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A new family of entropy estimators, constructed as a linear combination (weighted average) of nearest neighbor estimators with slightly different individual properties, is proposed. It is shown that a special suboptimal selection of the coefficients in the linear combination results in a polynomial reduction of the estimator's bias, which continues the line of work of P. Grassberger on entropy estimation. Computer simulation results are provided.

This paper revisits the causal relationship between education and earnings, or the returns to education, using Thailand’s socio-economic household survey data. We show that, with the minimum modeling assumption, the causal effect of education on earnings can be nonparametrically identified only when there is no unobserved ability affecting both education and earning, and when the selection mechanisms are conditionally independent to earnings conditioning on potential experience and education. The causal effects of education on earnings are estimated using a nonparametric approach with selection bias adjustment and parametric approaches with selection bias and ability bias adjustments. The results show different estimates for returns to education across model specifications, indicating the importance of the bias adjustments and parametric assumptions.

The need to determine the directionality of interactions between neural signals is a key requirement for analysis of multichannel recordings. Approaches most commonly used are parametric, typically relying on autoregressive models. A number of concerns have been expressed regarding parametric approaches, thus there is a need to consider alternatives. We present an alternative nonparametric approach for construction of directionality measures for bivariate random processes. The method combines time and frequency domain representations of bivariate data to decompose the correlation by direction. Our framework generates two sets of complementary measures, a set of scalar measures, which decompose the total product moment correlation coefficient summatively into three terms by direction and a set of functions which decompose the coherence summatively at each frequency into three terms by direction: forward direction, reverse direction and instantaneous interaction. It can be undertaken as an addition to a standard bivariate spectral and coherence analysis, and applied to either time series or point-process (spike train) data or mixtures of the two (hybrid data). In this paper, we demonstrate application to spike train data using simulated cortical neurone networks and application to experimental data from isolated muscle spindle sensory endings subject to random efferent stimulation.

The incessantly growing demand for energy consumption and the significance of the availability of sustainable energy for achieving long term economic growth defines the importance of forecasting energy statistics. This paper analyses and forecasts actual energy consumption data for EU-27 nations using both parametric and nonparametric time series forecasting techniques. Singular Spectrum Analysis (SSA) is adopted as the nonparametric time series analysis and forecasting technique and the results from SSA are compared with ARIMA, which is a parametric forecasting technique.

This paper seeks to analyse and evaluate Sri Lanka's energy consumption forecasts, more specifically, electricity, petroleum, coal and renewable electricity consumption using a variety of parametric and nonparametric forecasting techniques. The Sri Lankan economy is emerging following the end of a prolonged civil war, and thus this topic is opportune as accurate forecasts of energy requirements are indispensable for sustaining the ongoing rapid economic expansion. We also consider evaluating the appropriateness of parametric and nonparametric energy forecasting methods for Sri Lanka. In addition, this paper marks the introductory application of SSA for forecasting in Sri Lanka, and the results from SSA are compared against the popular benchmarks of ARIMA, ETS, HW, TBATS, and NN. We find statistically significant evidence proving that the SSA model outperforms ETS and HW at forecasting renewable electricity consumption, and also, that the SSA model outperforms ARIMA and TBATS models at forecasting coal consumption. On average, the SSA model is found to be best for energy consumption forecasting in Sri Lanka whilst the Neural Networks model is second best.

Bitcoin has received a lot of attention from both investors and analysts, as it forms the highest market capitalization in the cryptocurrency market. The use of parametric GARCH models to characterize the volatility of Bitcoin returns is widely observed in the empirical literature. In this paper, we consider an alternative approach involving nonparametric method to model and forecast Bitcoin return volatility. We show that the out-of-sample volatility forecast of the nonparametric GARCH model yields superior performance relative to an extensive class of parametric GARCH models. The improvement in forecasting accuracy of Bitcoin return volatility based on the nonparametric GARCH model suggests that this method offers an attractive and viable alternative to the commonly used parametric GARCH models.

In the introductory Section 1, the problems of statistical pattern recognition are defined, and a flow chart is presented to show how a classifier ought to be designed. In Section 2, the theoretically optimal (Bayes) classifier and its variations are introduced. The discussion is extended to show how the resulting classification (Bayes) error can be computed for some limited cases. Also, the upper and lower bounds of the Bayes error are shown. Section 3 discusses how a classifier is designed in practice. Linear, quadratic and piecewise classifiers are included. These are based on the expected vectors and co-variance matrices of underlying probability distributions. In practice, these vectors and matrices are not given, and must be estimated from an available set of samples. Consequently, the designed classifier variates and the classification error becomes a random variable. Section 4 discusses how the number of available samples affects the classification performance, and also how to allocate the samples into design and test. In Section 5, nonparametric techniques are presented. They are needed in the estimation of the Bayes error and the structure analysis of data, where a mathematical formula such as Gaussianness cannot be applied. Both the Parzen and k nearest neighbor approaches are discussed. Feature extraction and clustering are discussed in other chapters.

In the introductory Section 1, the problems of statistical pattern recognition are defined, and a flow chart is presented to show how a classifier ought to be designed. In Section 2, the theoretically optimal (Bayes) classifier and its variations are introduced. The discussion is extended to show how the resulting classification (Bayes) error can be computed for some limited cases. Also, the upper and lower bounds of the Bayes error are shown. Section 3 discusses how a classifier is designed in practice. Linear, quadratic and piecewise classifiers are included. These are based on the expected vectors and covariance matrices of underlying probability distributions. In practice, these vectors and matrices are not given, and must be estimated from an available set of samples. Consequently, the designed classifier variates and the classification error becomes a random variable. Section 4 discusses how the number of available samples affects the classification performance, and also how to allocate the samples into design and test. In Section 5, nonparametric techniques are presented. They are needed in the estimation of the Bayes error and the structure analysis of data, where a mathematical formula such as Gaussianness cannot be applied. Both the Parzen and k nearest neighbor approaches are discussed. Feature extraction and clustering are discussed in other chapters.