• Corpus ID: 54187764

A SPLINE-ASSISTED SEMIPARAMETRIC APPROACH TO NONPARAMETRIC MEASUREMENT ERROR MODELS

@article{Jiang2018ASS,
  title={A SPLINE-ASSISTED SEMIPARAMETRIC APPROACH TO NONPARAMETRIC MEASUREMENT ERROR MODELS},
  author={Fei Jiang and Yanyuan Ma},
  journal={arXiv: Statistics Theory},
  year={2018}
}
Nonparametric estimation of the probability density function of a random variable measured with error is considered to be a difficult problem, in the sense that depending on the measurement error prop- erty, the estimation rate can be as slow as the logarithm of the sample size. Likewise, nonparametric estimation of the regression function with errors in the covariate suffers the same possibly slow rate. The traditional methods for both problems are based on deconvolution, where the slow… 
5 Citations

Figures and Tables from this paper

Locally efficient estimation in generalized partially linear model with measurement error in nonlinear function
We investigate the errors in covariates issues in a generalized partially linear model. Different from the usual literature (Ma and Carroll in J Am Stat Assoc 101:1465–1474, 2006 ), we consider the
Semiparametric Statistical Estimation and Inference with Latent Information
TLDR
The relation between the unobservable variables and the instruments are used to devise consistent estimators for partially linear generalized single index models with binary response and the consistency, asymptotic normality of the estimator is established.
Measurement error models: from nonparametric methods to deep neural networks
TLDR
This paper proposes an efficient neural network design for estimating measurement error models, which utilizes recent advances in variational inference for deep neural networks, such as the importance weight autoencoder, doubly reparametrized gradient estimator, and non-linear independent components estimation.
Unfolding the Stroke-Ambulatory Blood Pressure Association : A Functional Framework
TLDR
This work uses the BOSS study to investigate the controversial relationship between stroke-related clinical outcomes and post stroke blood pressure, and proposes a functional analysis pipeline to analyze the ambulatory blood pressure trajectories more effectively.

References

SHOWING 1-10 OF 30 REFERENCES
Methodology for non‐parametric deconvolution when the error distribution is unknown
In the non‐parametric deconvolution problem, to estimate consistently a density or distribution from a sample of data contaminated by additive random noise, it is often assumed that the noise
Bayesian Smoothing and Regression Splines for Measurement Error Problems
TLDR
Bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error are described and the frequentist mean squared error properties of the fully Bayesian method are better than those of ICM and also of previously proposed frequentist methods, at least in the examples.
Bayesian semiparametric regression in the presence of conditionally heteroscedastic measurement and regression errors
TLDR
Bayesian semiparametric methodology based on mixtures of B-splines and mixtures induced by Dirichlet processes that relaxes restrictive assumptions about the density of the covariate and the densities of the regression and the measurement errors and vastly outperforms existing methods.
Density Estimation in the Presence of Heteroscedastic Measurement Error
We consider density estimation when the variable of interest is subject to heteroscedastic measurement error. The density is assumed to have a smooth but unknown functional form that we model with a
Nonparametric regression with errors in variables
The effect of errors in variables in nonparametric regression estimation is examined. To account for errors in covariates, deconvolution is involved in the construction of a new class of kernel
Optimal Rates of Convergence for Deconvolving a Density
Abstract Suppose that the sum of two independent random variables X and Z is observed, where Z denotes measurement error and has a known distribution, and where the unknown density f of X is to be
A consistent nonparametric density estimator for the deconvolution problem
The problem of nonparametric estimation of a probability density function when the sample observations are contaminated with random noise is studied. A particular estimator fn(x) is proposed which
SPLINE ESTIMATORS FOR THE FUNCTIONAL LINEAR MODEL
TLDR
This work considers a regression setting where the response is a scalar and the predictor is a random function defined on a compact set of R, and studies an estimator based on a B-splines expansion of the functional coefficient which generalizes ridge regression.
Locally efficient semiparametric estimators for functional measurement error models
A class of semiparametric estimators are proposed in the general setting of functional measurement error models. The estimators follow from estimating equations that are based on the semiparametric
Discrete-transform approach to deconvolution problems
If Fourier series are used as the basis for inference in deconvolution problems, the effects of the errors factorise out in a way that is easily exploited empirically. This property is the
...
1
2
3
...