The main objective of this thesis is the development of a nonparametric sequential estimation
technique for the off-pulse interval(s) of a source function originating from a pulsar. It is important
to identify the off-pulse interval of each pulsar accurately, since the properties of the off-pulse
emissions are further researched by astrophysicists in an attempt to detect potential emissions
from the associated pulsar wind nebula (PWN). The identification technique currently used in the
literature is subjective in nature, since it is based on the visual inspection of the histogram estimate
of the pulsar light curve. The developed nonparametric estimation technique is not only objective
in nature, but also accurate in the estimation of the off-pulse interval of a pulsar, as evident from
the simulation study and the application of the developed technique to observed pulsar data.
The first two chapters of this thesis are devoted to a literature study that provides background
information on the pulsar environment and -ray astronomy, together with an explanation of the
on-pulse and off-pulse interval of a pulsar and the importance thereof for the present study. This
is followed by a discussion on some fundamental circular statistical ideas, as well as an overview
of kernel density estimation techniques. These two statistical topics are then united in order to
illustrate kernel density estimation techniques applied to circular data, since this concept is the
starting point of the developed nonparametric sequential estimation technique.
Once the basic theoretical background of the pulsar environment and circular kernel density
estimation has been established, the new sequential off-pulse interval estimator is formulated. The
estimation technique will be referred to as `SOPIE'. A number of tuning parameters form part
of SOPIE, and therefore the performed simulation study not only serves as an evaluation of the
performance of SOPIE, but also as a mechanism to establish which tuning parameter configurations
consistently perform better than some other configurations.
In conclusion, the optimal parameter configurations are utilised in the application of SOPIE to
pulsar data. For several pulsars, the sequential off-pulse interval estimators are compared to the
off-pulse intervals published in research papers, which were identified with the subjective \eye-ball"
technique. It is found that the sequential off-pulse interval estimators are closely related to the
off-pulse intervals identified with subjective visual inspection, with the benefit that the estimated
intervals are objectively obtained with a nonparametric estimation technique. / PhD (Statistics), North-West University, Potchefstroom Campus, 2014
| Identifer | oai:union.ndltd.org:NWUBOLOKA1/oai:dspace.nwu.ac.za:10394/12199 |
| Date | January 2014 |
| Creators | Schutte, Willem Daniël |
| Source Sets | North-West University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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