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.

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.

Application of sequential nonparametric confidence bands in finance

In a nonparametric setting, the functional form of the relationship between the response variable and the associated predictor variables is assumed to be unknown when data is fitted to the model. Non-parametric regression models can be used for the same types of applications such as estimation, prediction, calibration, and optimization that traditional regression models are used for. The main aim of nonparametric regression is to highlight an important structure in the data without any assumptions about the shape of an underlying regression function. Hence the nonparametric approach allows the data to speak for itself. Applications of sequential procedures to a nonparametric regression model at a given point are considered.

The primary goal of sequential analysis is to achieve a given accuracy by using the smallest possible sample sizes. These sequential procedures allow an experimenter to make decisions based on the smallest number of observations without compromising accuracy. In the nonparametric regression model with a random design based on independent and identically distributed pairs of observations (X ,Y ), where the regression function m(x) is given bym(x) = E(Y X = x), estimation of the Nadaraya-Watson kernel estimator (m (x)) NW and local linear kernel estimator (m (x)) LL for the curve m(x) is considered. In order to obtain asymptotic confidence intervals form(x), two stage sequential procedure is used under which some asymptotic properties of Nadaraya-Watson and local linear estimators have been obtained.

The proposed methodology is first tested with the help of simulated data from linear and nonlinear functions. Encouraged by the preliminary findings from simulation results, the proposed method is applied to estimate the nonparametric regression curve of CAPM.

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.

How do perceptions of local neighborhood relate to adolescents` walking and cycling?

Purpose. To examine how perceptions of the local neighborhood relate to adolescents' walking and cycling. Design. Exploratory cross-sectional study. Setting. Birth cohort from the Nepean Hospital, Sydney, Australia. Subjects. Three hundred forty-seven adolescents (79.1 % response rate; 49.6% boys; mean age - 13.0 ± 0.2 years) and their parents. Measures. Self-report and parental-report questionnaires. Results. Multiple linear regressions, adjusted for level of maternal education, revealed that boys who reported having many peers to hang out with locally, cycled for recreation (β = 0.242, p = .006) or for transport (β = 0.141, p = . 046) more often, and walked for transport for longer (β = 0.129, p = .024) on weekdays. For girls this variable was related to cycling for recreation on weekends (β = 0.164, p = .006) and walking to school (β = 0.118, p = .002). Adolescents who waved/talked to neighbors walked for transport more often (boys, β = 0.149, p = .037; girls, β = 0.119, p = .012). Girls who perceived local roads to be safe spent more time walking for transport on weekdays (β = 0.183, p = .007) and for exercise on weekends (β = 0.184, p = . 034). Parents' perception of heavy traffic was negatively associated with boys' walking for transport (β = -0.138, p = .037) and many aspects of girls' walking and cycling. Conclusion. Social interaction and road safety may be important predictors of adolescents' walking and cycling in their neighborhood. Limitations are the use of self-report and cross-sectional data. Longitudinal studies may clarify these relations.

The determination of the local conditions for void initiation in front of a crack tip for materials with second-phase particles

A procedure is proposed to determine, for second-phase particles near a crack tip, the maximum particle stresses at the moment of void initiation by either particle fracture or particle/matrix interface separation. A digital image analysis system is applied to perform a quantitative analysis of corresponding fracture surface regions from stereo image pairs taken in the scanning electron microscope. The fracture surface analysis is used to measure, for individual particles, the crack tip opening displacement at the moment of void initiation and the particle location with respect to the crack tip. From these data, the stress tensor at the moment of void initiation is calculated from the Hutchinson–Rice–Rosengren (HRR) field theory. The corresponding average local stresses within the particle are evaluated by a non-linear Mori–Tanaka-type approach. These stresses are compared to estimates according to the models by Argon et al. [A.S. Argon, J. Im, R. Safoglu, Metall. Trans. 6 (1975) 825] and Beremin [F.M. Beremin, Metall. Trans. 12 (1981) 723]. The procedure is demonstrated on an Al6061–10% Al2O3 metal matrix composite.

Are perceptions of the local environment related to neighbourhood satisfaction and mental health in adults?

Background: Perceptions of environmental attributes can influence satisfaction with where people live and mental health status. We examined the association between perceived environmental characteristics, neighbourhood satisfaction, and self-rated mental health.

Methods: We report cross-sectional data from the Physical Activity in Localities and Community Environments (PLACE) study in Australia (n = 2194). Self-report data included socio-demographics, perceived attributes of the environment, neighbourhood satisfaction (NS) and mental health status. Neighbourhood SES was obtained through census data. Factor analysis was used to identify dimensions of NS. Generalized linear models were used to examine associations between NS and perceived environment characteristics and whether aspects of NS were independently associated with mental health.

Results: NS factors identified were safety and walkability, access to destinations, social network, travel network, and traffic and noise. Perceived environmental characteristics of aesthetics and greenery, land use mix – diversity, street connectivity, traffic safety, infrastructure for walking, access to services and barriers to walking were found to be positively associated with these factors. Traffic load and crime were negatively associated. Three NS factors (safety and walkability, social network, and traffic and noise) were independent predictors of mental health.

Conclusions: Neighbourhood satisfaction may mediate the association between perceived environmental characteristics and measures of mental health in adults.

Organisational development in local government

To a significant extent, Australian local government CEOs have opportunity to enhance their current understandings of and attitudes towards human resource imperatives such as organisational culture, employee empowerment and non-linear management practices. Improvements in these areas could better achieve organisational results as HR strategy intentions would be aided by congruent applications.

Quantifying heteroskedasticity using slope of local variances index

In econometrics, heteroskedasticity refers to the case when the variances of the error terms of the data in hand are not equal. Heteroskedastic time series are challenging to different forecasting models. However, all available solutions adopt the strategy of accommodating heteroskedasticity in the time series and consider it as a type of noise. Some statistical tests were developed over the past three decades to determine whether a time series features heteroskedastic behaviour. This paper presents a novel strategy to handle this problem by deriving a quantifying measure for heteroskedasticity. The proposed measure relies on the definition of heteroskedasticity as a time-variant variance in the time series. In this work, heteroskedasticity is measured by calculating local variances using linear filters, estimating variance trends, calculating changes in variance slopes, and finally obtaining the average slope angle. The results confirm that the proposed index complies with the widely popular heteroskedasticity tests.

Landscapes in transition : local perceptions of indigenous and European settlement changes along the Victorian coast

Around the world coastal areas are witnessing dramatic changes due to the consequences of the growth of human settlements. Rapid urban expansion in coastal settlements due to ‘life style migration’ impacts negatively on environmental coastal amenities that are the driving factor behind the attraction of these areas. The Victorian Coast in Australia is under stress, with the growth pattern of coastal settlements in a sprawling linear fashion resulting in devastating effects on the natural coastal environment, biodiversity and the loss of cultural heritage. The Victorian coast is rich in history, and the coastal towns are often described in literature as places with ‘sense of place’, or referred to as place character. This place character has been formed over many years with the interaction between social histories and natural environments woven together across time. This paper reviews the transition of the landscapes along the Great Ocean Road coastal region, and ask the question how can a potential Generative Plan be developed to establish a process to keep the place character of coastal towns. The proposed plan considers the interrelationships of nature and people as fundamental to forming place character, from the time of Indigenous habitation before European settlement, to the current day of rapid increased developments scattered along this coast.

An artificial waterway and road restrict movements and alter home ranges of endangered arboreal marsupial

Artificial linear structures can cause habitat fragmentation by restricting movements of animals and altering home ranges. The negative impacts of these linear structures, especially of those other than roads, on arboreal species have been rarely studied even though these species can be greatly affected because of their fidelity to the canopy. We studied the home ranges of an endangered arboreal marsupial, the western ringtail possum (Pseudocheirus occidentalis), with a focus on the impacts of a road and an artificial waterway on their movement. We radiotracked 18 females and 19 males along a major road and an artificial waterway near Busselton, Western Australia, for 3 years and estimated home ranges using an a-local convex hull (a-LoCoH) estimator. No possum crossed the road successfully during the monitoring period while one crossed the waterway. Males had a mean home range size of 0.31 ± 0.044 (SE) ha, almost double that of the females at 0.16 ± 0.017 ha. Possums near the waterway had larger home ranges (0.30 ± 0.048 ha) than those near the road (0.19 ± 0.027 ha), and the size increased with proximity to the waterway, probably due to the greater availability of nearby canopy connections and the lower availability of preferable foliage. These results demonstrate that both the road and waterway represent significant physical barriers to possums, and the artificial waterway influenced home ranges more severely than the road. This suggests that linear infrastructure other than roads can affect movements of strictly arboreal animals, and negative impacts of these structures need to be assessed and mitigated by reconnecting their habitat, just as those of roads.