In reliability studies, the goal is to gain knowledge about a product's failure times or life expectancy. Precedence tests do not require large sample sizes and are used in reliability studies to compare the life-time distributions from two samples. Precedence tests are useful since they provide reliable results early in a life-test and the surviving units can be used in other tests. Ng and Balakrishnan (2010) proposed a precedence-type test based on the Kaplan-Meier estimator of the cumulative distribution function. A precedence-type test based on the Nelson-Aalen estimator of the cumulative hazard function has been proposed. This test was developed for both Type-II right censoring and progressive Type-II right censoring. Numerical results, including illustrative examples, critical values and a power study have been provided. The results from this test were compared with those from the test based on the Kaplan-Meier estimator.

One of the difficult issues in detection theory is to design a robust detector that takes into account the actual distribution of the original data. The most commonly used statistical detection model for blind detection is Gaussian distribution. Specifically, linear correlation is an optimal detection method in the presence of Gaussian distributed features. This has been found to be sub-optimal detection metric when density deviates completely from Gaussian distributions. Hence, we formulate a detection algorithm that enhances detection probability by exploiting the true characterises of the original data. To understand the underlying distribution function of data, we employed the estimation techniques such as parametric model called approximated density ratio logistic regression model and semiparameric estimations. Semiparametric model has the advantages of yielding density ratios as well as individual densities. Both methods are applicable to signals such as watermark embedded in spatial domain and outperform the conventional linear correlation non-Gaussian distributed.

Generalized linear mixture models (GLMM) are widely used in statistical applications to model count and binary data. We consider the problem of nonparametric likelihood estimation of mixing distributions in GLMM's with multiple random effects. The log-likelihood to be maximized has the general form l(G)=Σi log∫f(yi,γ) dG(γ) where f(.,γ) is a parametric family of component densities, yi is the ith observed response dependent variable, and G is a mixing distribution function of the random effects vector γ defined on Ω. The literature presents many algorithms for maximum likelihood estimation (MLE) of G in the univariate random effect case such as the EM algorithm (Laird, 1978), the intra-simplex direction method, ISDM (Lesperance and Kalbfleish, 1992), and vertex exchange method, VEM (Bohning, 1985). In this dissertation, the constrained Newton method (CNM) in Wang (2007), which fits GLMM's with random intercepts only, is extended to fit clustered datasets with multiple random effects. Owing to the general equivalence theorem from the geometry of mixture likelihoods (see Lindsay, 1995), many NPMLE algorithms including CNM and ISDM maximize the directional derivative of the log-likelihood to add potential support points to the mixing distribution G. Our method, Direct Search Directional Derivative (DSDD), uses a directional search method to find local maxima of the multi-dimensional directional derivative function. The DSDD's performance is investigated in GLMM where f is a Bernoulli or Poisson distribution function. The algorithm is also extended to cover GLMM's with zero-inflated data. Goodness-of-fit (GOF) and selection methods for mixed models have been developed in the literature, however their application in models with nonparametric random effects distributions is vague and ad-hoc. Some popular measures such as the Deviance Information Criteria (DIC), conditional Akaike Information Criteria (cAIC) and R2 statistics are potentially useful in this context. Additionally, some cross-validation goodness-of-fit methods popular in Bayesian applications, such as the conditional predictive ordinate (CPO) and numerical posterior predictive checks, can be applied with some minor modifications to suit the non-Bayesian approach. / Graduate / 0463 / rabihsaab@gmail.com

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Generalized linear mixture models (GLMM) are widely used in statistical applications to model count and binary data. We consider the problem of nonparametric likelihood estimation of mixing distributions in GLMM's with multiple random effects. The log-likelihood to be maximized has the general form l(G)=Σi log∫f(yi,γ) dG(γ) where f(.,γ) is a parametric family of component densities, yi is the ith observed response dependent variable, and G is a mixing distribution function of the random effects vector γ defined on Ω. The literature presents many algorithms for maximum likelihood estimation (MLE) of G in the univariate random effect case such as the EM algorithm (Laird, 1978), the intra-simplex direction method, ISDM (Lesperance and Kalbfleish, 1992), and vertex exchange method, VEM (Bohning, 1985). In this dissertation, the constrained Newton method (CNM) in Wang (2007), which fits GLMM's with random intercepts only, is extended to fit clustered datasets with multiple random effects. Owing to the general equivalence theorem from the geometry of mixture likelihoods (see Lindsay, 1995), many NPMLE algorithms including CNM and ISDM maximize the directional derivative of the log-likelihood to add potential support points to the mixing distribution G. Our method, Direct Search Directional Derivative (DSDD), uses a directional search method to find local maxima of the multi-dimensional directional derivative function. The DSDD's performance is investigated in GLMM where f is a Bernoulli or Poisson distribution function. The algorithm is also extended to cover GLMM's with zero-inflated data. Goodness-of-fit (GOF) and selection methods for mixed models have been developed in the literature, however their application in models with nonparametric random effects distributions is vague and ad-hoc. Some popular measures such as the Deviance Information Criteria (DIC), conditional Akaike Information Criteria (cAIC) and R2 statistics are potentially useful in this context. Additionally, some cross-validation goodness-of-fit methods popular in Bayesian applications, such as the conditional predictive ordinate (CPO) and numerical posterior predictive checks, can be applied with some minor modifications to suit the non-Bayesian approach. / Graduate / 0463 / rabihsaab@gmail.com

One of the difficult issues in detection theory is to design a robust detector that takes into account the actual distribution of the original data. The most commonly used statistical detection model for blind detection is Gaussian distribution. Specifically, linear correlation is an optimal detection method in the presence of Gaussian distributed features. This has been found to be sub-optimal detection metric when density deviates completely from Gaussian distributions. Hence, we formulate a detection algorithm that enhances detection probability by exploiting the true characterises of the original data. To understand the underlying distribution function of data, we employed the estimation techniques such as parametric model called approximated density ratio logistic regression model and semiparameric estimations. Semiparametric model has the advantages of yielding density ratios as well as individual densities. Both methods are applicable to signals such as watermark embedded in spatial domain and outperform the conventional linear correlation non-Gaussian distributed.

隨著資訊科技的發展與網際網路的普及，音樂與電影光碟盜版的問題也逐年嚴重，然影音盜版不僅影響權利人團體，影音業者及創作者之生存，亦攸關我國智慧財產之發展，更常成為我國在國際貿易諮商上的重要課題。在種種緣由與現況下，得使國內許多產、官、學、研團體想去研究影音盜版的相關議題，以了解其嚴重程度如何，或有無較客觀合理的指標或評估方式?並進一步研擬有效方法來防範盜版問題進一步惡化，為此上述問題乃是本研究之源起。 目前所有的影音盜版研究，多著重在計算盜版率,探討盜版因素,盜版行為的心理與法制問題，皆還尚未針對影音盜版率，建構出可供學者推論的盜版率機率分配，及其他相關的數量研究，因此，本研究的主要實証方向，乃根據2004年經濟部智慧財產局(intellectual property office ministry of economic affairs,R.O.C)委託政治大學之消費者調查資料，就音樂CD、影音VCD/DVD兩部分，針對筆者有興趣之變項(性別、年齡、有無上網下載等)，(1)分別建構各自的混合分配並了解其分配間的差異與趨勢， (2)探討消費者對盜版行為的態度，(3)了解消費者對喜好的光碟所願付價格之差異，(4)建立盜版率分配的信賴帶，以及(5)針對現有的調查資料進行盜版辨別。 最後，就查緝盜版與維護智慧財產權兩方面，實證分析提供政府相關單位作為參考的依據，以求擬訂周詳且完善的措施來防範日益惡化的盜版問題。 / With the development of computer technology and widespread of internet, the piracy problem goes more serious. The piracy situation makes much influence not only on the rights of international oblige societies but also the growing of the intellectual properties in Taiwan. Moreover, it becomes the rock on the road of international commercial negotiations. Beyond the serious situation in the mean time, more researchers and relevant organizations on the island are trying to pay more attention to this important issue. This research intends to understand several questions: How is the actual situation on the piracy problem? Are there any objective evaluation ways? Are there any effective policies to prevent it from going deeper? These questions lead to this research. In the meantime, most of Audio & Video piracy research emphasized only on calculating the piracy rate, or the reasons, or the relevant psychological and law problems, but few on piracy quantitative studies. Therefore the mainly intention of this research is based on the data from the IPO(Intellectual Property Office Ministry of Economic Affairs, ROC), which is executing by National Chengchi University. As for the two parts concerning music CD and visual VCD/DVD, and the variables those I am highly interested including gender, age, education level, downloading or not. The empirical study results show as below: (1)The piracy rate distribution corresponds with the Mixed Model, that mean that it have been proportionally mixed two degenerate distribution (while X=0 and 100) with the Normal distribution. (2) On the facets of distribution differences and trends analysis, not only music CD and visual VCD/DVD, the results of the research by Mann-Whitney test and Kolmogorov-Smirnov two sample test both reveal the rising tendency of overall piracy rate. The generation of 20~29 years old is the mainly pirate group, moreover, higher education grades group does the more pirating behaviors, and lower income group intends more unauthorized copying conducts. Furthermore, along with the development of internet technology, the infringement behavior is more serious on the network connectors than the non-network downloaders. (3) Under surveying the opinions of consumers about the piracy, regardless of whether music or movies, the deviation is more serious on male than female, under 30-year-old than above, low educated than high, low income than high, pirate than non-pirate, downloaders than non-downloaders. The problem locates not only the lack of the concepts and recognition on the intellectual properties rights, but also the scarce of moral or legal limitations on the unauthorized rebuilding or downloading. But in the other curious facet, although the higher grade educated groups got more equitable standpoints on the piracy discussion, but evidenced depend upon the collected data they are also mainly the group who did the piracy behaviors more. (4) On the price range that a consumer would like to pay for, most of the pirate consumer tends to pay low price to buy the A/V goods, most of the non-pirating consumer group tends to pay general price to buy ones, and no significant difference of these two groups with high price, (5) On the facets of confidence bands on the whole music CD and visual VCD/DVD pirating rate, because of the specialties of pirating data- the higher frequency while the piracy rate values 0 and 100, so that the upper and lower bound reveals at 0 and 100. Futhermore, the confidence bands obtains from the population distribution function, therefore it’s suitable for the goodness-of-fit test. The results met the Kolmogorov-Smirnov one sample test. (6) On the data recognition facets, the logistic regression model of piracy is constructed in this research. Classification from the fitted logistic regression models, the results reveals 107 non-pirate are mis-judged to pirating behaviors, 186 pirating samples are neglected to non-pirate ones, the correct recognition rate goes high of 88 %. Key Words：Piracy Rate, Mixture Models, Mann-Whitney, Kolmogorov-Smirnov, Logistic Regression Model, Nonparametric Statistics.

Diss. Stockholm : Handelshögskolan, 2002.

Thesis--University of Oklahoma. / Bibliography: leaves 69-70.

Nous nous intéressons à l'équivalence asymptotique, au sens de Le Cam, entre différents modèles statistiques. Plus précisément, nous avons exploré le cas de modèles statistiques associés à l'observation discrète de processus à sauts ou de diffusions unidimensionnelles, ainsi que des modèles à densité plus classiques.Ci-dessous, nous présentons brièvement les différents chapitres de la thèse.Nous commençons par présenter tous nos résultats dans un premier chapitre introductif. Ensuite, dans le Chapitre 2 nous rappelons les points clés de la théorie de Le Cam sur les expériences statistiques en se plaçant dans un contexte non paramétrique.Les Chapitres 3 et 4 traitent de l'équivalence asymptotique pour des modèles statistiques associés à l'observation discrète (haute fréquence) de processus à sauts. Dans un premier temps nous nous focalisons sur un problème d'équivalence en ce qui concerne l'estimation de la dérive, supposée appartenir à une certaine classe fonctionnelle. Il s'avère (Chapitre 3) qu'il y a une équivalence asymptotique, en ce qui concerne l'estimation de la dérive, entre le modèle statistique associé à l'observation discrète d'un processus additif $X$ et le modèle statistique gaussien associé à l'observation discrète de la partie continue de $X$.Dans un deuxième temps, nous nous sommes intéressés au problème de l'estimation non paramétrique de la densité de Lévy $f$ relative à un processus de Lévy à sauts purs, $Y$. Le Chapitre 4 illustre l'équivalence asymptotique, en ce qui concerne l'estimation de $f$, entre le modèle statistique associé à l'observation discrète de $Y$ et un certain modèle de bruit blanc gaussien ayant $sqrt f$ comme dérive.Le Chapitre 5 présente une extension d'un résultat bien connu sur l'équivalence asymptotique entre un modèle à densité et un modèle de bruit blanc gaussien.Le Chapitre 6 étudie l'équivalence asymptotique entre un modèle de diffusion scalaire avec une dérive inconnue et un coefficient de diffusion qui tend vers zéro et le schéma d'Euler correspondant.Dans le Chapitre 7 nous présentons une majoration en distance $L_1$ entre les lois de processus additifs.Le Chapitre 8 est consacré aux conclusions et discute des extensions possibles des travaux de thèse. / The subject of this Ph.D. thesis is the asymptotic equivalence, in the Le Cam sense, between different statistical models. Specifically, we explore the case of statistical models associated with the discrete observation of jump processes or diffusion processes as well as more classical density models.Below, we briefly introduce the different chapters of this dissertation.We begin by presenting our results in a first introductory chapter. Then, in Chapter 2, we recall the key points of the Le Cam theory on statistical experiences focusing on a nonparametric context.Chapters 3 and 4 deal with asymptotic equivalences for statistical models associated with discrete observation (high frequency) of jump processes. First, we focus on an equivalence problem regarding the estimation of the drift, assumed to belong to a certain functional class. It turns out (Chapter 3) that there is an asymptotic equivalence, for what concerns the estimation of the drift, between the statistical model associated with the discrete observation of an additive process $X$ and the Gaussian statistical model associated with the discrete observation of the continuous part of $X$. Then we study the problem of nonparametric density estimation for the Lévy density $f$ of a pure jump Lévy process $Y$. Chapter 4 illustrates the asymptotic equivalence, for what concerns the estimation of $f$, between the statistical model associated with the discrete observation of $Y$ and a certain Gaussian white noise model having $sqrt f$ as drift.In Chapter 5 we present an extension of the well-known asymptotic equivalence between density estimation experiments and a Gaussian white noise model.Chapter 6 describes the asymptotic equivalence between a scalar diffusion model with unknown drift and with diffusion coefficient tending to zero and the corresponding Euler scheme. In Chapter 7 we present a bound for the $L_1$ distance between the laws of additive processes.Chapter 8 is devoted to conclusions and discusses possible extensions of the results of this thesis.