Semiparametric models for nonlinear spatio-temporal data with application to the United States housing prices indexes

Modelling spatio-temporal data has received significant attention, recently and is widely applied in many disciplines such as economics, environmental and social sciences. In economics, housing price is a real example that indicates the importance of modeling such data. Estimating the movement in housing prices is an important but challenging problem due to the difficulties associated with spatio-temporal interactions. One main challenge is that there is no natural spatial ordering and thus it is not as straightforward as in time series analysis to transform data to be stationary across space. In addition, it is a challenge to model spatio-temporal data collected at irregularly spaced sampling locations due to the potentially large number of parameters. Moreover, the complexity of the dependence structure requires new effective statistical methods for modeling and analysis. While nonparametric and semiparametric methods have been popular for nonlinear modeling of time series data in econometrics and statistics, they become increasingly challenging when extended to irregularly located spatio-temporal data with complex nonlinear structures. The literature on nonlinear spatio-temporal modelling is still rather rare except a few contributions recently done, for example, by (Lu et al., 2009), (Wikle and Hooten, 2010) and (Wikle and Holan, 2011). Therefore, the main aim of this thesis is to propose a class of semiparametric spatio-temporal autoregressive partially nonlinear regression models as a practical way to overcome these challenges. The main contributions of this thesis are summarised as follows: (1) In Chapter 2, a class of semiparametric spatio-temporal autoregressive partially nonlinear regression models is proposed. The proposed models not only permit location-varying nonlinear relationships between the response variable and the covariates but also allow for the dependence structure to be nonstationary over space while alleviating the ”curse of dimensionality” by using the popular idea of spatial weight matrix measuring the spatial interaction, which is assumed to be well defined as in spatial econometrics. Both the estimation and its finite- and large sample properties for the proposed models are established. (2) In order to more objectively let data decide the spatial interaction in the models, in Chapter 3, we propose a scheme of general data-driven models to estimate the spatial weights in the semiparametric spatio-temporal autoregressive partially nonlinear regression models by applying the adaptive lasso. Both estimation and its finite- and large-sample properties for this class of the general data-driven models are developed. (3) An improved scheme for such data-driven models with spatial weight matrix is presented in Chapter 4. For this class of the improved data-driven models, we develop a computationally feasible method for estimation and thus enable our methodology to be applicable in practice. Asymptotic properties of our proposed estimates are established and comparisons are made, in theory and via simulations, between estimates before and after spatial smoothing. (4) In empirical case studies, the proposed methodologies are applied to investigate the housing prices in relation to the mortgage rates in Chapter 2 and to the consumer price index in Chapter 3 and 4 for the 50 states and District of Columbia (DC) in the United States (U.S.). It is empirically found that such relationships could be of nonlinear features that help to improve the predictions and the third class of the improved data-driven models appears to work promisingly better.Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2016

Combining Two Exponentiated Families to Generate a New Family of Distributions

This article presents a new technique to generate distributions that have the ability to fit any complex data called the exponentiated exponentiated Weibull-X (EEW-X) family, and the exponentiated exponentiated Weibull exponential (EEWE) distribution is presented as a member of this family. The new distribution’s unknown parameters were calculated by applying the maximum likelihood method. Some statistical properties, such as quantile, Rényi entropy, order statistics, and median are obtained for the proposed distribution. A simulation study was performed for different cases to investigate the estimation method’s performance. Three real datasets have been applied in which the new distribution has shown more flexibility compared to some other distributions

Correction: A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family.

[This corrects the article DOI: 10.1371/journal.pone.0263673.]