Additive isotone regression

Mammen, Enno; Yu, Kyusang

doi:10.1214/074921707000000355

Cited by 35 publications

(32 citation statements)

References 41 publications

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“…More sophisticated procedures could also be developed to define other regions, not necessarily a simple order cone, in R D , that better reflect the relation between parameters and auxiliary information. For instance, the intersection cone given by the order cones associated with two or more auxiliary variables or the region defined by the sum of order cones as in Mammen and Yu (2007). The generalization of the procedure is possible using the corresponding algorithms from ORI and similar models and estimators such as those presented in this paper.…”

Section: Discussionmentioning

confidence: 99%

Small area estimators based on restricted mixed models

Rueda

Menéndez

Gomez

2010

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This paper proposes a new model-based approach to estimate small areas that extends the Fay-Herriot methodology. The new model is additive, with a random term to characterize the inter-area variability and a nonparametric mean function specification, defined using the information on an auxiliary variable. The most significant advantage of the proposal is that it avoids the model misspecification problem. The monotonicity is the only assumption about the functional form of the relationship between the variable of interest and the auxiliary one. Estimators for the area means are derived combining "Order Restricted Inference" and standard mixed model approaches. A large simulation experiment shows how the new approach outperforms the Fay-Herriot methodology in many scenarios. Besides, the new method is applied to the Australian farms data.

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Section: Discussionmentioning

confidence: 99%

Small area estimators based on restricted mixed models

Rueda

Menéndez

Gomez

2010

TEST

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“…, X id ) T are the predictor variables for the ith observation. Furthermore, 31 in (1), α 0 is the unknown intercept and {α l } d l=1 are unknown univariate smooth nonparametric functions. Without loss of 32 generality, we assume that the predictors X ′ i s are distributed on the compact support [0, 1] d and α l is theoretically centered 33 with E [α l (X l )] = 0, for l = 1, .…”

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confidence: 99%

Constrained polynomial spline estimation of monotone additive models

Wang

Xue

2015

Journal of Statistical Planning and Inference

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“…This can be thought of as a generalized additive (semiparametric) model under a monotonicity constraint. While the MLEs of the parameters (β, ψ 1 , ψ 2 ) can be computed using (iterative) convex optimization techniques, very little is known about the asymptotic behavior of the parameters at this point, though some recent work by Mammen and Yu (2007) on additive isotonic regression suggests certain possibilities. However a treatment of these additive models is outside the scope of this paper.…”

Section: Concluding Discussionmentioning

confidence: 99%

Semiparametric binary regression models under shape constraints with an application to Indian schooling data

Banerjee

Mukherjee

Mishra

2009

Journal of Econometrics

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a r t i c l e i n f oArticle history: Available online xxxx JEL classification: C1 Keywords:Convex minorants Likelihood ratio statistic School attendance Semiparametric binary regression a b s t r a c tWe consider estimation of the regression function in a semiparametric binary regression model defined through an appropriate link function (with emphasis on the logistic link) using likelihood-ratio based inversion. The dichotomous response variable ∆ is influenced by a set of covariates that can be partitioned as (X, Z ) where Z (real valued) is the covariate of primary interest and X (vector valued) denotes a set of control variables. For any fixed X , the conditional probability of the event of interest (∆ = 1) is assumed to be a non-decreasing function of Z . The effect of the control variables is captured by a regression parameter β. We show that the baseline conditional probability function (corresponding to X = 0) can be estimated by isotonic regression procedures and develop a likelihood ratio based method for constructing asymptotic confidence intervals for the conditional probability function (the regression function) that avoids the need to estimate nuisance parameters. Interestingly enough, the calibration of the likelihood ratio based confidence sets for the regression function no longer involves the usual χ 2 quantiles, but those of the distribution of a new random variable that can be characterized as a functional of convex minorants of Brownian motion with quadratic drift. Confidence sets for the regression parameter β can however be constructed using asymptotically χ 2 likelihood ratio statistics. The finite sample performance of the methods are assessed via a simulation study. The techniques of the paper are applied to data sets on primary school attendance among children belonging to different socio-economic groups in rural India.

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Additive isotone regression

Cited by 35 publications

References 41 publications

Small area estimators based on restricted mixed models

Small area estimators based on restricted mixed models

Constrained polynomial spline estimation of monotone additive models

Semiparametric binary regression models under shape constraints with an application to Indian schooling data

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