Optimal Smoothing Parameter Research Articles

Using 3D robust smoothing to fill land surface temperature gaps at the continental scale

Land surface temperature (LST) data derived from Moderate Resolution Imaging Spectroradiometer (MODIS) products has been widely applied in environmental studies, and natural disaster management. However missing data in space and time due to cloud contamination, cloud shadows and atmospheric conditions has hindered its application. Accurate gap filling algorithms for a large spatiotemporal scale of LST data are necessary to enhance the utility of this product. This study applied a three-dimensional (3-D) gap-filling method to fill gaps in 9 years of LST data over Australia (2002–2011). As the gap-filling method relies on a smoothing parameter that controls the accuracy of the reconstruction algorithm, we estimated optimal smoothing parameters to separately reconstruct daytime and nighttime LST products. The reconstructed LST were validated against ground-based LST obtained from the OzFlux network and recommendations made on appropriate smoothing parameters. The results demonstrate that the gap-filling algorithm provides an accurate approach to generating reconstructed LST products for a long period over large spatial scales.

Nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates

Allowing for the existence of irrelevant covariates, we study the problem of estimating a conditional quantile function nonparametrically with mixed discrete and continuous data. We estimate the conditional quantile regression function using the check-function-based kernel method and suggest a data-driven cross-validation (CV) approach to simultaneously determine the optimal smoothing parameters and remove the irrelevant covariates. When the number of covariates is large, we first use a screening method to remove the irrelevant covariates and then apply the CV criterion to those that survive the screening procedure. Simulations and an empirical application demonstrate the usefulness of the proposed methods.

Optimization of Process Conditions for Styrene Epoxidation Based on the Artificial Intelligence Method

AbstractA novel prediction and optimization method based on improved generalized regression neural network (GRNN) and particle swarm optimization (PSO) algorithm is proposed to optimize the process conditions for styrene epoxidation to achieve higher yields. This model was designed to optimize the five input parameters reaction temperature and time as well as catalyst, solvent, and oxidant dosage. The output of the improved GRNN was given to the PSO algorithm to optimize the process conditions. The optimal smoothing parameter σ of GRNN was chosen from the training sample with a minimum cross validation error. Under the five optimized process conditions the maximum yield reached 95.76 %. This innovative model of improved GRNN hybrid PSO algorithm proved to be a useful tool for optimization of process conditions for styrene epoxidation.

A smoothed Q‐learning algorithm for estimating optimal dynamic treatment regimes

AbstractIn this paper, we propose a smoothed Q‐learning algorithm for estimating optimal dynamic treatment regimes. In contrast to the Q‐learning algorithm in which nonregular inference is involved, we show that, under assumptions adopted in this paper, the proposed smoothed Q‐learning estimator is asymptotically normally distributed even when the Q‐learning estimator is not and its asymptotic variance can be consistently estimated. As a result, inference based on the smoothed Q‐learning estimator is standard. We derive the optimal smoothing parameter and propose a data‐driven method for estimating it. The finite sample properties of the smoothed Q‐learning estimator are studied and compared with several existing estimators including the Q‐learning estimator via an extensive simulation study. We illustrate the new method by analyzing data from the Clinical Antipsychotic Trials of Intervention Effectiveness–Alzheimer's Disease (CATIE‐AD) study.

Determination of Soil Salt Content Using a Probability Neural Network Model Based on Particle Swarm Optimization in Areas Affected and Non-Affected by Human Activities

Traditional partial least squares regression (PLSR) and artificial neural networks (ANN) have been widely applied to estimate salt content from spectral reflectance in many different saline environments around the world. However, these methods entail a great amount of calculation, and their accuracy is low. To overcome these problems, a probability neural network (PNN) model based on particle swarm optimization was used in this study to build soil salt content models. Furthermore, there is a clear correlation between the level of human activities and the degree of salinization of an environment. This paper is the first to discuss this matter. Here, the performance of the PNN model to estimate soil salt content from reflectance data was investigated in areas non-affected (Area A) and affected (Area B) by human activities. The study area is located in Xingjinag, China. Different mathematical procedures, five wave band intervals, and two types of signal input sources were used for cross analysis. The coefficient of determination (R2), root mean square error (RMSE), and ratio of performance to deviation (RPD) index values were compared to verify the reliability of the model. Particle swarm optimization was used to adjust the optimal smoothing parameters of the PNN model and to avoid the long training processes required by the traditional ANN. The results show that the optimal wave band interval of the PNN is between 1000 nm and 1350 nm in Area A and between 400 nm and 700 nm in Area B. The reciprocal (1/R) transformation after Savitzky-Golay (SG) smoothing of the signal source is optimal for both areas. The RPD for both is greater than 30, which shows that the PNN model is applicable to areas with and without human activities and the prediction results are very good. The results indicated that the optimal wave band intervals for PNN modeling differed in areas affected and non-affected by human activities. The optimal interval of the artificial activities region falls in the visible light portion of the spectrum, and the optimized wave band region without human activities falls in the near-infrared short-wave portion of the spectrum.

국소 선형 복합 분위수 회귀에서의 평활계수 선택

국소복합분위수 회귀모형을 활용한 비모수적 함수 추정방법이 높은 효율성과 더불어 활발히 연구되고 있다. 이러한 추정과정에 커널을 사용한 자료 평활방법이 대표적으로 사용되고 있으며, 그 성능은 커널보다는 평활계수의 선택 크게 의존한다. 한편, 회귀함수 추정방법의 성능을 평가하는 기준으로는 통상적으로 <TEX>$L_2$</TEX>-노름이 사용되어 평균제곱오차 또는 평균적분제곱오차를 최소화하는 평활계수의 선택에 대한 많은 연구가 진행되어 왔다. 본 논문에서는 국소선형 복합 분위수 회귀방법을 활용한 비모수 회귀모형 추정량의 성능을 결정하는 평활계수 선택의 최적성에 관해 연구하였다. 특히, 여러 장점을 가졌으나 수리적 어려움으로 연구가 미흡한 평균절대오차 및 평균적분절대오차를 최적의 기준으로 삼아 최적의 평활계수를 구하고 그 유일성에 관해 연구하였다. 나아가 기존의 평가기준인 평균제곱오차 및 평균적분제곱오차를 사용한 선택과의 관계를 파악하고 그 성능을 비교하였다. 이러한 과정에서 다양한 상황에서의 모의실험을 통해 제안한 방법의 특성을 규명하였다. Local composite quantile regression is a useful non-parametric regression method widely used for its high efficiency. Data smoothing methods using kernel are typically used in the estimation process with performances that rely largely on the smoothing parameter rather than the kernel. However, <TEX>$L_2$</TEX>-norm is generally used as criterion to estimate the performance of the regression function. In addition, many studies have been conducted on the selection of smoothing parameters that minimize mean square error (MSE) or mean integrated square error (MISE). In this paper, we explored the optimality of selecting smoothing parameters that determine the performance of non-parametric regression models using local linear composite quantile regression. As evaluation criteria for the choice of smoothing parameter, we used mean absolute error (MAE) and mean integrated absolute error (MIAE), which have not been researched extensively due to mathematical difficulties. We proved the uniqueness of the optimal smoothing parameter based on MAE and MIAE. Furthermore, we compared the optimal smoothing parameter based on the proposed criteria (MAE and MIAE) with existing criteria (MSE and MISE). In this process, the properties of the proposed method were investigated through simulation studies in various situations.

Localising Temperature Risk

On the temperature derivative market, modeling temperature volatility is an important issue for pricing and hedging. In order to apply pricing tools of financial mathematics, one needs to isolate a Gaussian risk factor. A conventional model for temperature dynamics is a stochastic model with seasonality and inter temporal autocorrelation. Empirical work based on seasonality and autocorrelation correction reveals that the obtained residuals are heteroscedastic with a periodic pattern. The object of this research is to estimate this heteroscedastic function so that after scale normalisation a pure standardised Gaussian variable appears. Earlier work investigated this temperature risk in different locations and showed that neither parametric component functions nor a local linear smoother with constant smoothing parameter are flexible enough to generally describe the volatility process well. Therefore, we consider a local adaptive modeling approach to find at each time point, an optimal smoothing parameter to locally estimate the seasonality and volatility. Our approach provides a more flexible and accurate fitting procedure of localised temperature risk process by achieving excellent normal risk factors.

Application of a probabilistic neural network for liquefaction assessment

This paper presents a hybrid probabilistic neural network (PNN) and particle swarm optimization (PSO) techniques to predict the soil liquefaction. The PSO algorithm is employed in selecting the optimal smoothing parameter of the PNN to improve the forecasting accuracy. Seven parameters such as earthquake magnitude, normalized peak horizontal acceleration at ground surface, standard penetration number, penetration resistance, relative compaction, mean grain diameter and groundwater table are selected as the evaluating indices. The predictions from the PSO-PNN model were compared with those from two models: back-propagation neural network (BPNN) model and support vector machine (SVM) model. The study concluded that the proposed PSO-PNN model can be used as a reliable approach for predicting soil liquefaction.

Online Variable Kernel Estimator

In this work, the authors propose a novel method called online variable kernel estimation of the probability density function (pdf). This new online estimator combines the characteristics and properties of two estimators namely nearest neighbors estimator and the Parzen-Rosenblatt estimator. Their approach allows a compact online adaptation of the estimated probability density function from the new arrival data. The performance of the online variable kernel estimator (OVKE) depends on the choice of the bandwidth. The authors present in this article a new technique for determining the optimal smoothing parameter of OVKE based on the maximum entropy principle (MEP). The robustness and performance of the proposed approach are demonstrated by examples of online estimation of real and simulated data distributions.

Shrinkage-based semiparametric density estimation

Shrinkage estimation is used to develop a semiparametric density estimator as a linear combination of a fully known parametric density function and a nonparametric density estimator. We determine the asymptotic properties of the shrinkage coefficient and of the semiparametric estimator’s integrated squared error. Moreover, we show that the proposed estimation methodology delivers density estimators that are more accurate than nonparametric estimators and that do not require the use of optimal smoothing parameters.

Localizing Temperature Risk

ABSTRACTOn the temperature derivative market, modeling temperature volatility is an important issue for pricing and hedging. To apply the pricing tools of financial mathematics, one needs to isolate a Gaussian risk factor. A conventional model for temperature dynamics is a stochastic model with seasonality and intertemporal autocorrelation. Empirical work based on seasonality and autocorrelation correction reveals that the obtained residuals are heteroscedastic with a periodic pattern. The object of this research is to estimate this heteroscedastic function so that, after scale normalization, a pure standardized Gaussian variable appears. Earlier works investigated temperature risk in different locations and showed that neither parametric component functions nor a local linear smoother with constant smoothing parameter are flexible enough to generally describe the variance process well. Therefore, we consider a local adaptive modeling approach to find, at each time point, an optimal smoothing parameter to locally estimate the seasonality and volatility. Our approach provides a more flexible and accurate fitting procedure for localized temperature risk by achieving nearly normal risk factors. We also employ our model to forecast the temperaturein different cities and compare it to a model developed in 2005 by Campbell and Diebold. Supplementary materials for this article are available online.

A production throughput forecasting system in an automated hard disk drive test operation using GRNN

Purpose: The goal of this paper is to develop a pragmatic system of a production throughput forecasting system for an automated test operation in a hard drive manufacturing plant. The accurate forecasting result is necessary for the management team to response to any changes in the production processes and the resources allocations.Design/methodology/approach: In this study, we design a production throughput forecasting system in an automated test operation in hard drive manufacturing plant. In the proposed system, consists of three main stages. In the first stage, a mutual information method was adopted for selecting the relevant inputs into the forecasting model. In the second stage, a generalized regression neural network (GRNN) was implemented in the forecasting model development phase. Finally, forecasting accuracy was improved by searching the optimal smoothing parameter which selected from comparisons result among three optimization algorithms: particle swarm optimization (PSO), unrestricted search optimization (USO) and interval halving optimization (IHO).Findings: The experimental result shows that (1) the developed production throughput forecasting system using GRNN is able to provide forecasted results close to actual values, and to projected the future trends of production throughput in an automated hard disk drive test operation; (2) An IHO algorithm performed as superiority appropriate optimization method than the other two algorithms. (3) Compared with current forecasting system in manufacturing, the results show that the proposed system’s performance is superior to the current system in prediction accuracy and suitable for real-world application.Originality/value: The production throughput volume is a key performance index of hard disk drive manufacturing systems that need to be forecast. Because of the production throughput forecasting result is useful information for management team to respond to any changing in production processes and resources allocation. However, a practically forecasting system for production throughput has not been described in detail yet. The experiments were conducted on a real data set from the final testing operation of hard disk drive manufacturing factory by using Visual Basics Application on Microsoft Excel© to develop preliminary forecasting system on testing and verification process. The experimental result shows that the proposed model is superior to the performance of the current forecasting system.

Combustion kinetics of pine sawdust biochar

The combustion kinetics of biochar derived from fast pyrolysis of pine sawdust was investigated by using nonisothermal thermogravimetric analysis under air atmosphere at different heating rates. The experimental conversion (α–T) curves contain some experimental errors, and the corresponding derivative conversion (dα/dT–T) curves have many fluctuations. Two strategies of obtaining the smooth dα/dT–T curves were used based on the robust locally weighted scatterplot smoothing method coupled with the corrected AIC smoothing parameter selection method. In the strategy of firstly smoothing α–T data and then differentiating smoothed α–T data, although the smoothed α–T data are relatively smooth, the dα/dT–T curves obtained from the differentiation of the smoothed α–T data have fluctuations. In the strategy of firstly differentiating α–T data and then smoothing dα/dT–T data, the obtained dα/dT–T curves with the optimal smoothing parameters are smooth enough, which indicates that the second strategy is effective. The isoconversional kinetic analysis of the smoothed dα/dT–T curves was performed by using the Friedman differential isoconversional method. The effective activation energies of biochar combustion were obtained and found to significantly vary with the conversion degree (from about 150 to 250 kJ mol−1 in the range of conversion degree from 0.05 to 0.95).

Analysis of a New Space-Time Parallel Multigrid Algorithm for Parabolic Problems

We present and analyze a new space-time parallel multigrid method for parabolic equations. The method is based on arbitrarily high order discontinuous Galerkin discretizations in time and a finite element discretization in space. The key ingredient of the new algorithm is a block Jacobi smoother. We present a detailed convergence analysis when the algorithm is applied to the heat equation and determine asymptotically optimal smoothing parameters, a precise criterion for semi-coarsening in time or full coarsening, and give an asymptotic two grid contraction factor estimate. We then explain how to implement the new multigrid algorithm in parallel and show with numerical experiments its excellent strong and weak scalability properties.

A semi-analytical performance prediction of a digital communication system using Fourier transform inversion

Analytical performance evaluation of a digital communication system remains a serious problem especially when a sophisticated digital signal processing is considered. Moreover, it is difficult to obtain the expected performance of such system using the Monte Carlo simulation method. In this paper, we propose a new semi-analytical approach for predicting error probability in a digital communication system. This approach is based on Fourier transform inversion formula to estimate the probability density function (pdf) of the observed soft sample at the receiver. Furthermore, we applied a bootstrap method for selecting the optimal smoothing parameter to make the proposed semi-analytical method more accurate. Simulation results show that the obtained semi-analytical error probability is close to the one measured using Monte Carlo simulation and provides a significant gain in terms of computing time. Besides, the use of the bootstrap method decreases the squared error between the true pdf and the estimated one.

Signal analysis via instantaneous frequency estimation of signal components

The empirical mode decomposition (EMD) algorithm, introduced by Huang et al. (Proc Roy Soc Lond Ser A Math Phys Eng Sci 454(1971):903–995, 1998), is arguably the most popular mathematical scheme for non-stationary signal decomposition and analysis. The objective of EMD is to separate a given signal into a number of components, called intrinsic mode functions (IMF’s) after which the instantaneous frequency (IF) and amplitude of each IMF are computed through Hilbert spectral analysis (HSA). On the other hand, the synchrosqueezed wavelet transform (SST), introduced by Daubechies and Maes (Wavelets in Medicine and Biology, pp. 527–546, 1996) and further developed by Daubechies et al. (Appl Comput Harmon Anal 30:243–261, 2011), is applied to estimate the IF’s of all signal components of the given signal, based on one single reference “IF function”, under the assumption that the signal components satisfy certain strict properties of a so-called adaptive harmonic model, before the signal components of the model are recovered. The objective of our paper is to develop a hybrid EMD-SST computational scheme by applying a “modified SST” to each IMF of the EMD, as an alternative approach to the original EMD-HSA method. While our modified SST assures non-negative instantaneous frequencies of the IMF’s, application of the EMD scheme eliminates the dependence on a single reference IF value as well as the guessing work of the number of signal components in the original SST approach. Our modification of the SST consists of applying vanishing moment wavelets (introduced in a recent paper by C.K. Chui, Y.-T. Lin and H.-T. Wu) with stacked knots to process signals on bounded or half-infinite time intervals, and spline curve fitting with optimal smoothing parameter selection through generalized cross-validation. In addition, we formulate a local cubic spline interpolation scheme for real-time realization of the EMD sifting process that improves over the standard global cubic spline interpolation, both in quality and computational cost, particularly when applied to bounded and half-infinite time intervals.

Multivariate Local Polynomial Kernel Estimators: Leading Bias and Asymptotic Distribution

Masry (1996b) provides estimation bias and variance expression for a general local polynomial kernel estimator in a general multivariate regression framework. Under smoother conditions on the unknown regression function and by including more refined approximation terms than that in Masry (1996b), we extend the result of Masry (1996b) to obtain explicit leading bias terms for the whole vector of the local polynomial estimator. Specifically, we derive the leading bias and leading variance terms of nonparametric local polynomial kernel estimator in a general nonparametric multivariate regression model framework. The results can be used to obtain optimal smoothing parameters in local polynomial estimation of the unknown conditional mean function and its derivative functions.

Targeted smoothing parameter selection for estimating average causal effects

The non-parametric estimation of average causal effects in observational studies often relies on controlling for confounding covariates through smoothing regression methods such as kernel, splines or local polynomial regression. Such regression methods are tuned via smoothing parameters which regulates the amount of degrees of freedom used in the fit. In this paper we propose data-driven methods for selecting smoothing parameters when the targeted parameter is an average causal effect. For this purpose, we propose to estimate the exact expression of the mean squared error of the estimators. Asymptotic approximations indicate that the smoothing parameters minimizing this mean squared error converges to zero faster than the optimal smoothing parameter for the estimation of the regression functions. In a simulation study we show that the proposed data-driven methods for selecting the smoothing parameters yield lower empirical mean squared error than other methods available such as, e.g., cross-validation.

Dynamic Block-Based Parameter Estimation for MRF Classification of High-Resolution Images

A Markov random field is a graphical model that is commonly used to combine spectral information and spatial context into image classification problems. The contributions of the spatial versus spectral energies are typically defined by using a smoothing parameter, which is often set empirically. We propose a new framework to estimate the smoothing parameter. For this purpose, we introduce the new concepts of dynamic blocks and class label cooccurrence matrices. The estimation is then based on the analysis of the balance of spatial and spectral energies computed using the spatial class co-occurrence distribution and dynamic blocks. Moreover, we construct a new spatially weighted parameter to preserve the edges, based on the Canny edge detector. We evaluate the performance of the proposed method on three data sets: a multispectral DigitalGlobe WorldView-2 and two hyperspectral images, recorded by the AVIRIS and the ROSIS sensors, respectively. The experimental results show that the proposed method succeeds in estimating the optimal smoothing parameter and yields higher classification accuracy values when compared with state-of-the-art methods.

A Novel Probability Density Estimating Method for Relative Altitudes of Civil

With the rapid development of civil aviation, the shortage of airspace resource is becoming one of the main limiting factors for air traffic transportation. Inspired by the ideas of reduced vertical separation minimum and reducing aircraft separation standard, this paper analyzes the distributing characteristics of civil aircraft tracks in cruising level space and presents a novel method for probability density estimation of civil aircraft tracks' relative altitudes in their cruising flight level spaces, and analyzes the distributing characteristics at their cruising altitude direction.The method is based on QAR data of enough random civil aircraft tracks from a domestic airline. First, we choose altitude data of each track's main cruise phase and calculate altitude values relative to the standard cruise altitude of respective cruising flight level, we call these processes as spatial alignment and the relative altitudes as relative-cruising altitudes or relative-cruise altitudes. Secondly, we do temporal alignment and figure out the relative altitude values of these tracks in panel data form. Then, we estimate the probability density of the relative altitude values using kernel density estimate method, with the least square cross-validation method choosing asymptotically optimal smoothing parameters. Finally, we figure out different confidence track bands, namely confidence interval limits, and do analysis.All the analysis results show that there is a great deal of airspace margin and space resource potential in each cruising levels. Hence there are a great possibility and expectation that the vertical separation minimum can be reduced again and add flight levels, which is beneficial to increase air traffic capacity and relieve traffic jams.