Extremum estimators and stochastic optimization methods

Submitted in partial fulfillment for the Requirements for the Degree of PhD in Mathematics, in the Speciality of Statistics in the Faculdade de Ciências e Tecnologia

Dealing with frame imperfections in a business survey: an empirical study using without replacement bootstrap

This paper approaches issues related to frame problems and nonresponse in surveys. These nonsampling errors affect the accuracy of the estimates whereas the estimators became biased and less precise. We analyse some estimation methods that deal with those problems and give an especial focus to post-stratification procedures.

Parameter estimation in the presence of auxiliary information

Dissertação para obtenção do Grau de Doutora em Estatística e Gestão de Risco, Especialidade em Estatística

A solution for estimates in software development projects

The Corporate world is becoming more and more competitive. This leads organisations to adapt to this reality, by adopting more efficient processes, which result in a decrease in cost as well as an increase of product quality. One of these processes consists in making proposals to clients, which necessarily include a cost estimation of the project. This estimation is the main focus of this project. In particular, one of the goals is to evaluate which estimation models fit the Altran Portugal software factory the most, the organization where the fieldwork of this thesis will be carried out. There is no broad agreement about which is the type of estimation model more suitable to be used in software projects. Concerning contexts where there is plenty of objective information available to be used as input to an estimation model, model-based methods usually yield better results than the expert judgment. However, what happens more frequently is not having this volume and quality of information, which has a negative impact in the model-based methods performance, favouring the usage of expert judgement. In practice, most organisations use expert judgment, making themselves dependent on the expert. A common problem found is that the performance of the expert’s estimation depends on his previous experience with identical projects. This means that when new types of projects arrive, the estimation will have an unpredictable accuracy. Moreover, different experts will make different estimates, based on their individual experience. As a result, the company will not directly attain a continuous growing knowledge about how the estimate should be carried. Estimation models depend on the input information collected from previous projects, the size of the project database and the resources available. Altran currently does not store the input information from previous projects in a systematic way. It has a small project database and a team of experts. Our work is targeted to companies that operate in similar contexts. We start by gathering information from the organisation in order to identify which estimation approaches can be applied considering the organization’s context. A gap analysis is used to understand what type of information the company would have to collect so that other approaches would become available. Based on our assessment, in our opinion, expert judgment is the most adequate approach for Altran Portugal, in the current context. We analysed past development and evolution projects from Altran Portugal and assessed their estimates. This resulted in the identification of common estimation deviations, errors, and patterns, which lead to the proposal of metrics to help estimators produce estimates leveraging past projects quantitative and qualitative information in a convenient way. This dissertation aims to contribute to more realistic estimates, by identifying shortcomings in the current estimation process and supporting the self-improvement of the process, by gathering as much relevant information as possible from each finished project.

Electrohysterogram signal component cataloging with spectral and time-frequency methods

The Electrohysterogram (EHG) is a new instrument for pregnancy monitoring. It measures the uterine muscle electrical signal, which is closely related with uterine contractions. The EHG is described as a viable alternative and a more precise instrument than the currently most widely used method for the description of uterine contractions: the external tocogram. The EHG has also been indicated as a promising tool in the assessment of preterm delivery risk. This work intends to contribute towards the EHG characterization through the inventory of its components which are: • Contractions; • Labor contractions; • Alvarez waves; • Fetal movements; • Long Duration Low Frequency Waves; The instruments used for cataloging were: Spectral Analysis, parametric and non-parametric, energy estimators, time-frequency methods and the tocogram annotated by expert physicians. The EHG and respective tocograms were obtained from the Icelandic 16-electrode Electrohysterogram Database. 288 components were classified. There is not a component database of this type available for consultation. The spectral analysis module and power estimation was added to Uterine Explorer, an EHG analysis software developed in FCT-UNL. The importance of this component database is related to the need to improve the understanding of the EHG which is a relatively complex signal, as well as contributing towards the detection of preterm birth. Preterm birth accounts for 10% of all births and is one of the most relevant obstetric conditions. Despite the technological and scientific advances in perinatal medicine, in developed countries, prematurity is the major cause of neonatal death. Although various risk factors such as previous preterm births, infection, uterine malformations, multiple gestation and short uterine cervix in second trimester, have been associated with this condition, its etiology remains unknown [1][2][3].

Orthogonal models, structure crossing, nesting and inference

We intend to study the algebraic structure of the simple orthogonal models to use them, through binary operations as building blocks in the construction of more complex orthogonal models. We start by presenting some matrix results considering Commutative Jordan Algebras of symmetric matrices, CJAs. Next, we use these results to study the algebraic structure of orthogonal models, obtained by crossing and nesting simpler ones. Then, we study the normal models with OBS, which can also be orthogonal models. We intend to study normal models with OBS (Orthogonal Block Structure), NOBS (Normal Orthogonal Block Structure), obtaining condition for having complete and suffcient statistics, having UMVUE, is unbiased estimators with minimal covariance matrices whatever the variance components. Lastly, see ([Pereira et al. (2014)]), we study the algebraic structure of orthogonal models, mixed models whose variance covariance matrices are all positive semi definite, linear combinations of known orthogonal pairwise orthogonal projection matrices, OPOPM, and whose least square estimators, LSE, of estimable vectors are best linear unbiased estimator, BLUE, whatever the variance components, so they are uniformly BLUE, UBLUE. From the results of the algebraic structure we will get explicit expressions for the LSE of these models.

Mapping the Pasture Steppe in Bayankhongor, Mongolia: comparison of classification methods, using Landsat-8 and geophysical data

Grasslands in semi-arid regions, like Mongolian steppes, are facing desertification and degradation processes, due to climate change. Mongolia’s main economic activity consists on an extensive livestock production and, therefore, it is a concerning matter for the decision makers. Remote sensing and Geographic Information Systems provide the tools for advanced ecosystem management and have been widely used for monitoring and management of pasture resources. This study investigates which is the higher thematic detail that is possible to achieve through remote sensing, to map the steppe vegetation, using medium resolution earth observation imagery in three districts (soums) of Mongolia: Dzag, Buutsagaan and Khureemaral. After considering different thematic levels of detail for classifying the steppe vegetation, the existent pasture types within the steppe were chosen to be mapped. In order to investigate which combination of data sets yields the best results and which classification algorithm is more suitable for incorporating these data sets, a comparison between different classification methods were tested for the study area. Sixteen classifications were performed using different combinations of estimators, Landsat-8 (spectral bands and Landsat-8 NDVI-derived) and geophysical data (elevation, mean annual precipitation and mean annual temperature) using two classification algorithms, maximum likelihood and decision tree. Results showed that the best performing model was the one that incorporated Landsat-8 bands with mean annual precipitation and mean annual temperature (Model 13), using the decision tree. For maximum likelihood, the model that incorporated Landsat-8 bands with mean annual precipitation (Model 5) and the one that incorporated Landsat-8 bands with mean annual precipitation and mean annual temperature (Model 13), achieved the higher accuracies for this algorithm. The decision tree models consistently outperformed the maximum likelihood ones.