Parametric Regression Techniques Research Articles

Distributed Multivariate Regression Using Wavelet-Based Collective Data Mining

This paper presents a method for distributed multivariate regression using wavelet-based collective data mining (CDM). The method seamlessly blends machine learning and the theory of communication with the statistical methods employed in parametric multivariate regression to provide an effective data mining technique for use in a distributed data and computation environment. The technique is applied to two benchmark data sets, producing results that are consistent with those obtained by applying standard parametric regression techniques to centralized data sets. Evaluation of the method in terms of mode accuracy as a function of appropriateness of the selected wavelet function, relative number of nonlinear cross-terms, and sample size demonstrates that accurate parametric multivariate regression models can be generated from distributed, heterogeneous, data sets with minimal data communication overhead compared to that required to aggregate a distributed data set. Application of this method to linear discriminant analysis, which is related to parametric multivariate regression, produced classification results on the Iris data set that are comparable to those obtained with centralized data analysis.

Automatic bandwidth selection for modified m-smoother*

Traditional parametric and nonparametric regression techniques encounter serious over smoothing problems when jump point discontinuities exist in the underlying mean function. Recently, Chu, Glad, Godtliebsen and Marron (1998) developed a method using a modified M-smoothing technique to preserve jumps and spikes while producing a smooth estimate of the mean function. The performance of Chu etal.'s (1998) method is quite sensitive to the choice of the required bandwidths g and h. Furthermore, it is not obvious how to extend certain commonly used automatic bandwidth selection procedures when jumps and spikes are present. In this paper we propose a rule of thumb method of choosing the smoothing parameters based on asymptotic optimal bandwidth formulas and robust estimates of unknown quantities. We also evaluate the proposed bandwidth selection method via a small simulation study.

Kriging with nonparametric variance function estimation.

A method for fitting regression models to data that exhibit spatial correlation and heteroskedasticity is proposed. It is well known that ignoring a nonconstant variance does not bias least-squares estimates of regression parameters; thus, data analysts are easily lead to the false belief that moderate heteroskedasticity can generally be ignored. Unfortunately, ignoring nonconstant variance when fitting variograms can seriously bias estimated correlation functions. By modeling heteroskedasticity and standardizing by estimated standard deviations, our approach eliminates this bias in the correlations. A combination of parametric and nonparametric regression techniques is used to iteratively estimate the various components of the model. The approach is demonstrated on a large data set of predicted nitrogen runoff from agricultural lands in the Midwest and Northern Plains regions of the U.S.A. For this data set, the model comprises three main components: (1) the mean function, which includes farming practice variables, local soil and climate characteristics, and the nitrogen application treatment, is assumed to be linear in the parameters and is fitted by generalized least squares; (2) the variance function, which contains a local and a spatial component whose shapes are left unspecified, is estimated by local linear regression; and (3) the spatial correlation function is estimated by fitting a parametric variogram model to the standardized residuals, with the standardization adjusting the variogram for the presence of heteroskedasticity. The fitting of these three components is iterated until convergence. The model provides an improved fit to the data compared with a previous model that ignored the heteroskedasticity and the spatial correlation.

Nonparametric regression in the presence of measurement error

Summary In many regression applications the independent variable is measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. We consider two diVerent approaches to nonparametric regression. The first uses the simex, simulation-extrapolation, method and makes no assumption about the distribution of the unobserved error-prone predictor. For this approach we derive an asymptotic theory for kernel regression which has some surprising implications. Penalised regression splines are also considered for fixed number of known knots. The second approach assumes that the error-prone predictor has a distribution of a mixture of normals with an unknown number of components, and uses regression splines. Simulations illustrate the results.

Nonparametric Kernel and Regression Spline Estimation in the Presence of Measurement Error

In many regression applications both the independent and dependent variables are measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. We consider two different nonparametric techniques, regression splines and kernel estimation, of which both can be used in the presence of measurement error. Within the kernel regression context, we derive the limit distribution of the SIMEX estimate. With the regression spline technique, two different methods of estimations are used. The first method is the SIMEX algorithm which attempts to estimate the bias, and remove it. The second method is a structural approach, where one hypothesizes a distribution for the independent variable which depends on estimable parameters. A series of examples and simulations illustrate the methods.

The risk of hemorrhage after radiosurgery for arteriovenous malformations.

Two hundred and one patients with arteriovenous malformations (AVMs) treated radiosurgically between May 1988 and February 1995 are analyzed in this study. Twelve patients sustained a posttreatment hemorrhage during this period. Pretreatment factors associated with increased hemorrhage risk were identified in 11 of these patients and included arterial aneurysms, venous aneurysms, venous outflow obstruction, periventricular location, prior embolization, and prior surgical treatment. A detailed statistical analysis, using both Poisson regression and parametric survival regression techniques, was undertaken to determine whether radiosurgery had any effect on the risk of hemorrhage, when compared to the natural history of the disease, in those patients in whom a complete angiographic cure was not achieved. No evidence was found to support a statistically significant departure from the natural hemorrhage rate at any time period after radiosurgical treatment. Significant risk factors for hemorrhage appeared to correlate with increasing AVM volume.

The out-of-sample forecasting performance of variable parameter exchange rate models in South Africa

In this article the out-of-sample forecasting performance of exchange rate determination is examined without imposing the restriction that coefficients are fixed over time. Both fixed and variable coefficient versions of conventional structural models are considered, with and without a lagged dependent variable. A Variable Parameter Regression (VPR) technique based on recursive application of the Kalman filter is used to improve the predictive performance of a class oi monetary exchange rate models.

Metodi di regressione non parametrica additiva e il caso "Projection Pursuit Regression"

This article presents a review of recent non parametric additive regression techniques that are appropriate for high dimensional data sets. These methods are related by the fact that they all use some type of additive approximation to describe the underlying regression model. The estimation of the regression function is obtained iteratively through backfitting procedures and the use of smoothers. The second part illustrate the Projection Pursuit Regression method by applying it to various data sets. Sample reuse techniques like bootstrap are used in order to study the particular problem of inference.

Static and dynamic forecasting of short-run demand for money

Previous studies of static and dynamic out-of-sample simulations of the demand for money have indicated a breakdown in the short-run real money balances over the past 1974 forecast period. Using the varying parameter regression technique, the findings of this paper demonstrate that previous results are misleading because the shift of the money demand is obscured by the constant coefficient estimation technique. Our estimation procedure has not only drastically improved both static and dynamic forecasts but has also solved the missing money puzzle.

Evidence of the Structural Stability of Short-Term Capital Flow

IN an earlier study, Hodgson and Holmes (1977) provided empirical evidence on the structural stability of short-term capital flow using the case of U.S.-Canadian net bank claims for the period 1955-I to 1974-I.1 Their findings indicated that the short-term capital flow underwent a significant structural change, and that the instability in the short-term capital flow may have been due to changes in interest rate sensitivity over time. However, as Garbade (1977) shows, the test procedure used by Hodgson and Holmes, labeled the cusum of squares test, has limitations for detecting structural change in the coefficients. The primary purpose of this paper is to present additional empirical evidence on the stability of U.S.-Canadian capital flow, obtained not only from the cusum of squares test, but also from the variable parameter regression technique. The use of the latter test is well justified in that it is somewhat more powerful and has the advantage of being able to isolate instability in individual regression coefficients. In section I we develop an analytical framework for short-term capital flow based on the portfolio balance approach. Section II presents the regression results for the U.S.-Canadian short-term capital flow. In section III we present a brief and heuristic description of the two stability test procedures as well as the results of these tests. Major conclusions are presented in section IV.

Simulation of the barley leaf rust epidemic: Structure and validation of BARSIM—I

This paper, the second in a series outlining development of a management information system for barley leaf rust in New Zealand, describes the structure and biological logic of the skeleton model BARSIM—I. Validation of biological system models is discussed and results of two statistical tests with BARSIM—I presented. Using a parametric (regression) technique, nine out of fifteen simulated epidemics were found to agree with field observations. With a non-parametric (Smirnov) test, model output was found in all instances to agree with field data. The relationship of simulation modelling to mathematical modelling of plant diseases is discussed.