Analysis of Poverty Dynamics in Canada (Working Paper 9)

While we know much about poverty (or “low income”) in Canada in a static context, our understanding of the underlying dynamics remains very limited. This is particularly problematic from a policy perspective and the country has been increasingly left out on an international level in this regard. The contribution of this paper is to report the results of an empirical analysis of low income (“poverty”) dynamics in Canada using the recently available “LAD” tax-based database. The paper first describes the general nature of individuals’ poverty profiles (how many are short-term versus longterm, etc.)., the breakdown of the poor population in any given year amongst these different types, and the characterisation of poverty profiles by sex and family type. It then reports the estimation of various econometric models, starting with a set which specifies entry into and exit from poverty in any given year as a function of a variety of personal attributes and situational characteristics, including family status and changes therein, province of residence, inter-provincial mobility, language, area size of residence and calendar year (to capture trend effects). A set of proper hazard models then adds duration effects to these specifications to see how exit and re-entry probabilities shift with the amount of time spent in a poverty spell or after having exited a previous spell. A final set of specifications then investigates “occurrence dependence” effects by including past poverty spells first in an entry model and then with respect to the probability of being poor in a given year. Policy implications are discussed.

The LiDAR Compass: Extremely Lightweight Heading Estimation with Axis Maps

This paper introduces the LiDAR compass, a bounded and extremely lightweight heading estimation technique that combines a two-dimensional laser scanner and axis maps, which represent the orientations of flat surfaces in the environment. Although suitable for a variety of indoor and outdoor environments, the LiDAR compass is especially useful for embedded and real-time applications requiring low computational overhead. For example, when combined with a sensor that can measure translation (e.g., wheel encoders) the LiDAR compass can be used to yield accurate, lightweight, and very easily implementable localization that requires no prior mapping phase. The utility of using the LiDAR compass as part of a localization algorithm was tested on a widely-available open-source data set, an indoor environment, and a larger-scale outdoor environment. In all cases, it was shown that the growth in heading error was bounded, which significantly reduced the position error to less than 1% of the distance travelled.

An R-package for the Estimation and Testing of Multiple Covariates and Biomarker Interactions for Survival Data Based on Local Partial Likelihood

When we study the variables that a ffect survival time, we usually estimate their eff ects by the Cox regression model. In biomedical research, e ffects of the covariates are often modi ed by a biomarker variable. This leads to covariates-biomarker interactions. Here biomarker is an objective measurement of the patient characteristics at baseline. Liu et al. (2015) has built up a local partial likelihood bootstrap model to estimate and test this interaction e ffect of covariates and biomarker, but the R code developed by Liu et al. (2015) can only handle one variable and one interaction term and can not t the model with adjustment to nuisance variables. In this project, we expand the model to allow adjustment to nuisance variables, expand the R code to take any chosen interaction terms, and we set up many parameters for users to customize their research. We also build up an R package called "lplb" to integrate the complex computations into a simple interface. We conduct numerical simulation to show that the new method has excellent fi nite sample properties under both the null and alternative hypothesis. We also applied the method to analyze data from a prostate cancer clinical trial with acid phosphatase (AP) biomarker.

Axis Mapping: The Estimation of Surface Orientations and its Applications in Vehicle Localization and Structural Geology

The map representation of an environment should be selected based on its intended application. For example, a geometrically accurate map describing the Euclidean space of an environment is not necessarily the best choice if only a small subset its features are required. One possible subset is the orientations of the flat surfaces in the environment, represented by a special parameterization of normal vectors called axes. Devoid of positional information, the entries of an axis map form a non-injective relationship with the flat surfaces in the environment, which results in physically distinct flat surfaces being represented by a single axis. This drastically reduces the complexity of the map, but retains important information about the environment that can be used in meaningful applications in both two and three dimensions. This thesis presents axis mapping, which is an algorithm that accurately and automatically estimates an axis map of an environment based on sensor measurements collected by a mobile platform. Furthermore, two major applications of axis maps are developed and implemented. First, the LiDAR compass is a heading estimation algorithm that compares measurements of axes with an axis map of the environment. Pairing the LiDAR compass with simple translation measurements forms the basis for an accurate two-dimensional localization algorithm. It is shown that this algorithm eliminates the growth of heading error in both indoor and outdoor environments, resulting in accurate localization over long distances. Second, in the context of geotechnical engineering, a three-dimensional axis map is called a stereonet, which is used as a tool to examine the strength and stability of a rock face. Axis mapping provides a novel approach to create accurate stereonets safely, rapidly, and inexpensively compared to established methods. The non-injective property of axis maps is leveraged to probabilistically describe the relationships between non-sequential measurements of the rock face. The automatic estimation of stereonets was tested in three separate outdoor environments. It is shown that axis mapping can accurately estimate stereonets while improving safety, requiring significantly less time and effort, and lowering costs compared to traditional and current state-of-the-art approaches.