Kernel Estimation Method Research Articles

Performance Recognition for Sulphur Flotation Process Based on Froth Texture Unit Distribution

As an important indicator of flotation performance, froth texture is believed to be related to operational condition in sulphur flotation process. A novel fault detection method based on froth texture unit distribution (TUD) is proposed to recognize the fault condition of sulphur flotation in real time. The froth texture unit number is calculated based on texture spectrum, and the probability density function (PDF) of froth texture unit number is defined as texture unit distribution, which can describe the actual textual feature more accurately than the grey level dependence matrix approach. As the type of the froth TUD is unknown, a nonparametric kernel estimation method based on the fixed kernel basis is proposed, which can overcome the difficulty when comparing different TUDs under various conditions is impossible using the traditional varying kernel basis. Through transforming nonparametric description into dynamic kernel weight vectors, a principle component analysis (PCA) model is established to reduce the dimensionality of the vectors. Then a threshold criterion determined by theTQstatistic based on the PCA model is proposed to realize the performance recognition. The industrial application results show that the accurate performance recognition of froth flotation can be achieved by using the proposed method.

Bias Reduction in Kernel Estimation of the Density Function of Cotton Fiber Length

Abstract. The non-parameter kernel estimation has become a dramatic method on fitting the distribution density function of cotton fiber length in theoretical research on fiber length. It can get a differentiable and integrable density function of cotton length distribution, and make the probability approach more effective on analysis and prediction of yarn performance. But, due to the requirements of the fitting smoothness, there is a bias between calculational index and measured value, especially to the short fiber content. This research uses the power function to fit the distribution of short fibers, then according to the principle of mixed distribution, revises the density function gotten by kernel estimation method, and gives a precise estimation of density function. The revised algorithm is more exact to fit the density function of fiber length. This approach is a new way to study the fiber length distribution and its effect on yarn properties both theoretically and practically.

Nonparametric Identification of Glucose-Insulin Process in IDDM Patient with Multi-meal Disturbance

Modern close loop control for blood glucose level in a diabetic patient necessarily uses an explicit model of the process. A fixed parameter full order or reduced order model does not characterize the inter-patient and intra-patient parameter variability. This paper deals with a frequency domain nonparametric identification of the nonlinear glucose-insulin process in an insulin dependent diabetes mellitus patient that captures the process dynamics in presence of uncertainties and parameter variations. An online frequency domain kernel estimation method has been proposed that uses the input–output data from the 19th order first principle model of the patient in intravenous route. Volterra equations up to second order kernels with extended input vector for a Hammerstein model are solved online by adaptive recursive least square (ARLS) algorithm. The frequency domain kernels are estimated using the harmonic excitation input data sequence from the virtual patient model. A short filter memory length of M = 2 was found sufficient to yield acceptable accuracy with lesser computation time. The nonparametric models are useful for closed loop control, where the frequency domain kernels can be directly used as the transfer function. The validation results show good fit both in frequency and time domain responses with nominal patient as well as with parameter variations.

Space-variant blur deconvolution and denoising in the dual exposure problem

In this paper we propose a space-variant blur estimation and effective denoising/deconvolution method for combining a long exposure blurry image with a short exposure noisy one. The blur in the long exposure shot is mainly caused by camera shake or object motion, and the noise in the underexposed image is introduced by the gain factor applied to the sensor when the ISO is set to an high value. Due to the space variant degradation, the image pair is divided into overlapping patches for processing. The main idea in the deconvolution algorithm is to incorporate a combination of prior image models into a spatially-varying deblurring/denoising framework which is applied to each patch. The method employs a kernel and parameter estimation method to choose between denoising or deblurring each patch. Experiments on both synthetic and real images are provided to validate the proposed approach.

Functional coefficient regression models with time trend

We consider the problem of estimating a varying coefficient regression model when regressors include a time trend. We show that the commonly used local constant kernel estimation method leads to an inconsistent estimation result, while a local polynomial estimator yields a consistent estimation result. We establish the asymptotic normality result for the proposed estimator. We also provide asymptotic analysis of the data-driven (least squares cross validation) method of selecting the smoothing parameters. In addition, we consider a partially linear time trend model and establish the asymptotic distribution of our proposed estimator. Two test statistics are proposed to test the null hypotheses of a linear and of a partially linear time trend models. Simulations are reported to examine the finite sample performances of the proposed estimators and the test statistics.

A Nonparametric Study on the Effects of Energy Consumption from some Energy Materials to Economic Growth in China

Based on the panel data of 29 provinces, municipalities and autonomous regions in China from 1995 to 2009, this paper uses non-parametric panel data models to mainly study the influences of coal, electricity, oil consumption to GDP. We find the following results: (1) local linear kernel estimation method shows that coal, electricity and oil consumptions have significant positive impacts on GDP; (2) the pointwise regression estimates of output elasticity for coal, electricity and oil consumptions with respect to five explanatory variables have shapes including “U”, inverted “U”, increasing and decreasing types

A Nonparametric Study on the Effects of Energy Consumption from some Energy Materials to Economic Growth in China

Based on the panel data of 29 provinces, municipalities and autonomous regions in China from 1995 to 2009, this paper uses non-parametric panel data models to mainly study the influences of coal, electricity, oil consumption to GDP. We find the following results: (1) local linear kernel estimation method shows that coal, electricity and oil consumptions have significant positive impacts on GDP; (2) the pointwise regression estimates of output elasticity for coal, electricity and oil consumptions with respect to five explanatory variables have shapes including “U”, inverted “U”, increasing and decreasing types

Estimation of the 25(OH) Vitamin D Threshold below which Secondary Hyperparathyroidism may Occur Among African Migrant Women in Paris

It has previously been shown that there is a threshold of serum 25-hydroxy vitamin D below which secondary hyperparathyroidism may occur. Our purpose was to estimate this threshold in a population of migrant African women living in Paris. Between February 2008 and December 2009, measurements of 25-hydroxy vitamin D and parathormone were performed in 165 African migrant women living in Paris. The estimation of 25-hydroxy vitamin D and parathormone marginal distributions as Gaussian mixtures, combined with a nonparametric kernel estimation method of the regression function of parathormone on 25-hydroxy vitamin D, provided the desired estimate of serum 25-hydroxy vitamin D threshold. In our sample of African women, our method has shown that serum 25-hydroxy vitamin D levels below 48 ± 2 nmol/L may induce an increase in parathormone concentrations. In this sample, our method provided a reliable estimate (95 % confidence interval) of the serum 25-hydroxy vitamin D level below which an increase in parathormone concentrations can be observed.

Estimation via corrected scores in general semiparametric regression models with error-prone covariates

This paper considers the problem of estimation in a general semiparametric regression model when error-prone covariates are modeled parametrically while covariates measured without error are modeled nonparametrically. To account for the effects of measurement error, we apply a correction to a criterion function. The specific form of the correction proposed allows Monte Carlo simulations in problems for which the direct calculation of a corrected criterion is difficult. Therefore, in contrast to methods that require solving integral equations of possibly multiple dimensions, as in the case of multiple error-prone covariates, we propose methodology which offers a simple implementation. The resulting methods are functional, they make no assumptions about the distribution of the mismeasured covariates. We utilize profile kernel and backfitting estimation methods and derive the asymptotic distribution of the resulting estimators. Through numerical studies we demonstrate the applicability of proposed methods to Poisson, logistic and multivariate Gaussian partially linear models. We show that the performance of our methods is similar to a computationally demanding alternative. Finally, we demonstrate the practical value of our methods when applied to Nevada Test Site (NTS) Thyroid Disease Study data.

Structural variation in genesis and landfall locations of North Atlantic tropical cyclones related to SST

The influence of sea surface temperature (SST) on the locations of the genesis and of landfall of tropical cyclones in the North Atlantic is analyzed. For that purpose, these locations are calculated from HURDAT and split into two disjoint subsets according to whether SST in the North Atlantic was above or below average in the year the corresponding storms occurred. Landfalls are investigated separately for the groups of cyclones categorized as tropical storms, minor hurricanes, or major hurricanes at the moment of landfall. The locations are considered realizations of inhomogeneous Poisson point processes, and the corresponding density functions are estimated with kernel estimation methods. In this way, any spatial structure inherent in the data is taken into account. These density functions are then compared with Monte Carlo methods from spatial statistics, which allows the detection of areas of statistically significant differences in the two sets with high and low SST, respectively. Results show many such areas, which is of relevance for the insurance industry and mathematical modelling of cyclones, as well as for decision support during the preparation for natural disasters.

Structural variation in genesis and landfall locations of North Atlantic tropical cyclones related to SST

The influence of sea surface temperature (SST) on the locations of the genesis and of landfall of tropical cyclones in the North Atlantic is analyzed. For that purpose, these locations are calculated from HURDAT and split into two disjoint subsets according to whether SST in the North Atlantic was above or below average in the year the corresponding storms occurred. Landfalls are investigated separately for the groups of cyclones categorized as tropical storms, minor hurricanes, or major hurricanes at the moment of landfall. The locations are considered realizations of inhomogeneous Poisson point processes, and the corresponding density functions are estimated with kernel estimation methods. In this way, any spatial structure inherent in the data is taken into account. These density functions are then compared with Monte Carlo methods from spatial statistics, which allows the detection of areas of statistically significant differences in the two sets with high and low SST, respectively. Results show many such areas, which is of relevance for the insurance industry and mathematical modelling of cyclones, as well as for decision support during the preparation for natural disasters.

An evaluation of spatial and temporal patterns of lightning- and human-caused forest fires in Alberta, Canada, 1980 - 2007

We used the K-function and kernel estimation methods to evaluate the spatial and temporal patterns of ignition locations of lightning- and human-caused forest fires in Alberta, Canada. Although both of these fire types have spatial patterns of cluster distribution, quantitative measures for evaluating the patterns in the province are lacking. Our results revealed annual differences in the spatial patterns between the two fire types, whereby fires caused by humans tended to be more clustered and had more complex spatial patterns than those caused by lightning. Spatial interactions of cluster and inhibition existed between the two fire types. Human-caused fires in the period 2003–07 were highly concentrated in the southern parts of the province, indicating the existence of an interaction between space and time. Kernel analysis confirmed the observation that in northern Alberta, lightning-caused fires were more likely to occur than human-caused fires; the opposite was true in southern Alberta. This study provided useful spatial information that is not obvious or cannot be inferred from visual examination of raw data. Such quantitative knowledge could lead to the development of fire-response and fire-suppression strategies appropriate to specific regions within the province.

Investigating the practicality of using radio tracking to determine home range and movements of Picathartidae

Radiotelemetry is an important tool used to aid the understanding and conservation of cryptic and rare birds. The two bird species of the family Picathartidae are little-known, secretive, forest-dwelling birds endemic to western and central Africa. In 2005, we conducted a radio-tracking trial of Grey-necked Picathartes Picathartes oreas in the Mbam Minkom Mountain Forest, southern Cameroon, using neck collar (two birds) and tail-mounted (four birds) transmitters to investigate the practicality of radio-tracking Picathartidae. Three birds with tail-mounted transmitters were successfully tracked with the fourth, though not relocated for radio tracking, resighted the following breeding season. Two of these were breeding birds that continued to provision young during radio tracking. One neck-collared bird was found dead three days after transmitter attachment and the other neither relocated nor resighted. As mortality in one bird was potentially caused by the neck collar transmitter we recommend tail-mounted transmitters in future radio-tracking studies of Picathartidae. Home ranges, shown using minimum convex polygon and kernel estimation methods, were generally small (<0.5 km2) and centred around breeding sites. A minimum of 60 fixes were found to be sufficient for home range estimation.

Forecast of value at risk for equity indices: an analysis from developed and emerging markets

PurposeThe purpose of this paper is to compare the performance of commonly used value at risk (VaR) estimation methods for equity indices from both developed countries and emerging markets.Design/methodology/approachIn addition to traditional time‐series models, this paper examines the recently developed nonparametric kernel estimator (KE) approach to predicting VaR. KE methods model tail behaviors directly and independently of the overall return distribution, so are better able to take into account recent extreme shocks.FindingsThe paper compares the performance and reliability of five major VaR methodologies, using more than 26 years of return data on 37 equity indices. Through back‐testing of the resulting models on a moving window and likelihood ratio tests, it shows that KE models produce remarkably good VaR estimates and outperform the other common methods.Practical implicationsFinancial assets are known to have irregular return patterns; not only the volatility but also the distributions themselves vary over time. This analysis demonstrates that a nonparametric approach (the KE method) can generate reliable VaR estimates and accurately capture the downside risk.Originality/valueThe paper evaluates the performance of several common VaR estimation approaches using a comprehensive sample of empirical data. The paper also reveals that kernel estimation methods can achieve remarkably reliable VaR forecasts. A detailed and complete investigation of nonparametric estimation methods will therefore significantly contribute to the understanding of the VaR estimation processes.

Transaction Size and Effective Spread: An Informational Relationship

The relationship between quantity traded and transaction costs has been one of the main focuses among financial scholars and practitioners. The purpose of this thesis is to investigate the informational relationship between these variables. Following insights and results of Milgrom (1981), Feldman (2004), and Feldman and Winer (2004), we use New York Stock Exchange (NYSE) data and kernel estimation methods to construct the distribution of one variable conditional on the other. Then, we study the information in these conditional distributions: the extent to which they are ordered by first order stochastic dominance (FOSD) and by the monotone likelihood ratio property (MLRP). We find that transaction size and effective spread are significantly correlated. FOSD, a necessary condition for a signaling equilibrium, holds under certain conditions. We start from 2-subsample case. We choose a cut-off point in transaction size and categorize the observations with transaction sizes smaller than the cut-off point into group low. The remaining data is classified as high. We repeat this procedure for all possible transaction size cut-off points. It turns out that FOSD holds nowhere. However, once we eliminate transactions at the quote midpoint, the crossings between exchange members not specialists, FOSD holds for all the cut-off points fewer than 15800 shares. The MLRP, a necessary and sufficient condition for the separating equilibrium to hold point by point of the conditional density functions, does not hold but might not be ruled out considering the error in the estimates. We also find that large trades are not necessarily associated with large spread. Instead, it is more likely that larger trades are transacted at the quote midpoint (again, the non-specialist crossings) than smaller trades. Our results confirm the findings of Barclay and Warner (1993) regarding the informativeness of medium-size transactions: we identify informational relationships between mid-size transactions and spreads but not for zero effective spreads and large transactions. That is, we identify two regimes, an informational one and a non-informational/liquidity one.

A filtered polynomial approach to density estimation

In this paper, a little known computational approach to density estimation based on filtered polynomial approximation is investigated. It is accompanied by the first online available density estimation computer program based on a filtered polynomial approach. The approximation yields the unknown distribution and density as the product of a monotonic increasing polynomial and a filter. The filter may be considered as a target distribution which gets fixed prior to the estimation. The filtered polynomial approach then provides coefficient estimates for (close) algebraic approximations to (a) the unknown density function and (b) the unknown cumulative distribution function as well as (c) a transformation (e.g., normalization) from the unknown data distribution to the filter. This approach provides a high degree of smoothness in its estimates for univariate as well as for multivariate settings. The nice properties as the high degree of smoothness and the ability to select from different target distributions are suited especially in MCMC simulations. Two applications in Sects. 1 and 7 will show the advantages of the filtered polynomial approach over the commonly used kernel estimation method.

Productivity, convergence and policy: a study of OECD countries and industries

This paper analyses trends in labour productivity and its underlying determinants in a panel of OECD countries from 1979 to 2002. Data Envelopment Analysis (DEA) is used to estimate a Malmquist measure of multifactor productivity (MFP) change. We decompose the growth in labour productivity into (i) net technological change (ii) input biased technical change (IBTC) (iii) efficiency change and (iv) capital accumulation. We analyse the effect of each of these factors in the transition towards the equilibrium growth paths of both labour productivity and per capita GDP for the OECD countries, controlling for the effects of different policies and institutions. The results indicate that on average gaps in productivity or income levels are narrowing down although there is no evidence to suggest that the entire OECD area comprises a single convergence “club”. Using kernel estimation methods we find that that labour productivity and per capita GDP are settling toward a twin peak (bimodal) distribution. Panel unit root tests over an extended (1960–2001) period provide general support for the convergence hypothesis. Analysis of the contributions of productivity growth within industries and sectoral composition changes show that aggregate productivity change is predominantly driven by ‘net’ within sector effects with very little contribution emerging from sectoral shifts (the ‘in-between’ static or dynamic effects resulting from higher or above average productivity industries gaining employment shares or low productivity industries losing shares).

Efficient Estimation of Population-Level Summaries in General Semiparametric Regression Models

This article considers a wide class of semiparametric regression models in which interest focuses on population-level quantities that combine both the parametric and the nonparametric parts of the model. Special cases in this approach include generalized partially linear models, generalized partially linear single-index models, structural measurement error models, and many others. For estimating the parametric part of the model efficiently, profile likelihood kernel estimation methods are well established in the literature. Here our focus is on estimating general population-level quantities that combine the parametric and nonparametric parts of the model (e.g., population mean, probabilities, etc.). We place this problem in a general context, provide a general kernel-based methodology, and derive the asymptotic distributions of estimates of these population-level quantities, showing that in many cases the estimates are semiparametric efficient. For estimating the population mean with no missing data, we show that the sample mean is semiparametric efficient for canonical exponential families, but not in general. We apply the methods to a problem in nutritional epidemiology, where estimating the distribution of usual intake is of primary interest and semiparametric methods are not available. Extensions to the case of missing response data are also discussed.

Capital Allocation for Credit Portfolios with Kernel Estimators

Determining contributions by sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often economic capital is measured as Value-at-Risk (VaR) of the portfolio loss distribution. For many of the credit portfolio risk models used in practice, the VaR contributions then have to be estimated from Monte Carlo samples. In the context of a partly continuous loss distribution (i.e. continuous except for a positive point mass on zero), we investigate how to combine kernel estimation methods with importance sampling to achieve more efficient (i.e. less volatile) estimation of VaR contributions.

Capital allocation for credit portfolios with kernel estimators

Determining the contributions of sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often, economic capital is measured as the Value-at-Risk (VaR) of the portfolio loss distribution. For many of the credit portfolio risk models used in practice, the VaR contributions then have to be estimated from Monte Carlo samples. In the context of a partly continuous loss distribution (i.e. continuous except for a positive point mass on zero), we investigate how to combine kernel estimation methods with importance sampling to achieve more efficient (i.e. less volatile) estimation of VaR contributions.