No description available.

Cluster analysis refers to a type of statistical method designed to identify homogeneous groups within complex, multivariate data sets. In this study two newly developed genetic cluster analysis algorithms, GENCLUS and GENCLUS+, were validated by comparing their performance against that of three popular clustering techniques (Ward's method, K-means w/ random seeds, K-means w/Ward's centroids) and in an elaborate Monte Carlo study. Additionally, the ability of GENCLUS+ to determine the correct number of clusters was compared against that of three conventional procedures (Calinski and Harabasz, C-index, trace W). GENCLUS and GENCLUS+ achieved Rand recovery values slightly inferior to those of conventional methods. However, GENCLUS+ appeared to perform better than conventional methods in an empirical analysis, and genetic method solutions appear to possess high internal cohesion and external isolation. The mixed results are interpreted as an indication of a discrepancy between cluster theory and conventional data generation techniques. / Ph. D.

Methods of calculating the inbreeding coefficient In a finite population undergoing recurrent selection (self-select-intercross in succeeding generations) were investigated. It was noted that, in a population under selection, the inbreeding coefficient does not provide the experimenter with a measure of expected degree of variability; instead an index of total heterozygosity is required, and such an Index was derived. Formulas necessary to calculate both the inbreeding coefficients and the heterozygosity indexes were derived for the cases: one-locus, two-allele, random selection; k independent loci and random selection; one-locus, two-allele and effective directional selection; and k linked loci with effective directional selection. These formulas Involved defining a generalized inbreeding coefficient and a generalized index of homozygosity (or heterozygosity) in terms of vectors whose components reflected the various possible patterns of genes identical by descent at a given stage of the recurrent selection breeding program. Formulas were derived whereby the mean and the variance of the total number of loci homozygous (or heterozygous) by descent or in state may be obtained. The progress of the panmictic index and/or the index of total heterozygosity through at least twenty-five cycles of recurrent selection was observed in computer-simulated populations ranging in sizes from ten through one hundred, assuming varying recombination probabilities both in the one-locus and in the two linked-loci case and assuming both minimum and maximum inbreeding selection patterns. Tables resulting from these simulated studies could be used to estimate minimum and maximum inbreeding coefficients and/or minimum and maximum heterozygosity indexes in experimental populations for which the initial conditions approximate those assumed in the simulated populations. It was observed that the coefficient of relationship in the source population was extremely important in tracing the progress of the degree of Inbreeding and/or total homozygosity, that linkage played a major role in promoting heterozygosity in a recurrent selection system, and that careful intercrossing rather than random mating in alternate generations of the recurrent selection cycle was important in promoting maximum heterozygosity in the selected population. In the simulated populations the effect of small population sizes was observed and, in general, indications were that unless more than five complete recurrent cycles are contemplated, increasing population size results In only relatively minor increases in panmixia, especially when linked loci are involved in the selected trait and when care Is taken to avoid a maximum inbreeding selection pattern. / Ph. D.

The underlying piecewise continuous surface of a digital image can be estimated through robust statistical procedures. This thesis contains a systematic Monte Carlo study of M-estimation and LMS estimation for image surface approximation, an examination of the merits of postprocessing and tuning various parameters in the robust estimation procedures, and a new robust variable order facet model paradigm. Several new goodness of fit measures are introduced, and systematically compared. It is shown that the M-estimation tuning parameters are not crucial, postprocessing is cheap and well worth the cost, and the robust variable order facet model algorithm (using M-estimation, new statistical goodness of fit measures, and postprocessing) manages to retain most of the statistical efficiency of Mestimation yet displays good robustness properties, and preserves the main geometric features of an image surface: step edges, roof edges and corners. / Master of Science

While a variety of researchers have identified periodic recurrences in infant behavioral state with various time-series techniques, the appropriateness of techniques which identify periodic recurrences in all infants at all ages have been questioned. The purpose of this study was to compare the utility of four time-series techniques used in the analysis of periodic recurrences in the behavioral state of 21 newborns during a 2 hour observation period. For quiet sleep, active sleep and awake states the period length of the major rhythm was estimated by 1) binary spectrum analysis, 2) binary autocorrelation, 3) renewal time analysis, and 4) kappa analysis. Repeated measures analysis of variance showed that the period lengths identified by renewal time analysis were significantly shorter than those identified by the other three techniques for quiet and active sleep. Further, the kappa analysis and binary autocorrelation showed that awake states were significantly shorter than both active sleep and quiet sleep. Pearson product-moment correlations showed that the relation between the periods for a given state identified by each analysis ranged from .01 to .83. The results indicate that 1) renewal time analysis is more sensitive to state interruptions than the other techniques, 2) awake states may have a different period length than either quiet sleep or active sleep, and 3) although the four techniques identified state recurrences in almost all of the neonates, only a smaller subgroup of neonates displayed a pattern of technique agreement that would indicate a clearly rhythmic pattern of states. / M.S.

The model used to estimate pallet life in the durability section of PDS is a composite of several computed "factors" which are intended to reflect the impact of design characteristics on pallet durability. The objective of this study was to evaluate the reliability of the estimates of joint performance and the resulting estimates of pallet life relative to the estimated joint performance. A series of delayed fastener axial withdrawal tests were performed on a wide range of pallet fasteners to evaluate the estimates of joint separation resistance that are used in the computation of the F ( 1) factor, the factor for joint separation resistance perpendicular to the pallet deck. This data, in addition to data obtained from previous studies, suggested that the model underestimated the delayed withdrawal performance of threaded nails. An improved relationship was derived for helically threaded, twisted square wire and annularly threaded nails which had the additional advantage of being sensitive to lumber moisture content both at the time of joint assembly and at the time of joint testing. Both the original and the improved relationships were found to grossly overpredict the withdrawal performance of plain shank nails and staples. A series of pallet corner drop tests were performed to evaluate the reliability of the estimates of joint torsional shear resistance that used in the computation of the F(2) factor, the factor for joint separation resistance parallel to the pallet deck. The pallets tested varied by lumber species, number of fastener couples, and fastener stiffness as measured by the MIBANT bend angle. The observed affect of changes in fastener stiffness on pallet diagonal rigidity was found to be accurately reflected in the computed F(2) values. The observed affect of changes in the number of fastener couples on pallet diagonal rigidity was overpredicted in the computed F(2) values. The observed affect of changes in the lumber specific gravity on pallet diagonal rigidity appeared to be overpredicted in the computed F(2) values but this might be due to the fact that the measured pallet distortions were adjusted to account for differences in pallet weights. Pallet weight is specific gravity dependent and adjusting pallet distortion by weight may have reduced the observed affect of specific gravity. It was not possible to statistically confirm a relationship between the estimates of pallet durability relative to pallet diagonal rigidity and observed pallet life. However, such a relationship appears likely. Also, the estimates of pallet durability were found to be conservative. / M.S.

No description available.

No description available.

Assignment (MComm)--Stellenbosch University, 2005. / ENGLISH ABSTRACT: Volatilty was originally seen to be constant and deterministic, but it was later realised that return series are non-stationary. Owing to this non-stationarity nature of returns, there were no reliable ex-post volatility measurements. Subsequently, researchers focussed on ex-ante volatility models. It was only then realised that before good volatility models can be created, reliable ex-post volatility measuremetns need to be defined. In this study we examine non-parametric ex-post volatility measurements in order to obtain approximations of the variances of non-stationary return series. A detailed mathematical derivation and discussion of the already developed volatility measurements, in particular the realised volatility- and DST measurements, are given In theory, the higher the sample frequency of returns is, the more accurate the measurements are. These volatility measurements referred to above, however, all have short-comings in that the realised volatility fails if the sample frequency becomes to high owing to microstructure effects. On the other hand, the DST measurement cannot handle changing instantaneous volatility. In this study we introduce a new volatility measurement, termed microstructure realised volatility, that overcomes these shortcomings. This measurement, as with realised volatility, is based on quadratic variation theory, but the underlying return model is more realistic. / AFRIKAANSE OPSOMMING: Volatiliteit is oorspronklik as konstant en deterministies beskou, dit was eers later dat besef is dat opbrengste nie-stasionêr is. Betroubare volatiliteits metings was nie beskikbaar nie weens die nie-stasionêre aard van opbrengste. Daarom het navorsers gefokus op vooruitskattingvolatiliteits modelle. Dit was eers op hierdie stadium dat navorsers besef het dat die definieering van betroubare volatiliteit metings 'n voorvereiste is vir die skepping van goeie vooruitskattings modelle. Nie-parametriese volatiliteit metings word in hierdie studie ondersoek om sodoende benaderings van die variansies van die nie-stasionêre opbrengste reeks te beraam. 'n Gedetaileerde wiskundige afleiding en bespreking van bestaande volatiliteits metings, spesifiek gerealiseerde volatiliteit en DST- metings, word gegee. In teorie salopbrengste wat meer dikwels waargeneem word tot beter akkuraatheid lei. Bogenoemde volatilitieits metings het egter tekortkominge aangesien gerealiseerde volatiliteit faal wanneer dit te hoog raak, weens mikrostruktuur effekte. Aan die ander kant kan die DST meting nie veranderlike oombliklike volatilitiet hanteer nie. Ons stel in hierdie studie 'n nuwe volatilitieits meting bekend, naamlik mikro-struktuur gerealiseerde volatiliteit, wat nie hierdie tekortkominge het nie. Net soos met gerealiseerde volatiliteit sal hierdie meting gebaseer wees op kwadratiese variasie teorie, maar die onderliggende opbrengste model is meer realisties.

No description available.