Thesis (PhD (Statistics and Actuarial Science))--University of Stellenbosch, 2007. / The smoothing of time series plays a very important role in various practical applications. Estimating
the signal and removing the noise is the main goal of smoothing. Traditionally linear smoothers were
used, but nonlinear smoothers became more popular through the years.
From the family of nonlinear smoothers, the class of median smoothers, based on order statistics, is the
most popular. A new class of nonlinear smoothers, called LULU smoothers, was developed by using
the minimum and maximum selectors. These smoothers have very attractive mathematical properties.
In this thesis their statistical properties are investigated and compared to that of the class of median
smoothers.
Smoothing, together with related concepts, are discussed in general. Thereafter, the class of median
smoothers, from the literature is discussed. The class of LULU smoothers is defined, their properties
are explained and new contributions are made. The compound LULU smoother is introduced and its
property of variation decomposition is discussed. The probability distributions of some LULUsmoothers
with independent data are derived. LULU smoothers and median smoothers are compared according
to the properties of monotonicity, idempotency, co-idempotency, stability, edge preservation, output
distributions and variation decomposition. A comparison is made of their respective abilities for signal
recovery by means of simulations. The success of the smoothers in recovering the signal is measured
by the integrated mean square error and the regression coefficient calculated from the least squares
regression of the smoothed sequence on the signal. Finally, LULU smoothers are practically applied.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/1124 |
| Date | 12 1900 |
| Creators | Jankowitz, Maria Dorothea |
| Contributors | Conradie, W. J., De Wet, T., University of Stellenbosch. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 2521458 bytes, application/pdf |
| Rights | University of Stellenbosch |
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