Diatrivē--Ethnikon Metsovion Polytechneion. / Title has been changed by stamp to: Systathmisis chōrostathmikou diktyou dia neas prosengistikēs methodou. Summary in English. Vita. Bibliography: p. [110]-111.

Thesis (Ph. D.)--University of Chicago, Dept. of Statistics, December 2002. / Includes bibliographical references. Also available on the Internet.

Thesis--Uppsala. / Includes bibliographical references (p. 138-144).

Thesis (M.S.)--Ohio University, November, 2005. / Title from PDF t.p. Includes bibliographical references (p. 71-74)

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xiii, 104 p.; also includes graphics (some col.). Includes bibliographical references (p. 101-104). Available online via OhioLINK's ETD Center

Thesis (M.S.)--Duquesne University, 2009. / Title from document title page. Abstract included in electronic submission form. Includes bibliographical references (p. 42) and index.

The focus of the research was on numerical errors committed in foundation phase mathematics. It therefore explored: (1) numerical errors learners in foundation phase mathematics encounter (2) relationships underlying numerical errors and (3) the implementable strategies suitable for understanding numerical error analysis in foundation phase mathematics (Grade 3). From 375 learners who formed the population of the study in the primary schools (16 in total), the researcher selected by means of a simple random sample technique 80 learners as the sample size, which constituted 10% of the population as response rate. On the basis of the research questions and informed by positivist paradigm, a quantitative approach was used by means of tables, graphs and percentages to address the research questions. A Likert scale was used with four categories of responses ranging from (A) Agree, (S A) Strongly Agree, (D) Disagree and (S D) Strongly Disagree. The results revealed that: (1) the underlying numerical errors that learners encounter, include the inability to count backwards and forwards, number sequencing, mathematical signs, problem solving and word sums (2) there was a relationship between committing errors and a) copying numbers b) confusion of mathematical signs or operational signs c) reading numbers which contained more than one digit (3) It was also revealed that teachers needed frequent professional training for development; topics need to change and lastly government needs to involve teachers at ground roots level prior to policy changes on how to implement strategies with regards to numerical errors in the foundational phase. It is recommended that attention be paid to the use of language and word sums in order to improve cognition processes in foundation phase mathematics. Moreover, it recommends that learners are to be assisted time and again when reading or copying their work, so that they could have fewer errors in foundation phase mathematics. Additionally it recommends that teachers be trained on how to implement strategies of numerical error analysis in foundation phase mathematics. Furthermore, teachers can use tests to identify learners who could be at risk of developing mathematical difficulties in the foundation phase.

No description available.

The vast number of different study variables or population characteristics and the different domains of interest in a survey, make it impractical and almost impossible to calculate and publish standard errors for each estimated value of a population variable or characteristic and each domain individually. Since estimated values are subject to statistical variation (resulting from the probability sampling), standard errors may not be omitted from the survey report. Estimated values can be evaluated only if their precision is known. The purpose of this research project is to study the feasibility of mathematical modeling to estimate the standard errors of estimated values of population parameters or characteristics in survey data sets and to investigate effective and user-friendly presentation methods of these models in reports. The following data sets were used in the investigation: • October Household Survey (OHS) 1995 - Workers and Household data set • OHS 1996 - Workers and Household data set • OHS 1997 - Workers and Household data set • Victims of Crime Survey (VOC) 1998 The basic methodology consists of the estimation of standard errors of the statistics considered in the survey for a variety of domains (such as the whole country, provinces, urban/rural areas, population groups, gender and age groups as well as combinations of these). This is done by means of a computer program that takes into consideration the complexity of the different sample designs. The direct calculated standard errors were obtained in this way. Different models are then fitted to the data by means of regression modeling in the search for a suitable standard error model. A function of the direct calculated standard error value served as the dependent variable and a function of the size of the statistic served as the independent variable. A linear model, equating the natural logarithm of the coefficient of relative variation of a statistic to a linear function of the natural logarithm of the size of the statistic, gave an adequate fit in most of the cases. Well-known tests for the occurrence of outliers were applied in the model fitting procedure. For each observation indicated as an outlier, it was established whether the observation could be deleted legitimately (e.g. when the domain sample size was too small, or the estimate biased). Afterwards the fitting procedure was repeated. The Australian Bureau of Statistics also uses the above model in similar surveys. They derived this model especially for variables that count people in a specific category. It was found that this model performs equally well when the variable of interest counts households or incidents as in the case of the VOC. The set of domains considered in the fitting procedure included segregated classes, mixed classes and cross-classes. Thus, the model can be used irrespective of the type of subclass domain. This result makes it possible to approximate standard errors for any type of domain with the same model. The fitted model, as a mathematical formula, is not a user-friendly presentation method of the precision of estimates. Consequently, user-friendly and effective presentation methods of standard errors are summarized in this report. The suitability of a specific presentation method, however, depends on the extent of the survey and the number of study variables involved. / Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2007. / Mathematics and Applied Mathematics / unrestricted

The market model, which relates securities returns to their systematic risk (β), plays a major role in finance. The estimation of β , in particular, is fundamental to many empirical studies and investment decisions. This dissertation develops a model which explains the observed serial correlations in returns and the intervaling effects which are inconsistent with the market model assumptions. The model accounts for thin trading and different frictions in the trading process and has as special cases other models of thin trading and frictions presented in the finance literature. The main assumption of the model is that the prices observed in the market and used to compute returns differ by an error from the true prices generated by a Geometric Brownian Motion model, hence its name, the error in prices (EIP) model. Three estimation methods for β are examined for the EIP model: the Maximum Likelihood (ML) method, the Least Squares (LS) method and a method of moments. It is suggested to view the EIP model as a missing information model and use the EM algorithm to find the ML estimates of the parameters of the model. The approximate small sample and asymptotic properties of the LS estimate of β are derived. It is shown that replacing the true covariances by their sample moments estimates leads to a convenient and familiar form for a consistent estimate of β. Finally, some illustrations of six different estimation methods for β are presented using simulated and real securities returns. / Business, Sauder School of / Graduate