STATISTICAL INFERENCE TECHNIQUES

Author: DAMILANO SCARPINELLO GABRIELA LILIANA.
Year: 2004.
University: AUTÓNOMA DE BARCELONA.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: ESCUELA DE POSTGRADO.

Summary: The thesis focuses on the study of the characteristics and processes of the inference Location and Scale Models. On the one hand, is characterized all models symmetrical location for which a linear combination of the average and median sample is a parameter estimator asintóticamente efficient localization. The resulting model, three parameters, can be understood as a distribution Normal Truncada Simetrizada. It also presented two alternative methods to estimate the parameters for their properties asintóticas, flights are competitors of the maximum likelihood estimators (GSS), one based on the "Curtosis Empirical", which was noted for its simplicity of calculation and a "Algorithm "Interactive that can be implemented easily using standard software that works with the distribution Normal Truncada simple. Studies are also being conducted based on simulations to compare the performance of different estimators when the sample size is small. Extending this finding to the particular case of estimator Hodges-Lehmann, characterized the distribution Logistics as the only model for location symmetrical which this estimate is asintóticamente efficient. Moreover, investigating procedures inference in location and scale models in the presence of censorship Type I (censored time) and demonstrates a sufficient condition for the uniqueness of the GSS. Moreover, applying the statistical Z *, based on the asymptotic approximation of higher order Saddlepoint, at intervals for estimation of the average population distribution Normal and the scale parameter of the distribution Extreme Value (Log-Weibull), and through simulations, are studying their behavior for small samples. The extension to the case of two samples is considered average for the comparison of samples paired and independent (problems Behrens-Fisher) and the comparison of the two parameters of scale distributions Extreme Value. While research is developed within the statistical mathematics, all the topics covered are illustrated with examples of application to practical situations.

Author: MARTÍNEZ CAMBLOR PABLO.
Year: 2004.
University: OVIEDO.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS - UNIVERSIDAD DE OVIEDO.

Summary: This thesis defines a measure of similarity (distance) between density functions that evaluates the area they have in common two absolutely continuous probability distributions. Since this measure builds a new statistical measure of respect seems to be a function of density and its estimation or similarity between several independent estimates of the same density function. Later is a theoretical study on the most important properties of this statistical measure calculated and vairanza and its the asymptotic distribution, as well as checking their convergence almost certainly, through techniques of stochastic processes. These theoretical results are used in the construction of a family of test scenarios to consider adjusting distribution to a theoretical model (goodness adjustment) and identity among various populations. In each of these contrasting analyzes their power using simulation methods and discusses the conditions for having a good performance. Finally, using techniques similar to the previous ones, is shown consistency bootstrap method softened and assesses its efficiency practice through simulations. This work is developed for one-dimensional variables, but in its final part gives some ideas for multivariate generalized to the case. The proposed method has the advantage of being able to compare more than two functions simultaneously density, possibly viewed as a generalization of the measure L1 and proving to be, at times, more powerful than the methods usually used in this type of contrasts.

Author: ARTIME CARLOS ENRIQUE.
Year: 2004.
University: OVIEDO.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FAC. CIENCIAS MATEMÁTICAS.

Summary: The report examines the mathematical properties of the art "genotipado batch" or "pools of DNA" and proposes new statistical methods for the better use of information. Stresses the multidisciplinary aspects of Biology, Statistics and Informatics. It discusses methods in the literature and proposes various generalizations concerning the mining lots, distribution of phenotypes, and so on. In the chapter entitled "Methods based on Remuestreo" proposes a new viewpoint to exploit the links between analysis genotipados batch and traditional methods, samples --- in individual DNA. It uses algorithms sampling, as the EM algorithm and its derivatives (MCEM, SEEM), as well as other techniques in this context (Extension of the method Bremer due to Sampford). It finally perform detailed comparisons of the gain accuracy of the technical proposals, using methods riculación.

Author: GARCÍA GALISTEO JULIA.
Year: 2004.
University: MÁLAGA.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: This paper presents a study from the point of view Bayesian, regression models dichotomous and its generalization to] case politómico.y of Poisson regression models. First, it generalizes the usual regression model dichotomous considering nexus arbitrary functions to verify certain minimum conditions, which call deterministic model. There will always be, in addition, the study of possible abnormal observations and is regarded as a criterion in choosing among several functions of the nexus of preferring one that is more immune to these comments, which leads to the consideration of functions that call link robust. It is proposed for two families of distributions as possible functions of the nexus, the family of t-Student distributions and the family of distributions Box- Tiao. Of those elected are those that are more robust that the functions of traditional nexus Logistics and Probit. These links can be found on the first play, when there are comments that abnormal many of the estimates and predictions are made with e] model considered to be much more stable, ie will be more insensitive to their presence. And secondly lugm ", it is possible to establish criteria that allow the detection of these remarks will not be necessary to eliminate them once detectadas- the original dataset. For a Poisson regression model and the regression Politómica also widespread models usual, ie the model Loglineal and Logistics Multivariante respectively, introduced as the general functions nexus belonging to a certain class to be introduced into the study of dichotomous model. A major problem usually occurs when analyzed heterogeneous data with these models is the sobredispersión. This issue focuses on a recital Bayesian models bayesianos hierarchical. Estimates of the parameters of the models surveyed generally obtained using samples of distibuciones post via MCMC procedures, in particular through the Metropolis-Hastings. order samples are great results asintóticos of these distributions. memory concludes with two appendices, Appendix C which illustrates the theory developed through examples with actual data and includes an application of the robust regression dichotomous the discriminant analysis robust. Lastly, in Appendix D is the program that has been developed with Mathematica, for the calculation of the maximum likelihood estimators in the regression model with dichotomous role as a link arbitrary, as well as the implementation the algorithm Metropolis-Hastings for deterministic model.

Author: PARDO FERNÁNDEZ JUAN CARLOS.
Year: 2005.
University: SANTIAGO DE COMPOSTELA.
Place of defense: FACULTAD DE MATEMÁTICAS.
Place of preparation: FACULTADE DE MATEMÁTICAS.

Summary: The regression is a fundamental problem in the statistics. A regression model describes the relationship between a variable or explanatory covariate and a variable response. If the variable response represents a time, often happens that the data is incomplete due to various reasons. A major source of incompleteness is censorship. The main objective of this thesis is to develop contrasts assumptions on the role of regression in various fields, both for comprehensive data to data censored. The contrasts are proposed based on the estimate of the distribution function from the mistakes of the regression model. In Chapter 1 we made a brief introduction on the new methods developed in this work. In Chapter 2 we propose a new method of comparing regression curves from a totally non parametrito. This lets you check the effect of covariates on the variables answer is the same in different groups of people. The idea of procediemento contrast studied in this thesis is to compare each poboblación the empirical distribution of waste with the empirical distribution of waste estimated assuming that the null hypothesis is true, through statistical contrast type and Kolmogorov-Smirnov Cramér-von Mises defined on an empirical process multidimensional. Also in this chapter explores a method to compare the distributions from the mistakes of the regression models in different groups. In Chapter 3 we extend the method of comparing regression curves proposed in the previous chapter to the situation where the variables are censored response. Finally, in Chapter 4 of this thesis we study a contrast adjustment for goodness parametric regression models in which the variable response is subject to censorship by the right. The parametric regression models are very attractive in many practical situations because it describes the relationship between the covariate and the variable response of a simple and usually the values of the parameters are interpretable. However, if the parametric model fails then the findings may be wrong. This motivates the development of contrasts goodness adjustment specific to verify the validity of a parametric model. The contrast is to compare two estimators of the distribution of errors regression model. In all cases tested theoretical results and describe mechanisms bootstrap to approximate the critical values of the corresponding contrasts. Also included simulation studies and applications to real data.

Author: RUFO BAZAGA MARÍA JESÚS.
Year: 2005.
University: EXTREMADURA.
Place of defense: ESCUELA POLITÉCNICA (CÁCERES).
Place of preparation: ESCUELA POLITÉCNICA. UNIVERSIDAD DE EXTREMADURA. CÁCERES.

Summary: This thesis presents a general framework for analyzing mixtures Bayesian models of finite natural exponential distributions families with quadratic variance. These families include distributions commonly used in statistical applications. First we consider the number of components known. In this context, the main challenges are the choice of distributions ante and resolving the problem of non identifiability of the parameters. The first problem is solved using a method based on the concept of distance Kullback-Leibler, while the second proposes an approach based on permutations of the coordinates of the points generated. To generate the distribution post is used muestrador Gibbs. In the event that the number of components is unknown, proposed methods to select among the various possible models by Bayes estimation factor. We have different approaches based on Monte Carlo methods. The technical proposals are valid for all models in which distributions are conjugated in advance. The generalization of the proposals is multidimensional distributions from a theoretical point of view, simple. We present the application to mixtures of distributions multinomiales. An important aspect in this kind of models is the sensitivity analysis. It proposes a method for approximating a measure of sensitivity as is the gradient. This technique particularly useful in models bayesianos resolved through Monte Carlo methods based on Markov chains. The main advantage is that it does not require additional sampling. Every proposed method is illustrated by the less an example. Finally, a chapter presents conclusions and future lines of inquiry.

Author: MARCOS RODRIGUES ANTONIO NUNO.
Year: 2005.
University: SALAMANCA.
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: The report examines and analyzes the concepts of excess kurtosis or multivariate, both empirical data to theoretical distributions, and in those cases in which the matrix of dispersion (variances and covariances) is inverse as those for which this matrix it is unique. The concept is important because it allows us to contrast the multivariate normality of a data table, which built tables quantiles of the multivariate kurtosis and, alternatively, give the same numerical approximations, which can be used for sample size n> 20. The report is divided into 5 chapters, and some appendices with Programs used, written in Mathematica, and a table of quantiles and kurtosis moments of the multivariate normal samples, sample sizes n = 4 (1) 30 (10) 100 , 150, 200 (100) 500, 1000 and the number of variables p = 2 (1) 12, p? No-2, ending with some conclusions and References. In the first chapter explores the concept of generalized inverse of a matrix and its properties. In Chapter 2 discusses the concepts of skew and kurtosis multivariate both for theoretical distributions to data tables, is still defined by Mardia, and definitions that extend to cases in which the scattering matrix is unique testing the general definition is independent of the reverse widespread use. In Chapter 3 discusses the properties of multivariate kurtosis, both theoretical distributions for empirical data; invariance is its low linear transformations that maintains the status of the scattering matrix, its effect on tests comparing averages, arrays dispersal, and its use as evidence of multivariate normality according to the test Mardia. In Chapter 4 we study, simulation, quantile and 4 first moments of the populations in kurtosis multivariate normal distribution theoretical approaches by an empirical distribution calculated with 50,000 observations simulated with a control in the mean and variance of the distribution ( theoretically that is known), and from there, we estimate the quantiles 0,005, 0,025, 0.05, 0.95, 0,975 and 0,995, which can establish the upper and lower limits of 90%, 95% and 99% of the population in kurtosis normal. Using simulated higher-order moments, adjust analytical expressions for the coefficients of asymmetry and the excess kurtosis sample multivariate approaches leading to the types of Cornish-Fisher and Edgeworth for quantiles and likely distribution of multivariate kurtosis, what cula greatly improves the approximations given by Mardia. In Chapter 5 we see some applications with specific data, ending with some Appendices Program, tables, Conclusions and References.

Author: PAGURA JOSÉ ALBERTO.
Year: 2006.
University: POLITÉCNICA DE VALENCIA.
Place of defense: Universidad Politécnica de Valencia.
Place of preparation: Universidad Politécnica de Valencia.

Summary: The overall objective of this research is proposing new alternatives and the comparative study of the various existing procedures for obtaining unilateral tolerance limits, in situations sampling bietápico balanced or unbalanced due to the so-called model analysis of variance effects random. Discusses First, the solutions proposed by various authors to obtain tolerance limits unilateral models balanced and proposes a modification of the method of Mee-Owen to improve their statistical properties. We evaluate the performance of the different methods by two simulation studies. The most important contribution of the thesis focuses on the case of unbalanced models, which are very important practice in the steel industry. The thesis proposes an original procedure, which requires only relatively simple calculations and the use of table t no-central. In the thesis compares this new procedure with existing so far in the statistical literature. As a general conclusion of these studies, we can say that the new procedure developed in this thesis is, because of its simplicity and good statistical properties, the best method currently available to solve the major problem of obtaining practical limits of tolerance unilateral starting samples bietápicas unbalanced.

Author: Molanes López Elisa Maria.
Year: 2006.
University: A CORUÑA.
Place of defense: Facultad de Informática.
Place of preparation: USC.

Summary: In this mongraph, kernel estimators of the relative density are presented and several global bandwidth selectors are designed to appropriately choose the smoothing parameter. In Chapter 1 a more detailed introductrion to survival analysis, the bootstrap technique, nonparametric curve estimation, two sample problems and relative curves is given. The simplest case when the data are completely observed is studied in Chapter 2. Several bandwidht selectors are designed for two kernel estimators of the relative density, based on plug-in ideas and the bootstrap technique. A simulation study presents some results where the behaviour of these anda a classical selector are compared. Chapter 3 deals with the problem of estimating the relative density with right censores and left truncated data. Three bandwidth selectors are proposed for the relative density kernel estimator considered for this scenario, and their performance, under different percentages of censoring and truncation, is checked througn a simulation study. In Chapter 4 a test for the null hypothesis of equal populations is designed using the relative distribution function via an empirical likelihood approach. Finally, Chapter 5 include two real data applications concerning prostate and gastricu cancer and Chapter 6 collects some future research lines.