Semiparametric Wavelet-Based JPEG IV Estimator for Endogenously Truncated Data

Abstract

A new and an enriched JPEG algorithm is provided for identifying redundancies in a sequence of irregular noisy data points which also accommodates a reference-free criterion function. Our main contribution is by formulating analytically (instead of approximating) the inverse of the transpose of JPEGwavelet transform without involving matrices which are computationally cumbersome. The algorithm is suitable for the widely-spread situations where the original data distribution is unobservable such as in cases where there is deficient representation of the entire population in the training data (in machine learning) and thus the covariate shift assumption is violated. The proposed estimator corrects for both biases, the one generated by endogenous truncation and the one generated by endogenous covariates. Results from utilizing 2,000,000 different distribution functions verify the applicability and high accuracy of our procedure to cases in which the disturbances are neither jointly nor marginally normally distributed. 10 Unlike the practice in some other studies applying only normally distributed disturbances. 11 Capital letters indicate random variables; lower case letters indicate realizations of these random variables.