Thesis (B.Sc. (Hons.)) --University of Adelaide, 1957. / Typewr. copy. Includes published material.

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The work in this thesis is concerned with the development and extension of techniques for the assessment of influence diagnostics in data that include censored observations. Various regression models with censored data are presented and we concentrate on two models which are the accelerated failure time model, where the errors are generated by mixtures of normal distributions,and the Cox proportional hazards model. For the former, both finite discrete and continuous mixtures are considered, and an EM algorithm is used to determine measures of influence for each case. For the Cox proportional hazards model, various approaches to approximating influence curves are investigated. One-step or few-step approximations are developed using an EM algorithm and compared with a Newton-Raphson approach. Cook's measures of local influence are also investigated for the detection of influential cases in the data. The validity of the proportional hazards assumptions is also investigated. The residuals of Schoenfeld are examined for the possibility of being used to detect time dependence of the covariates in the proportional hazards model. Estimates to describe the nature of the time dependency computed from these residuals are presented.

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A new approach to removing the growth trend from dendrochronological data is described. It is assumed that the growth trend can be described by an expression of the form a.x.ᵇ exp. (-cx), which has the attributes of an increment function, and that accelerated growth, due to release at various points in a tree's history, can be represented by additive components that have the same basic form. A method of estimation is presented, along with some results of preliminary testing. The method shows promise of being superior to currently available alternatives.

The CROS algorithm for crossdating tree-ring series has proved useful. Because it uses Student's t to test correlations which are not independent between autocorrelated tree-ring series, it does not give a good measure of the relative significance of high correlations. It can be improved by transforming the correlation coefficients to normally distributed values, and giving a conservative estimate of the significance of the highest of these by a revised t, derived from its studentized deviation from the mean value. The improved algorithm should help any dendrochronologist who routinely dates oak timbers.

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Time-related region-wide growth declines or increases due to environmental impacts are not readily detected in rings of young trees because the intrinsic age-related decrease in ring widths is too prominent. Standardization techniques often obscure gradual growth changes due to exogenous factors such as regional atmospheric deposition. The model presented here uses a linear aggregate analysis of ring widths that permits age to be held constant while time varies. Rigorous testing requires tree-ring observations from evenaged stands exhibiting a range of current ages normal for the species and region. With age held constant, the key variable is simply the calendar year to which given rings are dated, a measure of the passage of time. An application of the model is given in which a 36 -year growth decline is identified in 20- to 40- year-old Pinus taeda L. in the southeastern United States.