<p>The first part of this thesis is concerned with trend modelling of breast cancer mortality rates. By using an age-period-cohort model, the relative contributions of period and cohort effects are evaluated once the unquestionable existence of the age effect is controlled for. The result of such a modelling gives indications in the search for explanatory factors. While this type of modelling is usually performed with 5-year period intervals, the use of 1-year period data, as in Paper I, may be more appropriate.</p><p>The main theme of the thesis is the evaluation of the ability to detect signals in x-ray images of breasts. Early detection is the most important tool to achieve a reduction in breast cancer mortality rates, and computer-aided detection systems can be an aid for the radiologist in the diagnosing process.</p><p>The evaluation of computer-aided detection systems includes the estimation of distributions. One way of obtaining estimates of distributions when no assumptions are at hand is kernel density estimation, or the adaptive version thereof that smoothes to a greater extent in the tails of the distribution, thereby reducing spurious effects caused by outliers. The technique is described in the context of econometrics in Paper II and then applied together with the bootstrap in the breast cancer research area in Papers III-V.</p><p>Here, estimates of the sampling distributions of different parameters are used in a new model for free-response receiver operating characteristic (FROC) curve analysis. Compared to earlier work in the field, this model benefits from the advantage of not assuming independence of detections in the images, and in particular, from the incorporation of the sampling distribution of the system's operating point.</p><p>Confidence intervals obtained from the proposed model with different approaches with respect to the estimation of the distributions and the confidence interval extraction methods are compared in terms of coverage and length of the intervals by simulations of lifelike data.</p>

Η παρούσα διπλωματική εργασία πραγματεύεται την μελέτη της μεθόδου Bootstrap στα πλαίσια συμπλήρωσης των ελλείψεων της DEA, κατά τον υπολογισμό της τεχνικής αποτελεσματικότητας διαφόρων μονάδων λήψης αποφάσεων. Πιο συγκεκριμένα θα μελετηθεί η Bootstrap ως μέσο για τον υπολογισμό της μεροληψίας, και διαστημάτων εμπιστοσύνης των efficiency scores που προκύπτουν από την χρήση της DEA. Όπως θα φανεί, η DEA, ως μία εφαρμογή του γραμμικού προγραμματισμού, αποτελεί μία μη παραμετρική μέθοδο υπολογισμού της τεχνικής αποτελεσματικότητας και χαρακτηρίζεται από το μειονέκτημα της έλλειψης στατιστικών μεγεθών καθώς και την αδυναμία να ξεχωρίσει τον θόρυβο από την αναποτελεσματικότητα. Η Bootstrap από την άλλη, αποτελεί μία επαναληπτική εφαρμογή της DEA, η οποία καλείται να δώσει λύση στα παραπάνω προβλήματα. Σκοπός της παρούσας διπλωματικής είναι να ελέγξει τον βαθμό στον οποίο η Bootstrap καταφέρνει να εκπληρώσει αυτή την αποστολή. Για το σκοπό αυτό χρησιμοποιούνται πραγματικά δεδομένα που αφορούν ιχθυοκαλλιέργειες που δραστηριοποιούνται στην ελληνική επικράτεια, ενώ οι υπολογισμοί γίνονται μέσω των προγραμμάτων DEAP και PIM – DEA v2.0. / The present diplomatic essay treats the study of Bootstrap method within the bounds of completion of DEA deficiencies during the estimation of technical efficiency of several decision-making units. More precisely it will be scrutinized bootstrap as a mean of estimating biasness and the confidence intervals of the efficiency scores, which arise from the use of DEA. As it will be come clear, DEA as an implementation of linear programming, constitutes a non-parametric method of estimating technical efficiency and is characterized by the drawback of non-distinguishing the noise by the inefficiency. On the other hand, bootstrap constitutes a repetitive implementation of DEA, which is assigned to give a solution to the above questions. The purpose of this essay is to verify the degree in which bootstrap completes this mission. For this reason there are used real data, which concern fish farms that are placed in Greek territory while, the calculations are executed through the programs DEAP and PIM – DEA V2.0

The first part of this thesis is concerned with trend modelling of breast cancer mortality rates. By using an age-period-cohort model, the relative contributions of period and cohort effects are evaluated once the unquestionable existence of the age effect is controlled for. The result of such a modelling gives indications in the search for explanatory factors. While this type of modelling is usually performed with 5-year period intervals, the use of 1-year period data, as in Paper I, may be more appropriate. The main theme of the thesis is the evaluation of the ability to detect signals in x-ray images of breasts. Early detection is the most important tool to achieve a reduction in breast cancer mortality rates, and computer-aided detection systems can be an aid for the radiologist in the diagnosing process. The evaluation of computer-aided detection systems includes the estimation of distributions. One way of obtaining estimates of distributions when no assumptions are at hand is kernel density estimation, or the adaptive version thereof that smoothes to a greater extent in the tails of the distribution, thereby reducing spurious effects caused by outliers. The technique is described in the context of econometrics in Paper II and then applied together with the bootstrap in the breast cancer research area in Papers III-V. Here, estimates of the sampling distributions of different parameters are used in a new model for free-response receiver operating characteristic (FROC) curve analysis. Compared to earlier work in the field, this model benefits from the advantage of not assuming independence of detections in the images, and in particular, from the incorporation of the sampling distribution of the system's operating point. Confidence intervals obtained from the proposed model with different approaches with respect to the estimation of the distributions and the confidence interval extraction methods are compared in terms of coverage and length of the intervals by simulations of lifelike data.

In this thesis, estimation in simple linear regression model with one-fold nested error is studied. To estimate the fixed effect parameters, generalized least squares and maximum likelihood estimation procedures are reviewed. Moreover, Minimum Norm Quadratic Estimator (MINQE), Almost Unbiased Estimator (AUE) and Restricted Maximum Likelihood Estimator (REML) of variance of primary units are derived. Also, confidence intervals for the fixed effect parameters and the variance components are studied. Finally, the aforesaid estimation techniques and confidence intervals are applied to a real-life data and the results are presented

Este trabalho tem como objetivo calcular intervalos de confiança para altos quantis oriundos de distribuições de caudas pesadas. Para isso, utilizamos os métodos da aproximação pela distribuição normal, razão de verossimilhanças, {\\it data tilting} e gama generalizada. Obtivemos, através de simulações, que os intervalos calculados a partir do método da gama generalizada apresentam probabilidades de cobertura bem próximas do nível de confiança, com amplitudes médias menores do que os outros três métodos, para dados gerados da distribuição Weibull. Todavia, para dados gerados da distribuição Fréchet, o método da razão de verossimilhanças fornece os melhores intervalos. Aplicamos os métodos utilizados neste trabalho a um conjunto de dados reais, referentes aos pagamentos de indenizações, em reais, de seguros de incêndio, de um determinado grupo de seguradoras no Brasil, no ano de 2003 / In this work, confidence intervals for high quantiles from heavy-tailed distributions were computed. More specifically, four methods, namely, normal approximation method, likelihood ratio method, data tilting method and generalised gamma method are used. A simulation study with data generated from Weibull distribution has shown that the generalised gamma method has better coverage probabilities with the smallest average length intervals. However, from data generated from Fréchet distribution, the likelihood ratio method gives the better intervals. Moreover, the methods used in this work are applied on a real data set from 1758 Brazilian fire claims

Dementia disorders are difficult to detect in the early stages of the disease. Therefore, it is of importance to develop new methods in early diagnostics. The Uppsala Dalarna Dementia and Gait Study has established a new method in diagnosing early stages of cognitive impairments. The new method Timed-Up-and-Go (TUG) dual-task, combines a gait test with a verbal task. This thesis analyses nine TUG variables for healthy controls and discusses differences between two age groups, subjects younger than 72 years and subjects 72 years or older. Reliability of the new method is the primary focus point and is assessed using Intraclass Correlation Coefficients (ICC) and Bland-Altman plots. Normative reference values for the continuous variables are estimated with the help of bootstrap confidence intervals for the 2.5 and 97.5 percentiles. The results show that the three variables measuring the time to complete the test have good to excellent reliability, while variables that measure combinations of gait and verbal tasks show poor to moderate reliability. The lower reliability for these variables could be explained by them being ratios or differences of other variables. Differences in reliability can be seen between the age groups, where younger subjects have lower reliability partly due to homogeneity. Results show that the reference values of healthy controls are different for the two age groups.

The dissertation considers construction of confidence intervals for a cumulative distribution function F(z) and its inverse at some fixed points z and u on the basis of an i.i.d. sample where the sample size is relatively small. The sample is modeled as having the flexible Generalized Gamma distribution with all three parameters being unknown. This approach can be viewed as an alternative to nonparametric techniques which do not specify distribution of X and lead to less efficient procedures. The confidence intervals are constructed by objective Bayesian methods and use the Jeffreys noninformative prior. Performance of the resulting confidence intervals is studied via Monte Carlo simulations and compared to the performance of nonparametric confidence intervals based on binomial proportion. In addition, techniques for change point detection are analyzed and further evaluated via Monte Carlo simulations. The effect of a change point on the interval estimators is studied both analytically and via Monte Carlo simulations.

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Approved for public release; distribution in unlimited. / Budget limitations have reduced the number of military components available for testing, and time constraints have reduced the amount of time available for actual testing resulting in many items still operating at the end of test cycles. These two factors produce small test populations (small sample size) with "heavily" censored data. The assumption of "normal approximation" for estimates based on these small sample sizes reduces the accuracy of confidence bounds of the probability plots and the associated quantities. This creates a problem in acquisition analysis because the confidence in the probability estimates influences the number of spare parts required to support a mission or deployment or determines the length of warranty ensuring proper operation of systems. This thesis develops a method that simulates small samples with censored data and examines the error of the Fisher-Matrix (FM) and the Likelihood Ratio Bounds (LRB) confidence methods of two test populations (size 10 and 20) with three, five, seven and nine observed failures for the Weibull distribution. This thesis includes a Monte Carlo simulation code written in S-Plus that can be modified by the user to meet their particular needs for any sampling and censoring scheme. To illustrate the approach, the thesis includes a catalog of corrected confidence bounds for the Weibull distribution, which can be used by acquisition analysts to adjust their confidence bounds and obtain a more accurate representation for warranty and reliability work. / Civilian, Department of the Air Force