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Βελτιωμένα διαστήματα εμπιστοσύνης για την διασπορά κανονικού πληθυσμούΤαφιάδη, Μαρία 25 May 2009 (has links)
Η παρούσα μεταπτυχιακή διατριβή ανήκει στο επιστημονικό πεδίο της Στατιστικής Θεωρίας Αποφάσεων και αποσκοπεί στην κατασκευή βελτιωμένων διαστημάτων εμπιστοσύνης για την διασπορά ενός πληθυσμού που προέρχεται από κανονική κατανομή. Η μελέτη του προβλήματος της κατασκευής ενός διαστήματος εμπιστοσύνης για την διασπορά μιας κανονικής κατανομής, παρουσιάστηκε στην εργασία του Shorrock (1990). Ειδικότερα, ο Shorrock σε αυτή του τη μελέτη κατασκεύασε διαστήματα εμπιστοσύνης που εξαρτώνταν από την δειγματική διασπορά και από τον δειγματικό μέσο. Συγκεκριμένα, τα νέα αυτά διαστήματα έχουν το ίδιο μήκος με το κλασικό διάστημα εμπιστοσύνης για την διασπορά, αλλά έχουν ομοιόμορφα μεγαλύτερη πιθανότητα κάλυψης. Αρχικά, εξετάζουμε λεπτομερώς τα γνωστά διαστήματα εμπιστοσύνης και πιο συγκεκριμένα, το διάστημα εμπιστοσύνης ίσων ουρών, ελαχίστου μήκους, λόγου πιθανοφανειών και το αμερόληπτο διάστημα εμπιστοσύνης για να γίνουν οι απαραίτητες συγκρίσεις με τα διαστήματα που θα παραχθούν στη συνέχεια. Το πρώτo διάστημα κατασκευάζεται ακολουθώντας μία διαδικασία που είναι αντίστοιχη με την μεθοδολογία εύρεσης του εκτιμητή τύπου Stein, γι' αυτό και το διάστημα που προκύπτει, ονομάζεται διάστημα εμπιστοσύνης τύπου Stein. Η κατασκευή του επόμενου διαστήματος βασίζεται στην μεθοδολογία εύρεσης του εκτιμητή Brown (1968) γι' αυτό και ονομάζεται διάστημα εμπιστοσύνης τύπου Brown. Κατ' όπιν και σε αναλογία με την μεθοδολογία εύρεσης των εκτιμητών Brewster and Zidek (1964) γενικεύεται το προηγούμενο διάστημα κατασκευάζοντας το διάστημα εμπιστσύνης Brewster and Zidek, το οποίο αποδεικνύεται με τη σειρά του ότι, είναι ένα γενικευμένο διάστημα Bayes. Έτσι, κάνοντας τη σύγκριση ως προς την πιθανότητα κάλυψης μεταξύ των νέων αυτών διαστημάτων και του κλασικού διαστήματος εμπιστοσύνης αποδεικνύεται πως αυτή είναι ομοιόμορφα μεγλύτερη για τα νέα διαστήματα. / This master thesis belongs to Statistic Decision Theory field and its purpose is the construction of improved confidence intervals for a normal variance. These intervals were studied by Shorrock (1990). Especially, the usual confidence interval for the variance of a normal distribution, is a function of the sample variance alone. However, in his work Shorrock constructs intervals for variance that also depend on the sample mean. The new intervals have the same length as the shortest interval, depending only on the sample variance and have uniformly higher probability of coverage. Initially, we study well known confidence intervals such as, confidence interval with equal tails, confidence interval of minimum length and then we construct the improved ones. More specifically, we construct a confidence interval analogue of the point estimator in Stein (1964), a confidence interval analogue of the point estimator in Brown (1968) and a Brewster and Zidek (1974) confidence interval, which is also a generalized Bayes interval. Thus, we understand that the intervals above, are improved because they have uniformly greater coverage probability than the shortest one.
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Empirical Likelihood Confidence Intervals for Generalized Lorenz CurveBelinga-Hill, Nelly E. 28 November 2007 (has links)
Lorenz curves are extensively used in economics to analyze income inequality metrics. In this thesis, we discuss confidence interval estimation methods for generalized Lorenz curve. We first obtain normal approximation (NA) and empirical likelihood (EL) based confidence intervals for generalized Lorenz curves. Then we perform simulation studies to compare coverage probabilities and lengths of the proposed EL-based confidence interval with the NA-based confidence interval for generalized Lorenz curve. Simulation results show that the EL-based confidence intervals have better coverage probabilities and shorter lengths than the NA-based intervals at 100p-th percentiles when p is greater than 0.50. Finally, two real examples on income are used to evaluate the applicability of these methods: the first example is the 2001 income data from the Panel Study of Income Dynamics (PSID) and the second example makes use of households’ median income for the USA by counties for the years 1999 and 2006
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Bayesian and pseudo-likelihood interval estimation for comparing two Poisson rate parameters using under-reported dataGreer, Brandi A. Young, Dean M. January 2008 (has links)
Thesis (Ph.D.)--Baylor University, 2008. / Includes bibliographical references (p. 99-101).
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Statistical inference for normal means with order restrictions and applications to dose-response studies /Davis, Karelyn Alexandrea, January 2004 (has links)
Thesis (M.Sc.)--Memorial University of Newfoundland, 2004. / Bibliography: leaves 94-103.
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Some methods for the analysis of skewed data /Dinh, Phillip V. January 2006 (has links)
Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (leaves 99-105).
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Better Confidence Intervals for Importance SamplingSak, Halis, Hörmann, Wolfgang, Leydold, Josef January 2010 (has links) (PDF)
It is well known that for highly skewed distributions the standard method of using the t statistic for the confidence interval of the mean does not give robust results. This is an important problem for importance sampling (IS) as its final distribution is often skewed due to a heavy tailed weight distribution. In this paper, we first explain Hall's transformation and its variants to correct the confidence interval of the mean and then evaluate the performance of these methods for two numerical examples from finance which have closed-form solutions. Finally, we assess the performance of these methods for credit risk examples. Our numerical results suggest that Hall's transformation or one of its variants can be safely used in correcting the two-sided confidence intervals of financial simulations.(author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics
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An Analysis of Confidence Levels and Retrieval of Procedures Associated with Accounts Receivable ConfirmationsRogers, Violet C. (Violet Corley) 12 1900 (has links)
The study addresses whether differently ordered accounts receivable workprograms and task experience relate to differences in judgments, confidence levels, and recall ability. The study also assesses how treated and untreated inexperienced and experienced auditors store and recall accounts receivable workprogram steps in memory in a laboratory environment. Additionally, the question whether different levels of experienced auditors can effectively be manipulated is also addressed.
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Interval Estimation for Linear Functions of Medians in Within-Subjects and Mixed DesignsBonett, Douglas G., Price, Robert M. 01 May 2020 (has links)
The currently available distribution-free confidence interval for a difference of medians in a within-subjects design requires an unrealistic assumption of identical distribution shapes. A confidence interval for a general linear function of medians is proposed for within-subjects designs that do not assume identical distribution shapes. The proposed method can be combined with a method for linear functions of independent medians to provide a confidence interval for a linear function of medians in mixed designs. Simulation results show that the proposed methods have good small-sample properties under a wide range of conditions. The proposed methods are illustrated with examples, and R functions that implement the new methods are provided.
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Interval Estimation for the Ratio of Percentiles from Two Independent Populations.Muindi, Pius Matheka 12 August 2008 (has links) (PDF)
Percentiles are used everyday in descriptive statistics and data analysis. In real life, many quantities are normally distributed and normal percentiles are often used to describe those quantities. In life sciences, distributions like exponential, uniform, Weibull and many others are used to model rates, claims, pensions etc. The need to compare two or more independent populations can arise in data analysis. The ratio of percentiles is just one of the many ways of comparing populations. This thesis constructs a large sample confidence interval for the ratio of percentiles whose underlying distributions are known. A simulation study is conducted to evaluate the coverage probability of the proposed interval method. The distributions that are considered in this thesis are the normal, uniform and exponential distributions.
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Two Essays on High-Dimensional Inference and an Application to Distress Risk PredictionZhu, Xiaorui 22 August 2022 (has links)
No description available.
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