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.

EEG data classification using wavelet features selected by Wilcoxon statistics

This paper introduces a method to classify EEG signals using features extracted by an integration of wavelet transform and the nonparametric Wilcoxon test. Orthogonal Haar wavelet coefficients are ranked based on the Wilcoxon test’s statistics. The most prominent discriminant wavelets are assembled to form a feature set that serves as inputs to the naïve Bayes classifier. Two benchmark datasets, named Ia and Ib, downloaded from the brain–computer interface (BCI) competition II are employed for the experiments. Classification performance is evaluated using accuracy, mutual information, Gini coefficient and F-measure. Widely used classifiers, including feedforward neural network, support vector machine, k-nearest neighbours, ensemble learning Adaboost and adaptive neuro-fuzzy inference system, are also implemented for comparisons. The proposed combination of Haar wavelet features and naïve Bayes classifier considerably dominates the competitive classification approaches and outperforms the best performance on the Ia and Ib datasets reported in the BCI competition II. Application of naïve Bayes also provides a low computational cost approach that promotes the implementation of a potential real-time BCI system.

Blind source separation using second-order cyclostationary statistics

This paper studies the blind source separation (BSS) problem with the assumption that the source signals are cyclostationary. Identifiability and separability criteria based on second-order cyclostationary statistics (SOCS) alone are derived. The identifiability condition is used to define an appropriate contrast function. An iterative algorithm (ATH2) is derived to minimize this contrast function. This algorithm separates the sources even when they do not have distinct cycle frequencies .

Managing email overload with an automatic nonparametric clustering approach

Email overload is a recent problem that there is increasingly difficulty people have faced to process the large number of emails received daily. Currently this problem becomes more and more serious and it has already affected the normal usage of email as a knowledge management tool. It has been recognized that categorizing emails into meaningful groups can greatly save cognitive load to process emails and thus this is an effective way to manage email overload problem. However, most current approaches still require significant human input when categorizing emails. In this paper we develop an automatic email clustering system, underpinned by a new nonparametric text clustering algorithm. This system does not require any predefined input parameters and can automatically generate meaningful email clusters. Experiments show our new algorithm outperforms existing text clustering algorithms with higher efficiency in terms of computational time and clustering quality measured by different gauges.

Dispersion statistics and a sampling plan for Helicoverpa (Lepidoptera : Noctuidae) on fresh-market tomatoes (Lycopersicon esculentum)

Helicoverpa spp. is the primary pest in the Australian fresh-market tomato industry. We describe the spatial distribution of Helicoverpa spp. eggs on fresh-market tomato crops in the Goulburn Valley region of Victoria, and present a sequential sampling plan for monitoring population densities. The distribution of Helicoverpa spp. eggs was highly contagious, as indicated by a Taylor's b-value of 1.59. This high level of contagion meant that relatively large sample sizes would need to be collected to obtain an estimate of population density. High-precision sampling plans generally necessitated impractical sample sizes, and thus the plan we present is a relatively low-precision level plan (SE/mean = 0.3). Nonetheless, this level of precision is considered adequate for most agronomic scenarios. The plan was validated using a statistical re-sampling approach. The level of precision achieved was generally close to the nominal level. Likewise, the number of samples collected generally showed little departure from the theoretically calculated minimum sample size.

Diet, physical activity and obesity statistics

This publication provides statistics on diet, physical activity and obesity as these relate to the incidence and prevalence of CVD.

Coronary heart disease statistics

This is the fourteenth edition of Coronary heart statistics produced by the British Heart Foundation.

It is divided into 13 chapters.

* The first two chapters on mortality and morbidity deal with demographic trends in CHD and related diseases of the circulatory system.
* Following a section on treatment of CHD there are chapters on the main modifiable risk factors for the disease: smoking, an unhealthy diet, lack of physical activity, a high alcohol consumption, poor psychosocial wellbeing, raised blood pressure, raised blood cholesterol, obesity and diabetes.
* The final chapter provides information about the economic costs of CHD.

The compendium was published by the British Heart Foundation in May 2006.

Coronary heart disease statistics

This is the fifteenth edition of Coronary Heart Disease Statistics produced by the British Heart Foundation.

It is divided into 13 chapters.

* The first two chapters on mortality and morbidity deal with demographic trends in CHD and related diseases of the circulatory system.
* Following a section on treatment of CHD there are chapters on the main modifiable risk factors for the disease: smoking, an unhealthy diet, lack of physical activity, a high alcohol consumption, poor psychosocial wellbeing, raised blood pressure, raised blood cholesterol, obesity and diabetes.
* The final chapter provides information about the economic costs of CHD.

The compendium was published by the British Heart Foundation in July 2007.

Coronary heart disease statistics

This is the sixteenth edition of Coronary Heart Disease Statistics produced by the British Heart Foundation.

It is divided into 13 chapters.

* The first two chapters on mortality and morbidity deal with demographic trends in CHD and related diseases of the circulatory system.
* Following a section on treatment of CHD there are chapters on the main modifiable risk factors for the disease: smoking, an unhealthy diet, lack of physical activity, a high alcohol consumption, poor psychosocial wellbeing, raised blood pressure, raised blood cholesterol, obesity and diabetes.
* The final chapter provides information about the economic costs of CHD.

The compendium was published by the British Heart Foundation in July 2008.

European cardiovascular disease statistics

This is the third edition of European cardiovascular disease statistics. The first edition was published in 2000 when the European Union (EU) consisted of 15 Member States. After enlargement in 2004 and then again in 2007, there are now 27 Member States. Much has changed in the last seven years, but cardiovascular disease (CVD) remains the main cause of death in the EU. The European cardiovascular disease statistics was the first publication to bring together all the available sources of information about the burden of CVD in Europe, including data on death and illness, treatment, the prevalence of behavioural risk factors for CVD (smoking, diet, physical inactivity and alcohol consumption), and the prevalence of medical conditions associated with CVD (raised cholesterol, raised blood pressure, overweight and obesity, and diabetes). It
has become an indispensable resource for anybody working on reducing the burden of CVD in Europe or in public health generally.