Estimation and inference for mixture of partially linear additive models

Zhang, Yi; Pan, Weiquan

doi:10.1080/03610926.2020.1777305

Cited by 2 publications

(1 citation statement)

References 13 publications

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“…For a single covariate case, Xiang and Yao [9] showed that this parsimonious version of the model has more efficient estimates when the assumption is appropriate. To incorporate more covariates while avoiding the curse of dimensionality, Wu and Liu [10], Zhang and Zheng [11] and Zhang and Pan [12] introduced a series of semi-parametric mixture of partial and/or additive regression models where the component regression functions are assumed to be linear combinations of parametric and/or non-parametric functions of the covariates. To retain the non-parametric generality of the NPGMRs model while being immune to the curse of dimensionality, Xiang and Yao [13] introduced a semi-parametric mixture of single index models.…”

Section: Introductionmentioning

confidence: 99%

Fitting Non-Parametric Mixture of Regressions: Introducing an EM-Type Algorithm to Address the Label-Switching Problem

2022

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The non-parametric Gaussian mixture of regressions (NPGMRs) model serves as a flexible approach for the determination of latent heterogeneous regression relationships. This model assumes that the component means, variances and mixing proportions are smooth unknown functions of the covariates where the error distribution of each component is assumed to be Gaussian and hence symmetric. These functions are estimated over a set of grid points using the Expectation-Maximization (EM) algorithm to maximise the local-likelihood functions. However, maximizing each local-likelihood function separately does not guarantee that the local responsibilities and corresponding labels, obtained at the E-step of the EM algorithm, align at each grid point leading to a label-switching problem. This results in non-smooth estimated component regression functions. In this paper, we propose an estimation procedure to account for label switching by tracking the roughness of the estimated component regression functions. We use the local responsibilities to obtain a global estimate of the responsibilities which are then used to maximize each local-likelihood function. The performance of the proposed procedure is demonstrated using a simulation study and through an application using real world data. In the case of well-separated mixture regression components, the procedure gives similar results to competitive methods. However, in the case of poorly separated mixture regression components, the procedure outperforms competitive methods.

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Section: Introductionmentioning

confidence: 99%

Fitting Non-Parametric Mixture of Regressions: Introducing an EM-Type Algorithm to Address the Label-Switching Problem

2022

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A Novel EM-Type Algorithm to Estimate Semi-Parametric Mixtures of Partially Linear Models

2023

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Semi- and non-parametric mixture of normal regression models are a flexible class of mixture of regression models. These models assume that the component mixing proportions, regression functions and/or variances are non-parametric functions of the covariates. Among this class of models, the semi-parametric mixture of partially linear models (SPMPLMs) combine the desirable interpretability of a parametric model and the flexibility of a non-parametric model. However, local-likelihood estimation of the non-parametric term poses a computational challenge. Traditional EM optimisation of the local-likelihood functions is not appropriate due to the label-switching problem. Separately applying the EM algorithm on each local-likelihood function will likely result in non-smooth function estimates. This is because the local responsibilities calculated at the E-step of each local EM are not guaranteed to be aligned. To prevent this, the EM algorithm must be modified so that the same (global) responsibilities are used at each local M-step. In this paper, we propose a one-step backfitting EM-type algorithm to estimate the SPMPLMs and effectively address the label-switching problem. The proposed algorithm estimates the non-parametric term using each set of local responsibilities in turn and then incorporates a smoothing step to obtain the smoothest estimate. In addition, to reduce the computational burden imposed by the use of the partial-residuals estimator of the parametric term, we propose a plug-in estimator. The performance and practical usefulness of the proposed methods was tested using a simulated dataset and two real datasets, respectively. Our finite sample analysis revealed that the proposed methods are effective at solving the label-switching problem and producing reasonable and interpretable results in a reasonable amount of time.

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Estimation and inference for mixture of partially linear additive models

Cited by 2 publications

References 13 publications

Fitting Non-Parametric Mixture of Regressions: Introducing an EM-Type Algorithm to Address the Label-Switching Problem

Fitting Non-Parametric Mixture of Regressions: Introducing an EM-Type Algorithm to Address the Label-Switching Problem

A Novel EM-Type Algorithm to Estimate Semi-Parametric Mixtures of Partially Linear Models

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