Conventional Nonparametric Methods Research Articles

A novel lifetime analysis of repairable systems via Daubechies wavelets

AbstractIt is well-known that minimally repaired systems are characterized by non-homogeneous Poisson processes. When the underlying lifetime distribution function or its associated intensity function is completely known, the statistical inference of the cumulative number of failures/repairs is made through some standard techniques. On the other hand, when the parametric form of the lifetime distribution or the intensity function is not known, non-parametric inference techniques such as non-parametric maximum likelihood estimate (NPMLE) and kernel-based estimates are employed. Since these techniques are based on the underlying lifetime data, the resulting estimates of the cumulative number of failures/repairs with respect to the system operation time are discontinuous and troublesome in assessing the reliability measures such as reliability function and mean time to failure, etc. In this paper, we propose a novel lifetime analysis of the repairable systems via Daubechies wavelets. More specifically, we generalize the seminal Daubechies wavelet estimate by Kuhl and Bhairgond (Winter Simul Conf Proc 1:562–571, 2000) by combining the ideas on NPMLE and KMBs. In both simulation experiments and real data analyses, we investigate applicability of our Daubechies wavelet-based approaches and compare them with the conventional non-parametric methods.

Wavelet Estimation of Semi-parametric Regression Model

The semi-parametric regression model combines parametric and nonparametric regression. However, non-parametric estimation may provide flexible solutions to the problems suffers by the regression model, but the problem of dimensionality that this estimator suffers, which occurs due to the increasing number of explanatory variables, still remain, this, in turn, may reduce the accuracy of the estimation process. Estimate the non-parametric part of the semi-parametric models that can be studied using conventional non-parametric methods such as the Spline Smoothing and Kernel Smoothing. However, there are other non-parametric methods that can be used, therefore, in this paper, the semi-parametric regression model was estimated by employing the wavelet estimate for the soft threshold, according to the "Speckman" method, and then comparing it with the two methods, Nadaraya-Watson and Local Linear, through the implementation of simulation experiments that included different sample sizes and threshold values. The parametric part estimation of the partially linear model according to the least-squares method was not identical to those estimates using the Speckman method, that is because the least-squares method was not appropriate for the uneven nature of the number of weekly work hours. Simulation experiments have demonstrated the efficiency of the wavelet estimation method and its superiority over other methods. The above estimation methods were applied to real data related to the study of the production value for the public industrial sector in Iraq, and some factors affect it, such as the value of industrial supplies, the total wages of workers, and the number of workers.

Gini estimation under infinite variance

We study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index α∈(1,2)). We show that, in such a case, the Gini coefficient cannot be reliably estimated using conventional nonparametric methods, because of a downward bias that emerges under fat tails. This has important implications for the ongoing discussion about economic inequality.We start by discussing how the nonparametric estimator of the Gini index undergoes a phase transition in the symmetry structure of its asymptotic distribution, as the data distribution shifts from the domain of attraction of a light-tailed distribution to that of a fat-tailed one, especially in the case of infinite variance. We also show how the nonparametric Gini bias increases with lower values of α. We then prove that maximum likelihood estimation outperforms nonparametric methods, requiring a much smaller sample size to reach efficiency.Finally, for fat-tailed data, we provide a simple correction mechanism to the small sample bias of the nonparametric estimator based on the distance between the mode and the mean of its asymptotic distribution.

Gini Estimation Under Infinite Variance

We study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index α ∈ (1, 2)). We show that, in such a case, the Gini coefficient cannot be reliably estimated using conventional nonparametric methods, because of a downward bias that emerges in case of fat tails. This has important implications for the ongoing discussion about economic inequality. We start by discussing how the nonparametric estimator of the Gini index undergoes a phase transition in the symmetry structure of its asymptotic distribution, as the data distribution shifts from the domain of attraction of a light-tailed distribution to that of a fat-tailed one, especially in the case of infinite variance. We show how the nonparametric Gini bias increases with lower values of α. We then prove that maximum likelihood estimation outperforms nonparametric methods, requiring a much smaller sample size to reach efficiency. Finally, for fat-tailed data, we provide a simple correction mechanism to the small sample bias of the nonparametric estimator based on the distance between the mode and the mean of its asymptotic distribution.

A Comparative Study between Two Central Venous Access Techniques Performed by Junior Residents

Objective: To evaluate the outcomes of Central Venous Access (CVAs) performed by junior residents (i.e. first-year residents) using the Subclavian (SC) and Internal Jugular (IJ) approaches. Methods: A comparative study was carried out in a prospective cohort of patients who consecutively underwent SC or IJ CVAs performed by junior residents at our Department of General Surgery. Additionally, we examined the impact of learning curve on the success of the venipunctures. Statistical analyses were developed using conventional nonparametric methods. Results: Overall, success and morbidity rates in our sample were 81% and 18%, respectively. Successful rates did not significantly differ between IJ and SC approaches (80.35% and 81.81%, respectively; p = 0.942), among procedures performed from first to fourth quartile periods (72% vs. 80% vs. 80% vs. 92%, respectively; p = 0.854) or regardless of which junior residents performed it (p = 0.662). Similarly, morbidity rates did not differ significantly according to CVA techniques (17.85% vs. 18.18%; p = 0.825), quartile periods (28% vs. 16% vs. 20% vs. 8%; p = 0.832), or which junior residents performed it (p = 0.743). There were significantly more arterial punctures/ hematoma using the IJ approach (7% vs. 1%, p = 0.024) and catheter malpositions/nonprogression after the SC technique (1% vs. 6%, p = 0.012). Conclusions: There was a different profile of complication rates with no differences between the techniques in term of either successful or early morbidity. Our study suggests that both approaches may be used for surgical training of junior residents in general surgery.

NONPARAMETRIC COINTEGRATING REGRESSION WITH ENDOGENEITY AND LONG MEMORY

This paper explores nonparametric estimation, inference, and specification testing in a nonlinear cointegrating regression model where the structural equation errors are serially dependent and where the regressor is endogenous and may be driven by long memory innovations. Generalizing earlier results of Wang and Phillips (2009a,b,Econometric Theory25, 710–738,Econometrica77, 1901–1948), the conventional nonparametric local level kernel estimator is shown to be consistent and asymptotically (mixed) normal in these cases, thereby opening up inference by conventional nonparametric methods to a wide class of potentially nonlinear cointegrated relations. New results on the consistency of parametric estimates in nonlinear cointegrating regressions are provided, extending earlier research on parametric nonlinear regression and providing primitive conditions for parametric model testing. A model specification test is studied and confirmed to provide a valid mechanism for testing parametric specifications that is robust to endogeneity. But under long memory innovations the test is not pivotal, its convergence rate is parameter dependent, and its limit theory involves the local time of fractional Brownian motion. Simulation results show good performance for the nonparametric kernel estimates in cases of strong endogeneity and long memory, whereas the specification test is shown to be sensitive to the presence of long memory innovations, as predicted by asymptotic theory.

Functional data analysis for point processes with rare events

In various applications one encounters samples of objects, where each object consists of a small number of repeated event times observed over a fixed time interval. For such rare event data there are no flexible methods available that can be applied when the shapes of the intensity functions that generate the observed event times are not known, or vary substantially between objects. We model the underlying intensity functions as nonparametric object-specific random functions. Applying a novel functional method to obtain the covariance structure of the associated random densities, we reconstruct object-specific density functions that reflect the distribution of event times. We demonstrate in simulations that the proposed functional approach is superior to conventional nonparametric methods, as it borrows strength from the entire sample of objects rather than aiming at the estimation of each object's density separately. Our method is based on a key relationship that allows one to reduce the covariance estimation problem for random densities to the simpler problem of estimating a non-random joint density from pooled event times. We describe an application to model bid arrivals for a sample of online auctions, and also include asymptotic justifications of the methodology.

Analysis of hydrological trend for radioactivity content in bore-hole water samples using wavelet based denoising

A wavelet transform based denoising methodology has been applied to detect the presence of any discernable trend in 137Cs and 90Sr activity levels in bore-hole water samples collected four times a year over a period of eight years, from 2002 to 2009, in the vicinity of typical nuclear facilities inside the restricted access zones. The conventional non-parametric methods viz., Mann–Kendall and Spearman rho, along with linear regression when applied for detecting the linear trend in the time series data do not yield results conclusive for trend detection with a confidence of 95% for most of the samples. The stationary wavelet based hard thresholding data pruning method with Haar as the analyzing wavelet was applied to remove the noise present in the same data. Results indicate that confidence interval of the established trend has significantly improved after pre-processing to more than 98% compared to the conventional non-parametric methods when applied to direct measurements.

Nonparametric Fitting of Aerodynamic Data Using Smoothing Thin-Plate Splines

This paper introduces a nonparametric fitting method for the interpolation of aerodynamic observations over a large range of multiple angles of attack. The method is based on the employment of smoothing thin-plate spline class functions, a well-renewed mathematical tool for multivariate data mining based on the generalization of the univariate natural cubic splines, in which a roughness penalty criterion is used to produce very smooth predictive hypersurfaces. Compared with other methods, such as parametric or even conventional nonparametric methods, the use of a smoothing thin-plate spline is more effective, in that the predictive surface comes directly from the observed points, thus minimizing any intervention of the analyst aimed at introducing model parameters. This forms the basis for a very reliable fitting technique, in which model construction can be relatively easy to implement. An application of the method is carried out on a case study representative of some experimental data coming from a wind-tunnel campaign on a typical three-dimensional fuselage-shaped body, aimed at the acquisition of its aerodynamic coefficients over a rather extensive attitude range. Specifically, the application is focused on the body lift coefficient as a function of both angle of attack and sideslip angle. The data set is also interpolated using concurrent response-surface methods: namely, a linear model, a bivariate spline, a radial basis function network, a support vector regression technique, a regression kriging, and a moving-least-squares approach, alternatively known as local polynomial regression. Results of data fitting are assessed using a cross-validation approach and reveal a clear superiority of smoothing thin-plate spline over the other methods, leading to a more regular fitted surface and a more reliable prediction tool, even when some observations are omitted. This is important per se, but acquires even more significance when an aerodynamic test campaign is to be planned with the minimum number of experimental observations.

An anatomical and physiological model of the renal parenchyma-model development and parametric identification

Renal function is often characterized by the activity/time curves obtained by imaging the aorta and kidney. Non-parametric deconvolution of the activity/time curves is clinically useful as a diagnostic tool in determining renal transit times. Typically non-parametric deconvolution is performed using a technique that does not require a priori information, e.g. matrix-based and Fourier-transform methods. Using data filtering and conservation of mass constraints, non-parametric deconvolution continues to exhibit noise in the deconvolved curves. This noise hampers the identification of renal transit times. Given the shortcomings of non-parametric deconvolution, a parametric model of the renal response has been developed. The authors' model is shown to be anatomically and physiologically plausible. Here, the parametric model structure is used, in conjunction with experimental data, to estimate renal physiological parameters. These parameters include the filtration fraction, renal blood transit time and urine transit times. The model parameters are then related to the minimum transit time (MinTT), mean transit time (MTT), glomerular filtration rate (GFR) and parenchymal transit time index (PTTI). As deconvolution techniques often produce negative artifacts, Fine et al. (1993) developed a technique to determine an aorta background to minimize this effect. Here this work is extended to determine a reasonable renal background from aorta activity/time curves. Non-parametric deconvolution is used to provide initial estimates of model parameters. The model is then fitted to twelve healthy background-corrected kidneys by an iterative parameter-estimation technique. The normal values correspond to those reported in the literature. These normal values are then used to identify renal arterial stenosis in two renal hypertensive patients. The results suggest that parametric identification, based on a renal-retention-function model, may provide additional anatomical and physiological information that is not provided by conventional non-parametric methods.