We address the problem of estimating the difference between two probability densities. A naive approach is a two-step procedure that first estimates two densities separately and then computes their difference. However, such a two-step procedure does not necessarily work well because the first step is performed without regard to the second step and thus a small error in the first stage can cause...

This paper proposes the wave peak frequency tracking methods based on least squares identification algorithm. The disturbance model is transformed into an autoregressive moving average (ARMA) and a recursive extended (RELS) algorithm derived to identify parameters by using auxiliary idea. Furthermore, two-stage (2S-RELS) presented improve convergence speed hierarchical principle. A ship heading...

We consider the problem of estimating and testing for multiple breaks in a single equation framework with regressors that are endogenous, i.e., correlated with the errors. First, we show based on standard assumptions about the regressors, instruments and errors that the second stage regression of the instrumental variable procedure involves regressors and errors that satisfy all the assumptions...

vii List of Figures x List of Tables xi I Direct Minimization of the Equation Residuals 1

Iron is an essential element used as supplement in different dosage-forms. Different time and expenditure-consuming methods introduced for detection and determination of elemental ions such as atomic absorption. In this research, two different and routine methods containing ATR-IR and atomic absorption were applied to define the amount of iron in 198 samples containing different concentrations ...