Optimum experimental designs for models with a skewed error distribution : with an application to stochastic frontier models

In this thesis, optimum experimental designs for a statistical model possessing a skewed error distribution are considered, with particular interest in investigating possible parameter dependence of the optimum designs. The skewness in the distribution of the error arises from its assumed structure. The error consists of two components (i) random error, say V, which is symmetrically distributed with zero expectation, and (ii) some type of systematic error, say U, which is asymmetrically distributed with nonzero expectation. Error of this type is sometimes called 'composed' error. A stochastic frontier model is an example of a model that possesses such an error structure. The systematic error, U, in a stochastic frontier model represents the economic efficiency of an organisation. Three methods for approximating information matrices are presented. An approximation is required since the information matrix contains complicated expressions, which are difficult to evaluate. However, only one method, 'Method 1', is recommended because it guarantees nonnegative definiteness of the information matrix. It is suggested that the optimum design is likely to be sensitive to the approximation. For models that are linearly dependent on the model parameters, the information matrix is independent of the model parameters but depends on the variance parameters of the random and systematic error components. Consequently, the optimum design is independent of the model parameters but may depend on the variance parameters. Thus, designs for linear models with skewed error may be parameter dependent. For nonlinear models, the optimum design may be parameter dependent in respect of both the variance and model parameters. The information matrix is rank deficient. As a result, only subsets or linear combinations of the parameters are estimable. The rank of the partitioned information matrix is such that designs are only admissible for optimal estimation of the model parameters, excluding any intercept term, plus one linear combination of the variance parameters and the intercept. The linear model is shown to be equivalent to the usual linear regression model, but with a shifted intercept. This suggests that the admissible designs should be optimal for estimation of the slope parameters plus the shifted intercept. The shifted intercept can be viewed as a transformation of the intercept in the usual linear regression model. Since D_A-optimum designs are invariant to linear transformations of the parameters, the D_A-optimum design for the asymmetrically distributed linear model is just the linear, parameter independent, D_A-optimum design for the usual linear regression model with nonzero intercept. C-optimum designs are not invariant to linear transformations. However, if interest is in optimally estimating the slope parameters, the linear transformation of the intercept to the shifted intercept is no longer a consideration and the C-optimum design is just the linear, parameter independent, C-optimum design for the usual linear regression model with nonzero intercept. If interest is in estimating the slope parameters, and the shifted intercept, the C-optimum design will depend on (i) the design region; (ii) the distributional assumption on U; (iii) the matrix used to define admissible linear combinations of parameters; (iv) the variance parameters of U and V; (v) the method used to approximate the information matrix. Some numerical examples of designs for a cross-sectional log-linear Cobb-Douglas stochastic production frontier model are presented to demonstrate the nonlinearity of designs for models with a skewed error distribution. Torsney's (1977) multiplicative algorithm was implemented in finding the optimum designs.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Building an Aerial-Ground Robotics System for Precision Farming: An Adaptable Solution

The application of autonomous robots in agriculture is gaining increasing popularity thanks to the high impact it may have on food security, sustainability, resource use efficiency, reduction of chemical treatments, and the optimization of human effort and yield. With this vision, the Flourish research project aimed to develop an adaptable robotic solution for precision farming that combines the aerial survey capabilities of small autonomous unmanned aerial vehicles (UAVs) with targeted intervention performed by multi-purpose unmanned ground vehicles (UGVs). This paper presents an overview of the scientific and technological advances and outcomes obtained in the project. We introduce multi-spectral perception algorithms and aerial and ground-based systems developed for monitoring crop density, weed pressure, crop nitrogen nutrition status, and to accurately classify and locate weeds. We then introduce the navigation and mapping systems tailored to our robots in the agricultural environment, as well as the modules for collaborative mapping. We finally present the ground intervention hardware, software solutions, and interfaces we implemented and tested in different field conditions and with different crops. We describe a real use case in which a UAV collaborates with a UGV to monitor the field and to perform selective spraying without human intervention.Comment: Published in IEEE Robotics & Automation Magazine, vol. 28, no. 3, pp. 29-49, Sept. 202

Mapping for the Support of First Responders in Critical Domains

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Fully Autonomous Planning and Obstacle Negotiation on Rough Terrain Using Behavior Maps

To autonomously navigate on rough terrain is a challenging problem for mobile robots, requiring the ability to decide whether parts of the environment can be traversed or have to be bypassed, which is commonly known as Obstacle Negotiation (ON). In this paper, we introduce a planning framework that extends ON to the general case, where different types of terrain classes directly map to specific robot skills, such as climbing stairs and ramps. This extension is based on a new concept called behavior maps, which is utilized for the planning and execution of complex skills. Behavior maps are directly generated from elevation maps, i.e. two-dimensional grids storing in each cell the corresponding height of the terrain surface, and a set of skill descriptions. Results from extensive experiments are presented, showing that the method enables the robot to explore successfully rough terrain in real-time, while selecting the optimal trajectory in terms of costs for navigation and skill execution.Artificial Intelligence & Integrated Computer System

Behavior maps for online planning of obstacle negotiation and climbing on rough terrain

To autonomously navigate on rough terrain is a challenging problem for mobile robots, requiring the ability to decide whether parts of the environment can be traversed or have to be bypassed, which is commonly known as Obstacle Negotiation (ON). In this paper, we introduce a planning framework that extends ON to the general case, where different types of terrain classes directly map to specific robot skills, such as climbing stairs and ramps. This extension is based on a new concept called behavior maps, which is utilized for the planning and execution of complex skills. Behavior maps are directly generated from elevation maps, i.e. two-dimensional grids storing in each cell the corresponding height of the terrain surface, and a set of skill descriptions. Results from extensive experiments are presented, showing that the method enables the robot to explore successfully rough terrain in real-time, while selecting the optimal trajectory in terms of costs for navigation and skill execution.Artificial Intelligence & Integrated Computer System