1,267 research outputs found
Modeling and replicating statistical topology, and evidence for CMB non-homogeneity
Under the banner of `Big Data', the detection and classification of structure
in extremely large, high dimensional, data sets, is, one of the central
statistical challenges of our times. Among the most intriguing approaches to
this challenge is `TDA', or `Topological Data Analysis', one of the primary
aims of which is providing non-metric, but topologically informative,
pre-analyses of data sets which make later, more quantitative analyses
feasible. While TDA rests on strong mathematical foundations from Topology, in
applications it has faced challenges due to an inability to handle issues of
statistical reliability and robustness and, most importantly, in an inability
to make scientific claims with verifiable levels of statistical confidence. We
propose a methodology for the parametric representation, estimation, and
replication of persistence diagrams, the main diagnostic tool of TDA. The power
of the methodology lies in the fact that even if only one persistence diagram
is available for analysis -- the typical case for big data applications --
replications can be generated to allow for conventional statistical hypothesis
testing. The methodology is conceptually simple and computationally practical,
and provides a broadly effective statistical procedure for persistence diagram
TDA analysis. We demonstrate the basic ideas on a toy example, and the power of
the approach in a novel and revealing analysis of CMB non-homogeneity
Correcting for Measurement Error in Segmented Cox Model
Measurement error in the covariate of main interest (e.g. the exposure
variable, or the risk factor) is common in epidemiologic and health studies. It
can effect the relative risk estimator or other types of coefficients derived
from the fitted regression model. In order to perform a measurement error
analysis, one needs information about the error structure. Two sources of
validation data are an internal subset of the main data, and external or
independent study. For the both sources, the true covariate is measured (that
is, without error), or alternatively, its surrogate, which is error-prone
covariate, is measured several times (repeated measures). This paper compares
the precision in estimation via the different validation sources in the Cox
model with a changepoint in the main covariate, using the bias correction
methods RC and RR. The theoretical properties under each validation source is
presented. In a simulation study it is found that the best validation source in
terms of smaller mean square error and narrower confidence interval is the
internal validation with measure of the true covariate in a common disease
case, and the external validation with repeated measures of the surrogate for a
rare disease case. In addition, it is found that addressing the correlation
between the true covariate and its surrogate, and the value of the changepoint,
is needed, especially in the rare disease case
Audit fees in auditor switching
The auditor work is examining that a company's financial statements
faithfully reflect its financial situation. His wage, the audit fees, are not
fixed among all companies, but can be affected by the financial and structural
characteristics of the company, as well as the characteristics of the firm he
belongs to. Another factor that may affect his wage in an auditor switching,
which can be resulted from changes in the company that may influence the fees.
This paper examines the effect nature of the auditor switching on his wage, and
the factors of the company characteristics and the economy data which determine
the wage at switching. A product of the research are tools for predicting and
evaluating the auditor wage at switching. These tools are important for the
auditor himself, but also for the company manager to correctly determine the
wage due to the possibility that the quality of the audit work depends on its
fees. Two main results are obtained. First, the direction of the wage change in
the switching year depends on the economic stability of the economy. Second,
the switching effect on the direction and the change size in wage depends on
the change size in the company characteristics before and after switching - a
large change versus a stable one. We get that forecasting the change size in
wage for companies with a larger change is their characteristics is paralleled
to forecasting a wage increasing. And vice versa, forecasting the change size
in wage for companies with a stable change in their characteristics is
paralleled to forecasting a wage decreasing. But, whereas the former can be
achieved based on the company characteristics and macroeconomics factors, the
predictably of these characteristics and factors is negligible for the letter.Comment: 47 page
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