Statistical Analysis of the Asymmetrical Unemployement in Albania

The asymmetry of the business cycle has concerned economists for a long time. The main objective of this study is testing asymmetries of the business cycle in Albania, using quarterly rates of unemployment. The extant literature shows that economic time series data changes faster during contractions than expansions. We use information received from unemployment to test the asymmetries in the Albanian business cycle. The use data from January 01, 2000 to September 31, 2017. The data are received from the Bank of Albania. In this analysis we use non-parametric method. We conclude that the moments of the distribution analysis is not a powerful method to reach conclusive results

Bayesian classification and survival analysis with curve predictors

We propose classification models for binary and multicategory data where the predictor is a random function. The functional predictor could be irregularly and sparsely sampled or characterized by high dimension and sharp localized changes. In the former case, we employ Bayesian modeling utilizing flexible spline basis which is widely used for functional regression. In the latter case, we use Bayesian modeling with wavelet basis functions which have nice approximation properties over a large class of functional spaces and can accommodate varieties of functional forms observed in real life applications. We develop an unified hierarchical model which accommodates both the adaptive spline or wavelet based function estimation model as well as the logistic classification model. These two models are coupled together to borrow strengths from each other in this unified hierarchical framework. The use of Gibbs sampling with conjugate priors for posterior inference makes the method computationally feasible. We compare the performance of the proposed models with the naive models as well as existing alternatives by analyzing simulated as well as real data. We also propose a Bayesian unified hierarchical model based on a proportional hazards model and generalized linear model for survival analysis with irregular longitudinal covariates. This relatively simple joint model has two advantages. One is that using spline basis simplifies the parameterizations while a flexible non-linear pattern of the function is captured. The other is that joint modeling framework allows sharing of the information between the regression of functional predictors and proportional hazards modeling of survival data to improve the efficiency of estimation. The novel method can be used not only for one functional predictor case, but also for multiple functional predictors case. Our methods are applied to analyze real data sets and compared with a parameterized regression method

Bayesian Semi- and Non-parametric Analysis for Spatially Correlated Survival Data

Flexible incorporation of both geographical patterning and risk effects in cancer survival models is becoming increasingly important, due in part to the recent availability of large cancer registries. The analysis of spatial survival data is challenged by the presence of spatial dependence and censoring for survival times. Accurately modeling the risk factors and geographical pattern that explain the differences in survival is particularly of interest. Within this dissertation, the first chapter reviews commonlyused baseline priors, semiparametric and nonparametric Bayesian survival models and recent approaches for accommodating spatial dependence, both conditional and marginal. The last three chapters contribute three flexible survival models: (1) a proportional hazards model with areal-level covariate-adjusted frailties with application to county-level breast cancer survival data, (2) a marginal Bayesian nonparametric model for time to disease arrival of threatened amphibian populations, and (3) a generalized accelerated failure time model with spatial intrinsic conditionally autoregressive frailties with application to county-level prostate cancer data. An R package spBayesSurv is developed to examine all the proposed models along with some traditional spatial survival models

Change-point Problem and Regression: An Annotated Bibliography

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis

Applied Mathematics and Computational Physics

As faster and more efficient numerical algorithms become available, the understanding of the physics and the mathematical foundation behind these new methods will play an increasingly important role. This Special Issue provides a platform for researchers from both academia and industry to present their novel computational methods that have engineering and physics applications

Statistical learning of random probability measures

The study of random probability measures is a lively research topic that has attracted interest from different fields in recent years. In this thesis, we consider random probability measures in the context of Bayesian nonparametrics, where the law of a random probability measure is used as prior distribution, and in the context of distributional data analysis, where the goal is to perform inference given avsample from the law of a random probability measure. The contributions contained in this thesis can be subdivided according to three different topics: (i) the use of almost surely discrete repulsive random measures (i.e., whose support points are well separated) for Bayesian model-based clustering, (ii) the proposal of new laws for collections of random probability measures for Bayesian density estimation of partially exchangeable data subdivided into different groups, and (iii) the study of principal component analysis and regression models for probability distributions seen as elements of the 2-Wasserstein space. Specifically, for point (i) above we propose an efficient Markov chain Monte Carlo algorithm for posterior inference, which sidesteps the need of split-merge reversible jump moves typically associated with poor performance, we propose a model for clustering high-dimensional data by introducing a novel class of anisotropic determinantal point processes, and study the distributional properties of the repulsive measures, shedding light on important theoretical results which enable more principled prior elicitation and more efficient posterior simulation algorithms. For point (ii) above, we consider several models suitable for clustering homogeneous populations, inducing spatial dependence across groups of data, extracting the characteristic traits common to all the data-groups, and propose a novel vector autoregressive model to study of growth curves of Singaporean kids. Finally, for point (iii), we propose a novel class of projected statistical methods for distributional data analysis for measures on the real line and on the unit-circle

Nonparametric Econometric Methods and Application

The present Special Issue collects a number of new contributions both at the theoretical level and in terms of applications in the areas of nonparametric and semiparametric econometric methods. In particular, this collection of papers that cover areas such as developments in local smoothing techniques, splines, series estimators, and wavelets will add to the existing rich literature on these subjects and enhance our ability to use data to test economic hypotheses in a variety of fields, such as financial economics, microeconomics, macroeconomics, labor economics, and economic growth, to name a few

Vibration Monitoring: Gearbox identification and faults detection

L'abstract è presente nell'allegato / the abstract is in the attachmen