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

Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field

Why the poor in rural Malawi are where they are: An Analysis of the Spatial Determinants of the Local Prevalence of Poverty

"We examine the spatial determinants of the prevalence of poverty for small spatially defined populations in rural Malawi. Poverty prevalence was estimated using a small-area poverty estimation technique. A theoretical approach based on the risk chain conceptualization of household economic vulnerability guided our selection of a set of potential risk and coping strategies — the determinants of our model — that could be represented spatially. These were used in two analyses to develop global and local models, respectively. In our global model—a spatial error model — only eight of the more than two dozen determinants selected for analysis proved significant. In contrast, all of the determinants considered were significant in at least some of the local models of poverty prevalence. The local models were developed using geographically weighted regression. Moreover, these models provided strong evidence of the spatial nonstationarity of the relationship between poverty and its determinants. That is, in determining the level of poverty in rural communities, where one is located in Malawi matters. This result for poverty reduction efforts in rural Malawi implies that such efforts should be designed for and targeted at the district and subdistrict levels. A national, relatively inflexible approach to poverty reduction is unlikely to enjoy broad success." Authors' AbstractSpatial analysis (Statistics) ,Poverty mapping ,Spatial regression ,Poverty determinants ,

WATER COMMUNITIES IN THE REPUBLIC OF MACEDONIA: AN EMPIRICAL ANALYSIS OF MEMBERSHIP SATISFACTION AND PAYMENT BEHAVIOUR

The performance of Water Communities (WCs), a form of self-managing organisation for irrigation, in the Bregalnica region of the Republic of Macedonia is investigated. Analysis, drawing on primary survey data, focuses on the decision of farmers to join a WC (Heckman selection probit model), determinants of farmers’ satisfaction with their membership of WCs (ordered probit model) and factors associated with changes in farmers’ water payment behaviour (non-parametric CLAD model). Key determinants identified include transparency and trust with respect to the structure and operation of the WC, cost recovery rates, farm size and irrigation costs. Membership satisfaction is an important determinant of payment behaviour. Lessons for sustainable self-management are drawn.Irrigation, Self-management, Water User Associations, Eastern Europe, Macedonia,