Convergence of the Gasser-mmller Estimator under -mixing Condition
نویسنده
چکیده
This paper is devoted to convergence problems of the Gasser-MMller estima-tor for the regression function in a xed-design regression model. We prove the asymptotic normality and rates of uniform strong convergence for this type of estimators under the-mixing condition on the residuals. The proof of strong convergence is based on a Bernstein-type inequality which is very similar to that derived in an earlier paper by
منابع مشابه
Convergence of nonparametric estimators for a regression function
In this paper we prove the asymptotic normality and rates of strong convergence of some types of estimators for the regression function in a xed-design regression model. We consider the Gasser-MMller estimator and the Priestley-Chao estimator (univariate and multivariate). The proofs of asymptotic normality are based on a central limit theorem from an earlier paper by the author (1996, Stochast...
متن کاملWavelet Linear Density Estimation for a GARCH Model under Various Dependence Structures
We consider n observations from the GARCH-type model: S = σ2Z, where σ2 and Z are independent random variables. We develop a new wavelet linear estimator of the unknown density of σ2 under four different dependence structures: the strong mixing case, the β- mixing case, the pairwise positive quadrant case and the ρ-mixing case. Its asymptotic mean integrated squared error properties are ...
متن کاملEstimation of the Density and the Regression Function under Mixing Conditions Preprint M12/98
In this paper we derive rates of strong convergence for the kernel density estimator and for the Nadaraya-Watson estimator under the-mixing condition and under the condition of absolute regularity. A combination of an inequality of Bernstein type (Rio 1995) and an exponential inequality (cf. Fuk/Nagaev 1971) is the crucial tool for the proofs. Moreover, we consider the application of the main s...
متن کاملOn the Minimax Optimality of Block Thresholded Wavelets Estimators for ?-Mixing Process
We propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator based on block thresholding are investigated. It is found that the estimators achieve optimal minimax convergence rates over large class...
متن کاملStrong Convergence Rates of the Product-limit Estimator for Left Truncated and Right Censored Data under Association
Non-parametric estimation of a survival function from left truncated data subject to right censoring has been extensively studied in the literature. It is commonly assumed in such studies that the lifetime variables are a sample of independent and identically distributed random variables from the target population. This assumption is often prone to failure in practical studies. For instance, wh...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999