Nonparametric estimation of an additive model with a link function

By Joel L. Horowitz, Enno Mammen. 2002

154 citations recorded by the source corpus.

This paper describes an estimator of the additive components of a nonparametric additive model with a known link function. When the additive components are twice continuously differentiable, the estimator is asymptotically normally distributed with a rate of convergence in probability of n-2/5. This is true regardless of the (finite) dimension of the explanatory variable. Thus, in contrast to the existing asymptotically normal estimator, the new estimator has no curse of dimensionality. Moreover, the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a4720303031cf063637c1605f21c296e485c24ad

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Local Inference in Additive Models with Decorrelated Local Linear Estimator (2019, background): “In the low-dimensional setting, additive models have been carefully investigated from both the methodological and theoretical perspectives [4,20,21,25,27,41].”
Nonparametric inference with generalized likelihood ratio tests (2007, methodology): “This phenomenon was also revealed in Horowitz and Mammen (2004) and Jiang and Li (2007) using two-step estimation methods based on the least squares and the Mestimation, respectively.”
Oracally Efficient Two-Step Estimation of Generalized Additive Model (2013, unknown): “It is also worth noting that although Horowitz and Mammen (2004) had used the B-spline estimator for the first stage in simulation, their proof is valid only for using the orthogonal series estimator in stage one.”
Smooth backfitting in generalized additive models (2008, methodology): “We compared our maximum smoothed likelihood estimators (YPM) with the two-stage procedures of Horowitz and Mammen [8], denoted by HM.”
SPLINE-BACKFITTED KERNEL SMOOTHING OF ADDITIVE COEFFICIENT MODEL (2010, background): “Other alternatives for estimating model (1) that may satisfy criteria (i)–(iii) are possible extensions of the smoothed backfitting of Mammen, Linton, and Nielsen (1999) and Nielsen and Sperlich (2005), and the two-stage estimator of Horowitz and Mammen (2004).”
Backfitting and smooth backfitting for additive quantile models (2010, background): “Horowitz and Lee (2005) studied an extension of the two-stage procedure of Horowitz and Mammen (2004) to quantile regression.”
Intersection bounds: estimation and inference (2009, methodology): “eorem 7. We now reproduce the imposed conditions from the example for clarity. We note that it is also possible to develop similar conditions for nonlinear estimators, see for example Theorem 1(d) of [35]. We have that θn(v) = EPn[Yi|Vi = v], assumed to be a continuous function. There is an i.i.d. s”
Large Sample Properties of Matching Estimators for Average Treatment Effects (2004, background): “some criticism (e.g., Horowitz and Mammen, 2002; Angrist and Hahn, 2003; Robins and Ritov”
Nonparametric Estimation of an Additive Quantile Regression Model (2004, methodology): “The estimator presented here builds on the work of Horowitz and Mammen (2004) (hereinafter HM), who developed an estimator of the additive components of a nonparametric additive mean regression model with a link function.”
Estimation and Inference for Generalized Geoadditive Models (2020, methodology): “…spline method of Stone (1986), Xue and Liang (2010), and Wang et al. (2011); the kernel method of Yu, Park, and Mammen (2008), Yang, Sperlich, and Härdle (2003), and Liang et al. (2008); and the two-stage methods of Horowitz and Mammen (2004), Wang and Yang (2007), and Liu, Yang, and Härdle (2013).”
Spline-backfitted kernel smoothing of nonlinear additive autoregression model (2006, background): “Stronger and more obscure conditions are assumed for the two-stage estimation proposed by [12].”