLMFR) is one of the most fundamental models to assess the relation between two functional random variables. In this article, we propose a novel goodness-of-fit test for the FLMFR against a general, unspecified, alternative. The test statistic is formulated in terms of a Cramér-von Mises norm over a doubly projected empirical process which, using geometrical arguments, yields an easy-to-compute weighted quadratic norm. A resampling procedure calibrates the test through a wild bootstrap on the residuals and the use of convenient computational procedures. As a sideways contribution, and since the statistic requires a reliable estimator of the FLMFR, we discuss and compare several regularized estimators, providing a new one specifically convenient for our test. The finite sample behavior of the test is illustrated via a simulation study. Also, the new proposal is compared with previous significance tests. Two novel real data sets illustrate the application of the new test.

show abstract

“…with d a functional pseudometric, K a kernel function adapted to this situation, h a bandwidth parameter, ω a weight function, and P X the probability measure induced by X in H. Testing H 0 has also been considered by and Hilgert et al (2013), not in an omnibus way, but inside a Functional Linear Model (FLM): m(X) = X, ρ , where •, • represents the inner product in H and ρ ∈ H is the FLM parameter. For both approximations, omnibus or not, there have also been other papers which consider the functional response case; see, for example, Chiou and Müller (2007), Kokoszka et al (2008), and Bücher et al (2011).…”

Section: Introductionmentioning

confidence: 99%

Goodness-of-fit tests for the functional linear model based on randomly projected empirical processes

Cuesta-Albertos¹,

García‐Portugués²,

Febrero–Bande³

et al. 2019

Ann. Statist.

View full text Add to dashboard Cite

We consider marked empirical processes indexed by a randomly projected functional covariate to construct goodness-of-fit tests for the functional linear model with scalar response. The test statistics are built from continuous functionals over the projected process, resulting in computationally efficient tests that exhibit root-n convergence rates and circumvent the curse of dimensionality. The weak convergence of the empirical process is obtained conditionally on a random direction, whilst the almost surely equivalence between the testing for significance expressed on the original and on the projected functional covariate is proved. The computation of the test in practice involves calibration by wild bootstrap resampling and the combination of several p-values, arising from different projections, by means of the false discovery rate method. The finite sample properties of the tests are illustrated in a simulation study for a variety of linear models, underlying processes, and alternatives. The software provided implements the tests and allows the replication of simulations and data applications.The term "goodness-of-fit" was introduced at the beginning of the twentieth century by Karl Pearson, and, since then, there have been an enormous amount of papers devoted to this topic: first, concentrated on fitting a model for one distribution function, and, later, especially after the papers of Bickel and Rosenblatt (1973) and Durbin (1973), on more general models related with the regression function. Considering a regression model with random design Y = m(X) + ε, the goal is to test the goodness-of-fit of a class of parametric regression functions M Θ := {m θ : θ ∈ Θ ⊂ R q } to the data. This is the testing ofis the regression function of Y over X, and ε is a random error centred such that E [ε|X] = 0. The literature of goodness-of-fit tests for the regression function is vast, and we refer to González-Manteiga and Crujeiras (2013) for an updated review of the topic.Following the ideas on smoothing for testing the density function (Bickel and Rosenblatt, 1973), the pilot estimators usually considered for m were nonparametric, for example, the Nadaraya-Watson estimator (Nadaraya (1964), Watson (1964K (x − X j )/h , where K is a kernel function and h is a bandwidth parameter. Using these kinds of pilot estimators, statistical tests were given by T n = d m, mθ , with d

show abstract

Testing model assumptions in functional regression models

Cited by 11 publications

References 25 publications

Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors

Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors

A goodness‐of‐fit test for the functional linear model with functional response

Goodness-of-fit tests for the functional linear model based on randomly projected empirical processes

Contact Info

Product

Resources

About