Comportamiento del estimador máximo verosímil para un parámetro k-dimensional en modelos con restricciones

Esta tesis se enmarca en la Inferencia Estadística bajo restricciones. Esta rama de la Estadística apareció en la mitad de los años 50 e incluye un conjunto de técnicas diseñadas para hacer frente a la información adicional que a menudo se tiene sobre los parámetros desconocidos relevantes de un modelo estadístico. Ha habido avances significativos en este campo durante los últimos años, sin embargo, hay pocos resultados en un tema interesante como la Estimación con restricciones. Este es el tema principal que se trata en la tesis. Se considera la estimación de funciones lineales de los parámetros en los diferentes tipos de restricciones y se comparan los estimadores de máxima verosimilitud con y sin restricciones (MLE). Probamos resultados relevantes, incluyendo la importancia de la dirección central del cono (Abelson y Tukey (1963)) y la de la dimensión del espacio paramétrico. Entre otros resultados se demuestra que, en la estimación de la dirección central en el cono simple, el error cuadrático medio del MLE restringido puede ser mayor que el del EMV sin restricciones cuando k es suficientemente grande. Seguidamente se trata la estimación simultánea de los parámetros y se prueba un resultado muy fuerte bajo la hipótesis de una sola restricción, a saber, que la probabilidad de cubrimiento de conjuntos convexos y simétricos respecto del origen A, es mayor cuando el estimador correspondiente A+δ se centra utilizando como estimador de δ el MLE con restricciones y no en el MLE sin restricciones . También se demuestran resultados interesantes en la estimación simultánea bajo restricciones de orden. En vista de estos resultados anteriores se estudian algunos estimadores alternativos con el fin de determinar en qué medida el MLE es bueno o es mejorado por otros estimadores. Finalmente, se estudia un modelo a escala uniforme para comprobar si los resultados anteriores, obtenidos principalmente en modelos de localización, son válidos en este contexto. Se obtienen resultados tanto en la estimación de las funciones lineales como sobre la estimación simultánea bajo restricciones de orden.  Departamento de Estadística e Investigación Operativ

Circular Order Aggregation and its Application to Cell-cycle Genes Expressions

The aim of circular order aggregation is to find a circular order on a set of n items using angular values from p heterogeneous data sets. This problem is new in the literature and has been motivated by the biological question of finding the order among the peak expression of a group of cell cycle genes. In this paper, two very different approaches to solve the problem that use pairwise and triplewise information are proposed. Both approaches are analyzed and compared using theoretical developments and numerical studies, and applied to the cell cycle data that motivated the problem.Ministerio de Ciencia e Innovación grant (MTM2012-37129)Ministerio de Ciencia e Innovación grant MTM2015-71217-REuropean Social Fund within the Programa Operativo Castilla y León 2007–201

ERCIM 2013

In recent years there has been considerable interest in drawing inferences regarding order relationships among angular parameters. In particular, in biology the interest is to understand genes participating in cell cycle across multiple species and whether they are functionally conserved. The time to peak expression, known as phase angle, of such a gene can be mapped onto a unit circle. Biologists are not only interested in estimating the phase angles but in determining the relative order of expression of various genes. The final aim is to know whether the order of peak expression among cell cycle genes is conserved evolutionarily across species. These questions are challenging due to large variability among studies and to the circular nature of the data. A methodology to find the underlying circular order in a population is presented. We also propose a solution for the problem of testing equality of circular orders among two or more populations. Unbalanced samples and differences in distributions are taken into consideration. The proposed methodology is illustrated by analyzing data sets from three species: Schizosaccharomyces Pombe, Schizosaccharomyces Cerevisiae and Humans. As a result a set of genes is presented where the circular order is conserved across these three species

Order Restricted Inference for Oscillatory Systems for Detecting Rhythmic Signals

Many biological processes, such as cell cycle, circadian clock, menstrual cycles, are governed by oscillatory systems consisting of numerous components that exhibit rhythmic patterns over time. It is not always easy to identify such rhythmic components. For example, it is a challenging problem to identify circadian genes in a given tissue using time-course gene expression data. There is a great potential for misclassifying non-rhythmic as rhythmic genes and vice versa. This has been a problem of considerable interest in recent years. In this article we develop a constrained inference based methodology called Order Restricted Inference for Oscillatory Systems (ORIOS) to detect rhythmic signals. Instead of using mathematical functions (e.g. sinusoidal) to describe shape of rhythmic signals, ORIOS uses mathematical inequalities. Consequently, it is robust and not limited by the biologist’s choice of the mathematical model. We studied the performance of ORIOS using simulated as well as real data obtained from mouse liver, pituitary gland and data from NIH3T3, U2OS cell lines. Our results suggest that, for a broad collection of patterns of gene expression, ORIOS has substantially higher power to detect true rhythmic genes in comparison to some popular methods, while also declaring substantially fewer non-rhythmic genes as rhythmic.Spanish Ministerio de Ciencia e Innovación [MTM2015-71217-R]Spanish Ministerio de Educación, Cultura y Deporte [FPU14/04534]Intramural Research Program of the National Institute of Environmental Health Sciences (NIEHS) [Z01 ES101744-04

II Encuentro Galaico-Portugués de Biometría

The study of biological rhythms is receiving a lot of attention in the literature in recent years. At the core of this research lies the methodological problem of how to detect rhythmic signals in measured data. Night and day, or dark and light patterns impact on human health in many different ways. For this reason, researchers are studying the effect of sleep on the circadian clock in human body during various stages of life. Important components of this clock are the circadian genes which have rhythmic expression overtime with phases suitably matching the night and day. Consequently, the identification of rhythmic signals is a problem of considerable interest for biologists. In this work, we develop a novel statistical procedure to detect rhythmic signals in oscillatory systems based on Order Restricted Inference (ORI). This methodology is tested both on simulations and on real data bases. Moreover the obtained results are compared with the most widely extended rhythmicity detection algorithms in literature

LASR 2015

This work is motivated by a problem encountered in Molecular Biology where researchers are interested in correlating angular data from two oscillatory systems. The observations are the time to peak expression (also known as phase angle) of periodic genes under two different conditions (dose levels, organs or even species). In particular, we deal here with expression data from genes participating in the cell-cycle. Cell-biologists are often interested in drawing inferences regarding the phase angle of cell-cycle genes since they are considered to be associated with the gene’s biological function (Jensen et al 2006)

Dawai: an R Package for Discriminant Analysis With Additional Information

The incorporation of additional information into discriminant rules is receiving in- creasing attention as the rules including this information perform better than the usual rules. In this paper we introduce an R package called dawai, which provides the functions that allow to de ne the rules that take into account this additional information expressed in terms of restrictions on the means, to classify the samples and to evaluate the accuracy of the results. Moreover, in this paper we extend the results and de nitions given in previous papers (Fern andez, Rueda, and Salvador 2006, Conde, Fern andez, Rueda, and Salvador 2012, Conde, Salvador, Rueda, and Fern andez 2013) to the case of unequal co- variances among the populations, and consequently de ne the corresponding restricted quadratic discriminant rules. We also de ne estimators of the accuracy of the rules for the general more than two populations case. The wide range of applications of these pro- cedures is illustrated with two data sets from two di erent elds, i.e., biology and pattern recognition.Spanish Ministerio de Ciencia e Innovación (MTM2012-37129

A bootstrap based measure robust to the choice of normalization methods for detecting rhythmic features in high dimensional data

Producción CientíficaGene-expression data obtained from high throughput technologies are subject to various sources of noise and accordingly the raw data are pre-processed before formally analyzed. Normalization of the data is a key pre-processing step, since it removes systematic variations across arrays. There are numerous normalization methods available in the literature. Based on our experience, in the context of oscillatory systems, such as cell-cycle, circadian clock, etc., the choice of the normalization method may substantially impact the determination of a gene to be rhythmic. Thus rhythmicity of a gene can purely be an artifact of how the data were normalized. Since the determination of rhythmic genes is an important component of modern toxicological and pharmacological studies, it is important to determine truly rhythmic genes that are robust to the choice of a normalization method. In this paper we introduce a rhythmicity measure and a bootstrap methodology to detect rhythmic genes in an oscillatory system. Although the proposed methodology can be used for any high throughput gene expression data, in this paper we illustrate the proposed methodology using a publicly available circadian clock microarray gene-expression data. We demonstrate that the choice of normalization method has very little effect on the proposed methodology. Specifically, for any pair of normalization methods considered in this paper, the resulting values of the rhythmicity measure are highly correlated. Thus it suggests that the proposed measure is robust to the choice of a normalization method. Consequently, the rhythmicity of a gene is potentially not a mere artifact of the normalization method used. Lastly, as demonstrated in the paper, the proposed bootstrap methodology can also be used for simulating data for genes participating in an oscillatory system using a reference dataset.Estadística e Investigación OperativaMINECO grant MTM2015-71217-RMinisterio de Educación, Cultura y Deporte grant FPU14/0453

Robust detection of incipient faults in VSI-fed induction motors using quality control charts.

A considerable amount of papers have been published in recent years proposing supervised classifiers to diagnose the health of a machine. The usual procedure with these classifiers is to train them using data acquired through controlled experiments, expecting them to perform well on new data, classifying correctly the condition of a motor. But, obviously, the new motor to be diagnosed cannot be the same that has been used during the training process; it may be a motor with different characteristics and fed from a completely different source. These different conditions between the training process and the testing one can deeply influence the diagnosis. To avoid these drawbacks, in this paper a new method is proposed which is based on robust statistical techniques applied in Quality Control applications. The proposed method is based on the online diagnosis of the operating motor and can detect deviations from the normal operational conditions. A robust approach has been implemented using high-breakdown statistical techniques which can reliably detect anomalous data that often cause an unexpected overestimation of the data variability, reducing the ability of standard procedures to detect faulty conditions in earlier stages. A case study is presented to prove the validity of the proposed approach. Motors of different characteristics, fed from the power line and several different inverters, are tested. Three different fault conditions are provoked, broken bar, a faulty bearing and mixed eccentricity. Experimental results prove that the proposed approach can detect incipient faults

Isotonic boosting classification rules

In many real classi cation problems a monotone relation between some predictors and the classes may be assumed when higher (or lower) values of those predictors are related to higher levels of the response. In this paper, we propose new boosting algorithms, based on LogitBoost, that incorporate this isotonicity information, yielding more accurate and easily interpretable rules. These algorithms are based on theoretical developments that consider isotonic regression. We show the good performance of these procedures not only on simulations, but also on real data sets coming from two very different contexts, namely cancer diagnostic and failure of induction motors