Improved model checking methods for parametric models with responses missing at random

Sun, Zhihua; Chen, Feifei; Zhou, Xiao‐Hua; Zhang, Qingzhao

doi:10.1016/j.jmva.2016.11.003

Cited by 10 publications

(6 citation statements)

References 22 publications

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“…, similar to the one used in Sun and Wang (2009) and Sun et al (2017), among others, in multiple linear regression models. This equality justifies the use of the completed sample…”

Section: The Testing Problemmentioning

confidence: 99%

“…, where p (•) is the missing response operator (5), which is similar to the one used in Sun and Wang (2009), Sun et al (2017), Qin et al (2017), Bianco et al (2019), andBianco et al (2020), among others, in multiple linear regression models. This equality justifies the completed sample given by {…”

Section: The Testing Problemmentioning

confidence: 99%

“…Ciarleglio et al (2022) related through functional regression certain brain measures derived from electroencephalography containing missing observations and proposed several imputation methods. Beyond FDA, the MAR situation has been thoroughly studied in multiple linear regression; see, among others, González-Manteiga and Pérez-González (2006), Sun and Wang (2009), Li (2012), Sun et al (2017), Zheng et al (2020), Pérez González et al (2021, and references therein.…”

Section: Introductionmentioning

confidence: 99%

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Parameter estimation of the functional linear model with scalar response with responses missing at random

Febrero–Bande

Galeano

González–Manteiga

2017

Contributions to Statistics

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We construct a goodness-of-fit test for the Functional Linear Model with Scalar Response (FLMSR) with responses Missing At Random (MAR). For that, we extend an existing testing procedure for the case where all responses have been observed to the case where the responses are MAR. The testing procedure gives rise to a statistic based on a marked empirical process indexed by the randomly projected functional covariate. The test statistic depends on a suitable estimator of the functional slope of the FLMSR when the sample has MAR responses, so several estimators are proposed and compared. With any of them, the test statistic is relatively easy to compute and its distribution under the null hypothesis is simple to calibrate based on a wild bootstrap procedure. The behavior of the resulting testing procedure as a function of the estimators of the functional slope of the FLMSR is illustrated by means of several Monte Carlo experiments. Additionally, the testing procedure is applied to a real data set to check whether the linear hypothesis holds.

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“…, similar to the one used in Sun and Wang (2009) and Sun et al (2017), among others, in multiple linear regression models. This equality justifies the use of the completed sample…”

Section: The Testing Problemmentioning

confidence: 99%

Section: The Testing Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Parameter estimation of the functional linear model with scalar response with responses missing at random

Febrero–Bande

Galeano

González–Manteiga

2017

Contributions to Statistics

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“…Although the two test statistics we proposed have accurate limit distributions under

H_{0}

, when our sample size is small or even moderate, we must still use bootstrap calibration to obtain a precise significance level. Sun et al (2017) provided a bootstrap method for critical value calibration when the response variable is missing in the framework of mean regression. In the framework of quantile regression, Pérez‐González et al (2021) presented the wild bootstrap method when the response variable is missing at random.…”

Section: Asymptotic Propertiesmentioning

confidence: 99%

Powerful nonparametric checks for parametric single‐index quantile models with missing responses

Yuan

Liu

et al. 2022

Stat

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This paper considers the lack‐of‐fit test of parametric single‐index quantile models when the response variable is missing at random. The model's coefficients are estimated by an estimation method suitable for the quantile regression coefficients of the missing data. Simultaneously, an algorithm for solving the central subspace of the multidimensional quantile regression model with missing responses is proposed. Based on the central quantile regression subspace, we construct two‐dimensional reduction adaptive‐to‐model test statistics suitable for randomly missing response variables to avoid the curse of dimensionality. Under the null hypothesis and local alternative hypothesis, the asymptotic properties of the test statistics are obtained. The proposed testing methods are shown to be consistent and able to detect local alternative hypothetical models converging to the null model at the rate of order Ofalse(n−1false/2h−1false/4false). A consistent bootstrap method is proposed to determine the critical values, and its asymptotic properties are established. The simulation results show that the proposed method is superior to existing methods in terms of both empirical size and power in the case of multidimensional and even high‐dimensional covariables. The ACTG Protocol 175 data set is analyzed to demonstrate the application of the testing procedures. Supplementary materials for this article are available online.

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“…The main motivations of expressing H 0 as in ( 7) are that (i) R pro t (β, u; θ * ) is based on unconditional moment restrictions, implying that we can avoid the use of tuning parameters such as bandwidths when estimating R pro t (β, u; θ * ); and (ii) R pro t (β, u; θ * ) depends on covariates only through the one-dimensional projection β ⊤ X, greatly reducing the dimensionality of the problem. Indeed, this dimension-reduction device has been proven valuable in many contexts that need to deal with a large number of covariates; see, e.g., Escanciano (2006), García-Portugués et al (2014), Sun et al (2017), Zhu et al (2017), and Kim et al (2020); for an overview, see Guo and Zhu (2017). However, it is worth mentioning that (7) involves not only a single process R pro t (β, u; θ * ) as is commonly the case in the specification testing literature (see Escanciano, 2008 for an exception), but J different processes R pro t (β, u; θ * ) associated with the treatment levels t. From (7), one natural way to proceed is to compute the generalized residuals marked empirical process based on the projections 1…”

Section: Specification Tests Based On Double Projectionsmentioning

confidence: 99%

Specification tests for generalized propensity scores using double projections

Sant’Anna¹,

Song²

2020

Preprint

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This paper proposes a new class of nonparametric tests for the correct specification of generalized propensity score models. The test procedure is based on two different projection arguments, which lead to test statistics with several appealing properties. They accommodate high-dimensional covariates; are asymptotically invariant to the estimation method used to estimate the nuisance parameters and do not requite estimators to be root-n asymptotically linear; are fully data-driven and do not require tuning parameters, can be written in closed-form, facilitating the implementation of an easy-to-use multiplier bootstrap procedure. We show that our proposed tests are able to detect a broad class of local alternatives converging to the null at the parametric rate. Monte Carlo simulation studies indicate that our double projected tests have much higher power than other tests available in the literature, highlighting their practical appeal.

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Improved model checking methods for parametric models with responses missing at random

Cited by 10 publications

References 22 publications

Parameter estimation of the functional linear model with scalar response with responses missing at random

Parameter estimation of the functional linear model with scalar response with responses missing at random

Powerful nonparametric checks for parametric single‐index quantile models with missing responses

Specification tests for generalized propensity scores using double projections

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