We consider the problem of choice of norms in discrete approximation. First, we describe properties of the standard l1, l2 and l∞ norms, and their essential characteristics for using as error criteria in discrete approximation. After that, we mention the possibility of applications of the so-called total least squares and total least lp norm, for finding the best approximation. Finally, we take...

The creative capital possessed by the members of the creative class in region is either acquired through education or present innately in these members. Therefore, the creative infrastructure in the region is the sum of a part representing creative capital obtained through education and a second part denoting creative capital present innately in the creative class members. A researcher wishes t...

This note formalizes bias and inconsistency results for ordinary least squares (OLS) on the linear probability model and provides sufficient conditions for unbiasedness and consistency to hold. The conditions suggest that a btrimming estimatorQ may reduce OLS bias. D 2005 Elsevier B.V. All rights reserved.

A censored variable has a large fraction of observations at the minimum or maximum. Because the censored variable is not observed over its entire range ordinary estimates of the mean and variance of a censored variable will be biased. Ordinary least squares (OLS) estimates of its regression on a set of explanatory variables will also be biased. These estimates are not consistent, i.e., the bias...

This paper explores the correlates of career satisfaction among Canadian managers, professionals and executives, specifically the career satisfaction experience of both visible minority and non-visible minority immigrants. Survey data collected from over 13,000 managers, professionals and executives in 43 Canadian organizations were analysed using the ordinary least squares multiple regression ...

This paper demonstrates that the randomization-based “Neyman” and constanteffects estimators for the variance of estimated average treatment effects are equivalent to a variant of White’s “heteroskedasticity-robust” estimator and the homoskedastic ordinary least squares (OLS) estimator, respectively.

ii @Copyright 2012, Xiaomeng Bian iii Dedication This dissertation is dedicated to all I have ever learnt from. Sincerely. iv Acknowledgement First, I would like to give my sincere thanks to my families: my parents, uncles and aunties, brothers and sisters, and my in-heaven grandparents. Their selfless love and firm support encourage me to face all the challenges in my study-and-life time.

Let Y =XΘZ′ + E be the growth curve model with E distributed with mean 0 and covariance In ⊗Σ, where Θ, Σ are unknown matrices of parameters and X, Z are known matrices. For the estimable parametric transformation of the form γ =CΘD′ with given C and D, the twostage generalized least-squares estimator γ̂(Y) defined in (7) converges in probability to γ as the sample size n tends to infinity and, ...

We consider a linear model with normally distributed but heteroscedastic errors. When the error variances are functionally related to the regression parameter, one can use either maximum likelihood or generalized least squares to estimate the regression parameter. We show that maximum likelihood is much more sensitive to small misspecifications in the functional relationship between the error v...