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Probability theory is a branch of statistics, a science that employs mathematical methods of collection, organization, and interpretation of data, with applications in practically all scientific areas. This book provides a comprehensive overview of probability theory. It discusses some fundamental aspects of pure and applied probability theory and explores its use in solving a large array of problems. Topics addressed include complex probability, the stability of algorithms in statistical modeling, the non-homogeneous Hofmann process, and more.
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These notes are based on a regional set of lectures on curve estimation in the context of independent and dependent observations given at the University of California, Davis during June 1989. Much of these lectures is concerned with probability density or regression function estimation when observations are independent.
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The fine structure of earnings is defined by a theoretically meaningful decomposition of the covariance matrix of earnings (or log earnings) time series. A three-element variance components model is proposed for analyzing earnings of young workers. These components are interpreted as the effects of differential on-the-job training (OJT) and differential economic ability. Several properties of these components and relationships between them are deduced from the OJT model. Background noise generated by a nonstationary first-order autoregressive process, with heteroscedastic innovations and time-varying AR parameters is also assumed present in observed earnings. ML estimates are obtained for all parameters of the model for a sample of Swedish males. The results are consistent with the view that the OJT mechanism is an empirically significant phenomenon in determining individual earnings profiles.
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Panel data based on various longitudinal surveys have become ubiquitous in economics in recent years. Estimation using the analysis of covariance approach allows for control of various "individual effects" by estimation of the relevant relationships from the "within" dimension of the data. Quite often, however, the "within" results are unsatisfactory, "too low" and insignificant. Errors of measurement in the independent variables whose relative importance gets magnified in the within dimension are often blamed for this outcome. However, the standard errors-in-variables model has not been applied widely, partly because in the usual micro data context it requires extraneous information to identify the parameters of interest. In the panel data context a variety of errors-in-variables models may be identifiable and estimable without the use of external instruments. We develop this idea and illustrate its application in a relatively simple but not uninteresting case: the estimation of "labor demand" relationships, also known as the "short run increasing returns to scale" puzzle.
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This paper gives an alternative derivation of a Monte Carlo method that has been used to study robust estimators. Extensions of the technique to the regression case are also considered and some computational points are briefly mentioned.
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