Use Of Nonparametric Regression Research Articles

Non-parametric regression for hypothesis testing in hospitality and tourism research

The goal of this paper is to promote the use of Non-Parametric Regression (NPR) for hypothesis testing in hospitality and tourism research. In contrast to linear regression models, NPR frees researchers from the need to impose a priori specification on functional forms, thus allowing more flexibility and less vulnerability to misspecification problems. Importantly, we discuss in this paper a Bayesian approach to NPR using a Gaussian Process Prior (GPP). We illustrate the advantages of this method using an interesting application on internationalization and hotel performance. Specifically, we show how in contrast to linear regression, NPR decreases the risk of making incorrect hypothesis statements by revealing the true and full relationship between the variables of interest.

Discussion of “Bayesian design of experiments for generalized linear models and dimensional analysis with industrial and scientific application”

We would like to start by congratulating the authors on some very interesting work. Indeed, the use of nonparametric regression (Bayesian or otherwise) to smooth out “noisy” evaluations of optimali...

A ROBUST SPEECH RECOGNITION SYSTEM USING A GENERAL REGRESSION NEURAL NETWORK

General Regression Neural Networks (GRNN) have been applied to phoneme identification and isolated word recognition in clean speech. In this paper, the authors extended this approach to Arabic spoken word recognition in adverse conditions. In fact, noise robustness is one of the most challenging problems in Automatic Speech Recognition (ASR) and most of the existing recognition methods, which have shown to be highly efficient under noise free conditions, drastically fail drastically in noisy environments. The proposed system has been tested for Arabic digit recognition at different Signal-to-Noise Ratio (SNR) levels and under four noisy conditions: multitalker babble background, car production hall (factory), military vehicle (leopard tank) and fighter jet cockpit (buccaneer) issued from NOISEX-92 data base. The proposed scheme was successfully compared to similar recognizers based on the Multilayer Perceptron (MLP), the Elman Recurrent Neural Network (RNN) and the discrete Hidden Markov Model (HMM). The experimental results show that the use of nonparametric regression with an appropriate smoothing factor (spread) improved the generalization power of the neural network and the global performance of the speech recognizer in noisy environments.

An efficient speech recognition system in adverse conditions using the nonparametric regression

General Regression Neural Networks (GRNN) have been applied to phoneme identification and isolated word recognition in clean speech. In this paper, the authors extended this approach to Arabic spoken word recognition in adverse conditions. In fact, noise robustness is one of the most challenging problems in Automatic Speech Recognition (ASR) and most of the existing recognition methods, which have shown to be highly efficient under noise-free conditions, fail drastically in noisy environments. The proposed system was tested for Arabic digit recognition at different Signal-to-Noise Ratio (SNR) levels and under four noisy conditions: multispeakers babble background, car production hall (factory), military vehicle (leopard tank) and fighter jet cockpit (buccaneer) issued from NOISEX-92 database. The proposed scheme was successfully compared to the similar recognizers based on the Multilayer Perceptrons (MLP), the Elman Recurrent Neural Network (RNN) and the discrete Hidden Markov Model (HMM). The experimental results showed that the use of nonparametric regression with an appropriate smoothing factor (spread) improved the generalization power of the neural network and the global performance of the speech recognizer in noisy environments.

Detecting discontinuities in nonparametric regression curves and surfaces

The existence of a discontinuity in a regression function can be inferred by comparing regression estimates based on the data lying on different sides of a point of interest. This idea has been used in earlier research by Hall and Titterington (1992), Muller (1992) and later authors. The use of nonparametric regression allows this to be done without assuming linear or other parametric forms for the continuous part of the underlying regression function. The focus of the present paper is on assessing the evidence for the presence of a discontinuity within a regression function through examination of the standardised differences of `left' and `right' estimators at a variety of covariate values. The calculations for the test are carried out through distributional results on quadratic forms. A graphical method in the form of a reference band to highlight the sources of the evidence for discontinuities is proposed. The methods are also developed for the two covariate case where there are additional issues associated with the presence of a jump location curve. Methods for estimating this curve are also developed. All the techniques, for the one and two covariate situations, are illustrated through applications.

The Use of Non-Parametric Regression to Investigate the Sensitivities of High-Speed Direct Injection Diesel Emissions and Fuel Consumption to Engine Parameters

A recently developed non-parametric regression (NPR) method, namely the component selection and smoothing operator (COSSO), was applied to a high-speed direct injection (HSDI) diesel engine optimization problem to analyse the complex correlations between NO x and soot emissions, and fuel consumption responses and control factors. Seven control factors were considered, including swirl ratio, fuel injection pressure, intake air boost pressure, exhaust gas recirculation (EGR), start-of-injection timings for each pulse of two-pulse injections, and the dwell between the injections. The responses are non-linearly and non-monotonically correlated to the control factors, which feature complex interactions. The models were constructed by extracting information from an undesigned and unevenly distributed data sample, whose size is small with regard to the high dimensionality of the inputs. The models perform well, as shown by cross-validations. This success reveals the potential of NPR methods as powerful analysis tools for problems of this type. Based on the current proposed well-constructed models, the importance of the control factors could be ranked according to their significance in the models, and interactions between control factors and their influence on responses could be quantitatively assessed. For example, a two-pulse injection featuring a very early first injection and a second injection well past top dead centre of compression provides excellent performance. The start-of-second-injection timing is shown to be most influential for fuel consumption and interactions between the boost pressure and the start-of-first-injection timing are important. Similarly, as expected, EGR is the most important main factor for NO x emissions, while the main and interaction effects of the second-injection timing and EGR are also very significant. All main and interaction effects were significant for soot emissions. With a complete and continuous description of response surfaces available using the method, response values at untried parameter points can also be estimated, and possibly optimal solutions can be derived without being restrained by specified search grid resolution. Moreover, the solutions can be diversified to meet various criteria. The potential of using the proposed NPR method for assisting optimal parameter search is also discussed.

Illustrating the Use of Nonparametric Regression to Assess Differential Item and Bundle Functioning Among Multiple Groups

The purpose of this article is to illustrate the use of nonparametric regression with kernel smoothing (Ramsay, 1991), as implemented with the computer program TESTGRAF (Ramsay, 2000), to investigate differential item or bundle functioning among multiple groups. Nonparametric regression is a flexible procedure used to estimate and display the relation between the probability that examinees with a given proficiency level will choose different options to multiple-choice items. The unit of analysis can be an item or a bundle of items. It can also be used to detect differential performance across two or more groups of examinees matched on overall proficiency. We present three examples to illustrate how nonparametric regression can be applied to multilingual, multicultural data to study group differences.

Illustrating the Use of Nonparametric Regression to Assess Differential Item and Bundle Functioning Among Multiple Groups

Illustrating the Use of Nonparametric Regression to Assess Differential Item and Bundle Functioning Among Multiple Groups

Response Surfaces for the Mean and Variance Using a Nonparametric Approach

Engineers and statisticians must consider both the expected value and the process variance when specifying appropriate operating conditions for an industrial process. One approach estimates separate models for the response and for the process variance. In many cases, ordinary least squares does not produce a very good fit to the process variance data. This paper investigates the use of nonparametric regression to estimate the process variance. The response function is then estimated in two ways: (1) using a weighted least squares framework, and (2) using another nonparametric regression for the response. An example illustrates how these methodologies can be used to suggest optimal operating conditions.

Discussion of the Paper by Hall and Johnstone

Discussion of the Paper by Hall and Johnstone

On the use of nonparametric regression for model checking

SUMMARY The use of nonparametric regression is explored to check the fit of a parametric regression model. The principal aim is to check the validity of the regression curve rather than necessarily to detect outliers. A pseudo likelihood ratio test is developed to provide a global assessment of fit and simulation bands are used to indicate the nature of departures from the model. The types of data considered include discrete response variables, where standard diagnostic techniques are often not appropriate, and first-order autoregressive series. Several numerical examples are given. Nonparametric regression can be used in an informal graphical way to assess the relationship between a response and an explanatory variable. In this paper we aim to develop more formal methods of assessing the assumptions of a parametric model, in particular when regression diagnostics of the type developed for normal linear models are not readily available. The principal aim is to check the validity of the systematic part of the model by comparing a nonparametric estimate of the regression curve with a parametric one. Such a comparison may also identify outliers, although the distinction between outliers and model inadequacy is not always easy. Two techniques are used to assess the fit of a parametric model. In ? 2, confidence bands are constructed around the fitted regression curve by simulation. A comparison of these with the nonparametric curve gives an indication of the nature of any departures from the model. In ? 3, a pseudo likelihood ratio test is developed. This provides a quantitative global assessment of fit. In applying these ideas, special emphasis is given to discrete data, and notably logistic regression, because of the difficulty in applying standard residual-based model checking techniques to this type of response variable. A Poisson regression example is discussed in ? 4. However, the underlying ideas have wider applications. Autoregressive time series of order 1 are discussed in ? 6. Sections 5 and 7 discuss general issues. We first discuss the context of binary regression with a single covariate and the difficulties caused by the discreteness of the response variable. The observed data are assumed to be of the form (xi, yi, ni), where xi is a covariate value, and yi has a binomial