Hoeffding’s inequality provides a probability bound for the deviation between the average of n independent bounded random variables and its mean. This paper introduces two inequalities that extend Hoeffding’s inequality to panel data, which consists of several mutually independent sequences...

Linear errors-in-covariables models are considered, assuming the availability of independent validation data on the covariables in addition to primary data on the response variable and surrogate covariables. We first develop an estimated empirical loglikelihood with the help of validation data...

We consider a semiparametric model that parameterizes the conditional density of the response, given covariates, but allows the marginal distribution of the covariates to be completely arbitrary. Responses may be missing. A likelihood-based imputation estimator and a...

A partially linear model is considered when the responses are missing at random. Imputation, semiparametric regression surrogate and inverse marginal probability weighted approaches are developed to estimate the regression coefficients and the nonparametric function, respectively. All the...

Consider the partial linear models of the formY=X[tau][beta]+g(T)+e, where thep-variate explanatoryXis erroneously measured, and bothTand the responseYare measured exactly. LetXbe the surrogate variable forXwith measurement error. Let the primary data set be that containing independent...

In this paper, some nonparametric approaches of density function estimation are developed when censoring indicators are missing at random. A conditional mean score based estimator and a mean score estimator are suggested, respectively. The two estimators are proved to be asymptotically normal...

Consider partial linear models of the form Y=X[tau][beta]+g(T)+e with Y measured with error and both p-variate explanatory X and T measured exactly. Let be the surrogate variable for Y with measurement error. Let primary data set be that containing independent observations on and the validation...

This paper develops estimation approaches for nonparametric regression analysis with surrogate data and validation sampling when response variables are measured with errors. Without assuming any error model structure between the true responses and the surrogate variables, a regression...

Varying coefficient error-in-covariables models are considered with surrogate data and validation sampling. Without specifying any error structure equation, two estimators for the coefficient function vector are suggested by using the local linear kernel smoothing technique. The proposed...