The additive model affected by missing completely at random in the covariate

Nittner, Thomas

doi:10.1007/bf02892060

Cited by 3 publications

(5 citation statements)

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“…The studied regression model is Y = m(X) + σ (X) where is standard normal and m(x) is either x, or −x + x 2 , or x − 4x 2 +2x 3 suggested in Nittner (2004). As it is explained in Efromovich (1999, chap. 2), polynomials are challenging nonparametric curves for the cosine basis used by the orthogonal series estimator "nonp".…”

Section: Other Topicsmentioning

confidence: 98%

“…We begin with testing performance of the proposed in Section 2 data-driven nonparametric regression estimator (in what follows referred to as "nonp") for small samples. Apart of an imputation procedure of Nittner (2003Nittner ( , 2004, there are no nonparametric peers to compare with. As a result, the underlying idea of the study is to compare "nonp" with known parametric estimators recommended for missing data.…”

Section: Other Topicsmentioning

confidence: 99%

“…The nonparametric estimator "nonp" is also compared with a nonparametric estimator "nonp.im" motivated by Nittner (2003Nittner ( , 2004)-"nonp.im" imputes predictors using the "nearest neighbor I" method recommended in that articles and then uses the nonparametric estimator of Section 2 with h(y) ≡ 1 and δ l ≡ 1.…”

Section: Other Topicsmentioning

confidence: 99%

“…The first two are imputation procedures from R-library "mice" of Van Buuren and Groothuis-Oudshoorn (2011): (i) The predictive mean matching "pmm," which in our study performed identically to the "nearest neighbor I" recommended in Nittner (2003Nittner ( , 2004 for nonparametric regression; (ii) The Bayesian linear regression "norm." Note that "mice" employs multiple imputation recommended in the literature; see a discussion in Little and Rubin (2002) and Van Buuren and Groothuis-Oudshoorn (2011).…”

Section: Other Topicsmentioning

confidence: 99%

“…It is shown, both theoretically and numerically, that imputation of missing predictors may improve the efficiency. Other popular methods include a likelihood approach, inverse-probability weighting, EM and Bayesian procedures; see reviews and recent results in Horton and Kleiman (2007), Chen, Hong, and Torozzi (2008), Zhou, Wan, and Wang (2008), Qin, Zhang, and Leung (2009), and Wang and Chen (2009). Furthermore, numerical studies of Nittner (2003Nittner ( , 2004 indicate that imputation may be useful for nonparametric regression.…”

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confidence: 97%

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Nonparametric Regression With Predictors Missing at Random

Efromovich¹

2011

Journal of the American Statistical Association

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Nonparametric regression with predictors missing at random (MAR), where the probability of missing depends only on observed variables, is considered. Univariate predictor is the primary case of interest. A new adaptive orthogonal series estimator is developed. Large sample theory shows that the estimator is rate-minimax and it is also sharp-minimax whenever predictors are missing completely at random (MCAR). Furthermore, confidence bands, estimation of nuisance functions, including conditional probability of observing the predictor, design density and scale, and multiple regression are also considered. Numerical study and a real example show feasibility of the proposed methodology for small samples. Supplementary materials, containing results of the numerical study, are available online.

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Section: Other Topicsmentioning

confidence: 98%

Section: Other Topicsmentioning

confidence: 99%

Section: Other Topicsmentioning

confidence: 99%