A Law of Ti~e Iterated Locarithm for Nonparametric Regression Function Estimators*

نویسنده

  • Wolfgang HardIe
چکیده

to Summary: We prove a law of the iterated logarithm for nonparametric regression function estimators using strong approximations to the two dimensional empirical process. We consider the case of Nadaraya-Watson kernel estimators and of esti-mators based on orthogonal polynomials when the marginal density of the design variable X is unknown or known.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Wavelets for Nonparametric Stochastic Regression with Pairwise Negative Quadrant Dependent Random Variables

We propose a wavelet based stochastic regression function estimator for the estimation of the regression function for a sequence of pairwise negative quadrant dependent random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator are investigated. It is found that the estimators have similar properties to their counterparts st...

متن کامل

An Extension of the Hardy-littlewood Strong Law

A strong law is established for linear statistics that are weighted sums of a random sample. Using an observation of Cheng (1995a) about the Bernstein and Kolmogorov inequalities, we present an extension to the Hardy-Littlewood strong law under certain moment conditions on the weights and the distribution. As a byproduct, the Marcinkiewicz-Zygmund strong law and the law of the iterated logarith...

متن کامل

Asymptotic Behaviors of the Lorenz Curve for Left Truncated and Dependent Data

The purpose of this paper is to provide some asymptotic results for nonparametric estimator of the Lorenz curve and Lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. First, we show that nonparametric estimator of the Lorenz curve is uniformly strongly consistent for the associated Lorenz curve. Also, a strong Gaussian approximation for ...

متن کامل

Differenced-Based Double Shrinking in Partial Linear Models

Partial linear model is very flexible when the relation between the covariates and responses, either parametric and nonparametric. However, estimation of the regression coefficients is challenging since one must also estimate the nonparametric component simultaneously. As a remedy, the differencing approach, to eliminate the nonparametric component and estimate the regression coefficients, can ...

متن کامل

Feasible Multivariate Nonparametric Regression Estimation Using Weak Separability

One of the main practical problems of nonparametric regression estimation is the curse of dimensionality. The curse of dimensionality arises because nonparametric regression estimates are dependent variable averages local to the point at which the regression function is to be estimated. The number of observations ‘local’ to the point of estimation decreases exponentially with the number of dime...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008