Censored regression models with autoregressive errors: A likelihood‐based perspective

Schumacher, Fernanda L.; Lachos, Víctor H.; Dey, Dipak K.

doi:10.1002/cjs.11338

Cited by 15 publications

(22 citation statements)

References 26 publications

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“…Following Barndorff-Nielsen and Schou, 24 the autoregressive process can be reparameterized using a one-to-one, continuous and differentiable transformation in order to simplify the conditions for stationarity. For details on the estimation of the autoregressive coefficients, we refer to Schumacher et al, 25 and see also Lin and Lee 26,27 for details on estimation of LMM with AR(p) dependence. The model formulated in (3) and (4) with error covariance i = 2 e R i , where R i is given by (13), i = 1, … , n, will be denoted AR(p)-SMSN-LMM.…”

Section: Autoregressive Dependence Of Order Pmentioning

confidence: 99%

Scale mixture of skew‐normal linear mixed models with within‐subject serial dependence

Schumacher

Lachos

Matos

2021

Statistics in Medicine

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In longitudinal studies, repeated measures are collected over time and hence they tend to be serially correlated. These studies are commonly analyzed using linear mixed models (LMMs), and in this article we consider an extension of the skew-normal/independent LMM, where the error term has a dependence structure, such as damped exponential correlation or autoregressive correlation of order p. The proposed model provides flexibility in capturing the effects of skewness and heavy tails simultaneously when continuous repeated measures are serially correlated. For this robust model, we present an efficient EM-type algorithm for parameters estimation via maximum likelihood and the observed information matrix is derived analytically to account for standard errors. The methodology is illustrated through an application to schizophrenia data and some simulation studies. The proposed algorithm and methods are implemented in the new R package skewlmm.

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Section: Autoregressive Dependence Of Order Pmentioning

confidence: 99%

Scale mixture of skew‐normal linear mixed models with within‐subject serial dependence

Schumacher

Lachos

Matos

2021

Statistics in Medicine

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“…Here we do not focus on ML estimation. The interested reader is referred to Schumacher et al (2017) for further details.…”

Section: Estimation Via the Saem Algorithmmentioning

confidence: 99%

“…The dataset is depicted in Figure 3. Previous studies indicate that we should choose p to be 1 in our AR(p)-CR model (for more details see Schumacher et al 2017). The estimated parameters are presented in Table 6.…”

Section: Application To a Real Dataset: Total Phosphorus Concentrationmentioning

confidence: 99%

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Influence diagnostics for censored regression models with autoregressive errors

Schumacher

Lachos

Vilca

et al. 2018

Aus NZ J of Statistics

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Summary Observations collected over time are often autocorrelated rather than independent, and sometimes include observations below or above detection limits (i.e. censored values reported as less or more than a level of detection) and/or missing data. Practitioners commonly disregard censored data cases or replace these observations with some function of the limit of detection, which often results in biased estimates. Moreover, parameter estimation can be greatly affected by the presence of influential observations in the data. In this paper we derive local influence diagnostic measures for censored regression models with autoregressive errors of order p (hereafter, AR(p)‐CR models) on the basis of the Q‐function under three useful perturbation schemes. In order to account for censoring in a likelihood‐based estimation procedure for AR(p)‐CR models, we used a stochastic approximation version of the expectation‐maximisation algorithm. The accuracy of the local influence diagnostic measure in detecting influential observations is explored through the analysis of empirical studies. The proposed methods are illustrated using data, from a study of total phosphorus concentration, that contain left‐censored observations. These methods are implemented in the R package ARCensReg.

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“…For instance, Zeger & Brookmeyer () discussed maximum likelihood estimation for censored autoregressive models, Lee () proposed a simulated likelihood method for dynamic Tobit models, Park et al () developed an imputation algorithm for autoregressive moving average (ARMA) models, Monokroussos () proposed a Markov Chain Monte Carlo procedure with data augmentation for limited time series data including censored data as a special case, and Mohammad () considered a quasi‐EM algorithm for censored ARMA models. More recently, Schumacher et al () proposed a stochastic approximation of the EM algorithm and Wang & Chan () proposed a quasi‐likelihood method for censored regression models with autoregressive errors. All these methods require some parametric distributional assumptions on the disturbances, such as normality, which ease some computational challenges but may be too restrictive and violated in applications.…”

Section: Introductionmentioning

confidence: 99%

Copula‐based semiparametric analysis for time series data with detection limits

Tang

Wang

2019

Can J Statistics

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The analysis of time series data with detection limits is challenging due to the high‐dimensional integral involved in the likelihood. Existing methods are either computationally demanding or rely on restrictive parametric distributional assumptions. We propose a semiparametric approach, where the temporal dependence is captured by parametric copula, while the marginal distribution is estimated non‐parametrically. Utilizing the properties of copulas, we develop a new copula‐based sequential sampling algorithm, which provides a convenient way to calculate the censored likelihood. Even without full parametric distributional assumptions, the proposed method still allows us to efficiently compute the conditional quantiles of the censored response at a future time point, and thus construct both point and interval predictions. We establish the asymptotic properties of the proposed pseudo maximum likelihood estimator, and demonstrate through simulation and the analysis of a water quality data that the proposed method is more flexible and leads to more accurate predictions than Gaussian‐based methods for non‐normal data. The Canadian Journal of Statistics 47: 438–454; 2019 © 2019 Statistical Society of Canada

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Censored regression models with autoregressive errors: A likelihood‐based perspective

Cited by 15 publications

References 26 publications

Scale mixture of skew‐normal linear mixed models with within‐subject serial dependence

Scale mixture of skew‐normal linear mixed models with within‐subject serial dependence

Influence diagnostics for censored regression models with autoregressive errors

Copula‐based semiparametric analysis for time series data with detection limits

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