OWA operators in linear regression and detection of outliers

We consider the use of Ordered Weighted Averaging (OWA) in linear regression. Our goal is to replace the traditional least squares, least absolute deviation, and maximum likelihood criteria with an OWA function of the residuals. We obtain several high breakdown robust regression methods as special cases (least median, least trimmed squares, trimmed likelihood methods). We also present new formulations of regression problem. OWA-based regression is particularly useful in the presence of outliers.

OWA operators in regression problems

We consider an application of fuzzy logic connectives to statistical regression. We replace the standard least squares, least absolute deviation, and maximum likelihood criteria with an ordered weighted averaging (OWA) function of the residuals. Depending on the choice of the weights, we obtain the standard regression problems, high-breakdown robust methods (least median, least trimmed squares, and trimmed likelihood methods), as well as new formulations. We present various approaches to numerical solution of such regression problems. OWA-based regression is particularly useful in the presence of outliers, and we illustrate the performance of the new methods on several instances of linear regression problems with multiple outliers.

GeoConnect : geographic and connectivity-aware routing protocol for wireless sensor network

Sensor nodes are closely tied with their geographic location and their connectivity. In recent years many routing protocols have been developed to provide efficient strategy. But most of them are either focus on the geographic proximity or on connectivity. However in sparse network, Geographic routing would fail at local dead ends where a node has no neighbour closer to destination. In contrast, connectivity-based routing may result in non-optimal path and overhead management. In this paper we designed a scalable and distributed routing protocol, GeoConnect, which considers geographic proximity and connectivity for choosing next hop. In GeoConnecl, we construct a new naming system that integrates geographic and connectivity information into a node identification. We use dissimilarity function to compute the dissimilarity and apply a distributed routing algorithm to route packets. The experimental results show that GeoConnect routing provides robust and better performance than sole geographic routing or connectivity routing.

Neighbourhood physical activity environments and adiposity in children and mothers : a three-year longitudinal study

Background Although neighbourhood environments are often blamed for contributing to rising levels of obesity, current evidence is based predominantly on cross-sectional samples. This study examined associations between objectively-measured environmental characteristics of neighbourhoods and adiposity cross-sectionally and longitudinally over three years in children and their female carers.

Methods Longitudinal study of 140 5-6 year-old and 269 10-12 year-old children and their female carers (n = 369). At baseline (2001) and follow-up (2004), height and weight were measured among children and self-reported among female carers, and were used to compute BMI z-scores and BMI, respectively. A Geographic Information System determined access to destinations (public open spaces, sports options, walking/cycling tracks), road connectivity (density of cul-de-sacs and intersections, proportion of 4-way intersections, length of 'access' paths (overpasses, access lanes, throughways between buildings)) and traffic exposure (length of 'busy' and 'local' roads) within 800 m and 2 km of home. Univariate and multivariable linear regression analyses examined associations between environmental characteristics and BMI/BMI z-scores at baseline and change in BMI/BMI z-scores over the three years.

Results Cross-sectionally, BMI z-score was inversely associated with length (km) of access paths within 800 m (b = -0.50) and 2 km (b = -0.16) among younger and number of sport/recreation public open spaces (b = -0.14) and length (km) of 'access' paths (b = -0.94) within 800 m and length of local roads within 2 km (b = -0.01) among older children. Among female carers, BMI was associated with length (km) of walking/cycling tracks (b = 0.17) and busy roads (b = -0.34) within 800 m. Longitudinally, the proportion of intersections that were 4-way (b = -0.01) within 800 m of home was negatively associated with change in BMI z-score among younger children, while length (km) of access paths (b = 0.18) within 800 m was significant among older children. Among female carers, options for aerobics/fitness and swimming within 2 km were associated with change in BMI (B = -0.42).

Conclusion A small number of neighbourhood environment features were associated with adiposity outcomes. These differed by age group and neighbourhood scale (800 m and 2 km) and were inconsistent between cross-sectional and longitudinal findings. However, the results suggest that improvements to road connectivity and slowing traffic and provision of facilities for leisure activities popular among women may support obesity prevention efforts.

Availability of sports facilities as moderator of the intention - sports participation relationship among adolescents

This longitudinal study aimed to identify individual and environmental predictors of adolescents’ sports participation and to examine whether availability of sports facilities moderated the intention–behaviour relation. Data were obtained from the ENvironmental Determinants of Obesity in Rotterdam SchoolchildrEn study (2005/2006 to 2007/2008). A total of 247 adolescents (48% boys, mean age at follow-up 15 years) completed the surveys at baseline and follow-up. At baseline, adolescents completed a survey that assessed engagement in sports participation, attitude, subjective norm, perceived behavioural control and intention towards sports participation. Availability of sports facilities (availability) was assessed using a geographic information system. At follow-up, sports participation was again examined. Multiple logistic regression analyses were conducted to test associations between availability of sports facilities, theory of planned behaviour variables and the interaction of intention by availability of sports facilities, with sports participation at follow-up. Simple slopes analysis was conducted to decompose the interaction effect. A significant availability × intention interaction effect [odds ratio: 1.10; 95% confidence interval: 1.00–1.20] was found. Simple slopes analysis showed that intention was more strongly associated with sports participation when sports facilities were more readily available. The results of this study indicate that the intention–sports participation association appears to be stronger when more facilities are available.

An index of unhealthy lifestyle is associated with coronary heart disease mortality rates for small areas in England after adjustment for deprivation

Indices of socio-economic deprivation are often used as a proxy for differences in the health behaviours of populations within small areas, but these indices are a measure of the economic environment rather than the health environment. Sets of synthetic estimates of the ward-level prevalence of low fruit and vegetable consumption, obesity, raised blood pressure, raised cholesterol and smoking were combined to develop an index of unhealthy lifestyle. Multi-level regression models showed that this index described about 50% of the large-scale geographic variation in CHD mortality rates in England, and substantially adds to the ability of an index of deprivation to explain geographic variations in CHD mortality rates.

Sequential fixed-width confidence bands for kernel regression estimation

We consider a random design model based on independent and identically distributed (iid) pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the unknown function m(x) when we have no precise information about the form of the true density, f(x) of X. We describe an estimation procedure of non-parametric regression model at a given point by some appropriately constructed fixed-width (2d) confidence interval with the confidence coefficient of at least 1−. Here, d(> 0) and 2 (0, 1) are two preassigned values. Fixed-width confidence intervals are developed using both Nadaraya-Watson and local linear kernel estimators of nonparametric regression with data-driven bandwidths.

The sample size was optimized using the purely and two-stage sequential procedure together with asymptotic properties of the Nadaraya-Watson and local linear estimators. A large scale simulation study was performed to compare their coverage accuracy. The numerical results indicate that the confidence bands based on the local linear estimator have the best performance than those constructed by using Nadaraya-Watson estimator. However both estimators are shown to have asymptotically correct coverage properties.

Two-stage sequential procedure for nonparametric regression estimation

In nonparametric statistics the functional form of the relationship between the response variable and its associated predictor variables is unspecified but it is assumed to be a smooth function. We develop a procedure for constructing a fixed width confidence interval for the predicted value at a specified point of the independent variable. The optimal sample size for constructing this interval is obtained using a two stage sequential procedure which relies on some asymptotic properties of the Nadaraya--Watson and local linear estimators. Finally, a large scale simulation study demonstrates the applicability of the developed procedure for small and moderate sample sizes. The procedure developed here should find wide applicability since many practical problems which arise in industry involve estimating an unknown function.

Sample size determination for kernel regression estimation using sequential fixed-width confidence bands

We consider a random design model based on independent and identically distributed pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the unknown function m(x) when we have no precise information about the form of the true density, f(x) of X. We describe an estimation procedure of non-parametric regression model at a given point by some appropriately constructed fixed-width (2d) confidence interval with the confidence coefficient of at least 1−. Here, d(> 0) and 2 (0, 1) are two preassigned values. Fixed-width confidence intervals are developed using both Nadaraya-Watson and local linear kernel estimators of nonparametric regression with data-driven bandwidths. The sample size was optimized using the purely and two-stage sequential procedures together with asymptotic properties of the Nadaraya-Watson and local linear estimators. A large scale simulation study was performed to compare their coverage accuracy. The numerical results indicate that the confi dence bands based on the local linear estimator have the better performance than those constructed by using Nadaraya-Watson estimator. However both estimators are shown to have asymptotically correct coverage properties.

Modelling for injection moulding process based on principal component regression method

Determination of the optimal operating condition for moulding process has been of special interest for many researchers. To determine the optimal setting, one has to derive the model of injection moulding process first which is able to map the relationship between the input process control factors and output responses. One of most popular modeling techniques is the linear least square regression due to its effectiveness and completeness. However, the least square regression was found to be very sensitive to the outliers and failed to provide a reliable model if the control variables are highly related with each other. To address this problem, a new modeling method based on principal component regression was proposed in this paper. The distinguished feature of our proposed method is it does not only consider the variance of covariance matrix of control variables but also consider the correlation coefficient between control variables and target variables to be optimised. Such a modelling method has been implemented into a commercial optimisation software and field test results demonstrated the performance of the proposed modelling method.

Spectral element modelling of wave propagation with boundary and structural discontinuity reflections

Spectral element method is very efficient in modelling high-frequency stress wave propagation because it works in the frequency domain. It does not need to use very fine meshes in order to capture high frequency wave energy as the time domain methods do, such as finite element method. However, the conventional spectral element method requires a throw-off element to be added to the structural boundaries to act as a conduit for energy to transmit out of the system. This makes the method difficult to model wave reflection at boundaries. To overcome this limitation, imaginary spectral elements are proposed in this study, which are combined with the real structural elements to model wave reflections at structural boundaries. The efficiency and accuracy of this proposed approach is verified by comparing the numerical simulation results with measured results of one dimensional stress wave propagation in a steel bar. The method is also applied to model wave propagation in a steel bar with not only boundary reflection, but also reflections from single and multiple cracks. The reflection and transmission coefficients, which are obtained from the discrete spring model, are adopted to quantify the discontinuities. Experimental tests of wave propagation in a steel bar with one crack of different depths are also carried out. Numerical simulations and experimental results show that the proposed method is effective and reliable in modelling wave propagation in one-dimensional waveguides with reflections from boundary and structural discontinuities. The proposed method can be applied to effectively model stress wave propagation for structural damage detection.