Nonlinear models with measurement errors subject to single-indexed distortion

Estimation in linear regression models with measurement errors subject to single-indexed distortion

In this paper, we consider statistical inference for linear regression models when neither the response nor the predictors can be directly observed, but are measured with errors in a multiplicative fashion and distorted as single index models of observable confounding variables. We propose a semiparametric profile least squares estimation procedure to estimate the single index. Then we develop ...

Partial linear single index models with distortion measurement errors

We study partial linear single index models when the response and the covariates in the parametric part are measured with errors and distorted by unknown functions of commonly observable confounding variables, and propose a semiparametric covariate-adjusted estimation procedure. We apply the minimum average variance estimation method to estimate the parameters of interest. This is different fro...

Nonlinear Models of Measurement Errors

Measure errors in economic data are pervasive and nontrivial in size. The presence of measurement errors causes biased and inconsistent parameter estimates and leads to erroneous conclusions to various degrees in economic analysis. The importance of measurement errors in analyzing the empirical implications of economic theories is highlighted in Milton Friedman’s seminal book on the consumption...

Nonlinear Models of Measurement Errors By

Guessing Subject to Distortion

We investigate the problem of guessing a random vector X within distortion level D. Our aim is to characterize the best attainable performance in the sense of minimizing, in some probabilistic sense, the number of required guesses G(X) until the error falls below D. The underlying motivation is that G(X) is the number of candidate codewords to be examined by a rate-distortion block encoder unti...