Semiparametric regression estimation using noisy nonlinear non invertible functions of the observations
نویسندگان
چکیده
We investigate a semiparametric regression model where one gets noisy non linear non invertible functions of the observations. We focus on the application to bearings-only tracking. We first investigate the least squares estimator and prove its consistency and asymptotic normality under mild assumptions. We study the semiparametric likelihood process and prove local asymptotic normality of the model. This allows to define the efficient Fisher information as a lower bound for the asymptotic variance of regular estimators, and to prove that the parametric likelihood estimator is regular and asymptotically efficient. Simulations are presented to illustrate our results.
منابع مشابه
Wavelet Threshold Estimator of Semiparametric Regression Function with Correlated Errors
Wavelet analysis is one of the useful techniques in mathematics which is used much in statistics science recently. In this paper, in addition to introduce the wavelet transformation, the wavelet threshold estimation of semiparametric regression model with correlated errors with having Gaussian distribution is determined and the convergence ratio of estimator computed. To evaluate the wavelet th...
متن کاملRobust high-dimensional semiparametric regression using optimized differencing method applied to the vitamin B2 production data
Background and purpose: By evolving science, knowledge, and technology, we deal with high-dimensional data in which the number of predictors may considerably exceed the sample size. The main problems with high-dimensional data are the estimation of the coefficients and interpretation. For high-dimension problems, classical methods are not reliable because of a large number of predictor variable...
متن کاملGeneralized Ridge Regression Estimator in Semiparametric Regression Models
In the context of ridge regression, the estimation of ridge (shrinkage) parameter plays an important role in analyzing data. Many efforts have been put to develop skills and methods of computing shrinkage estimators for different full-parametric ridge regression approaches, using eigenvalues. However, the estimation of shrinkage parameter is neglected for semiparametric regression models. The m...
متن کاملEstimation in a Semiparametric Modulated Renewal Process
We consider parameter estimation in a regression model corresponding to an iid sequence of censored observations of a finite state modulated renewal process. The model assumes a similar form as in Cox regression except that the baseline intensities are functions of the backwards recurrence time of the process and a time dependent covariate. As a result of this it falls outside the class of mult...
متن کاملNonparametric Estimation and Specification Testing in Nonstationary Time Series Models
In this paper, we consider both estimation and testing problems in a nonlinear time series model with nonstationarity. A nonparametric estimation method is proposed to estimate a sequence of nonparametric departure functions. We also propose a test statistic to test whether the regression function is of a known parametric nonlinear form. The power function of the proposed nonparametric test is ...
متن کامل