Local Linear Fitting Research Articles

Local Label Point Correction for Edge Detection of Overlapping Cervical Cells.

Accurate labeling is essential for supervised deep learning methods. However, it is almost impossible to accurately and manually annotate thousands of images, which results in many labeling errors for most datasets. We proposes a local label point correction (LLPC) method to improve annotation quality for edge detection and image segmentation tasks. Our algorithm contains three steps: gradient-guided point correction, point interpolation, and local point smoothing. We correct the labels of object contours by moving the annotated points to the pixel gradient peaks. This can improve the edge localization accuracy, but it also causes unsmooth contours due to the interference of image noise. Therefore, we design a point smoothing method based on local linear fitting to smooth the corrected edge. To verify the effectiveness of our LLPC, we construct a largest overlapping cervical cell edge detection dataset (CCEDD) with higher precision label corrected by our label correction method. Our LLPC only needs to set three parameters, but yields 30–40% average precision improvement on multiple networks. The qualitative and quantitative experimental results show that our LLPC can improve the quality of manual labels and the accuracy of overlapping cell edge detection. We hope that our study will give a strong boost to the development of the label correction for edge detection and image segmentation. We will release the dataset and code at: https://github.com/nachifur/LLPC.

Semiparametric inferences for panel data models with fixed effects via nearest neighbor difference transformation

In this paper, we propose a simple method to estimate a partially varying-coefficient panel data model with fixed effects. By taking difference upon the nearest neighbor of the smoothing variables to remove the fixed effects, we employ the profile least squares method and local linear fitting to estimate the parametric and nonparametric parts, respectively. Moreover, a functional form specification test and a nonparametric Hausman type test are constructed and their asymptotic properties are derived. Monte Carlo simulations are conducted to examine the finite sample performance of our estimators and test statistics.

3D surface reconstruction of small height object based on thin structured light scanning

Aiming at the problem of 3D surface reconstruction of small height objects, a method based on the scanning principle with thin structured light is proposed. The laser fringe is produced by a laser light source. It scans the surface of small height object under the control of a precise motion control system, and is integrated with a stereo light microscope and two cameras to form a complete structured light profilometry system. This method is very suitable for 3D surface reconstruction of small height objects. In order to deal with the phenomenon of "cracking" and local uneven brightness in microscope fringe image, the fringe image sequence is captured under different camera exposure parameters, and the quality of fringe image is improved by image fusion. The location of pixels on the center line of laser stripes is detected by the Loess local second-order fitting method, and the positions of these pixels are smoothed and predicted by using the Lowess local linear fitting method. The deformation of the laser stripe center curve is calculated by constructing a baseline, and the 3D surface reconstruction of the object with small height is realized in the image space. Taking the small characters on the surface of Chinese coins and human hair as test samples, their 3D surfaces are constructed by using the method proposed in this paper. The reconstructed 3D surface shapes are highly consistent with the real 3D surface shapes of objects.

Penalized Parametric PET Image Estimation Using Local Linear Fitting

Positron emission tomography (PET) is a powerful imaging tool for quantifying physiological information. Particularly, parametric PET imaging has been increasingly investigated because the voxel-wise spatial distribution of tracer kinetics can be achieved, which is suitable for identifying heterogeneous tracer uptake. Our goal is to provide a fast and accurate parametric imaging method by utilizing the full-dose image. In this article, we propose a novel penalized parametric imaging in which dynamic images are reconstructed frame by frame, and then voxel-wise kinetic parameters are iteratively estimated by a kinetic-domain penalty using a local linear fitting (LLF) that utilizes a full-dose static image as a prior in the penalty. In our optimization, a dual-domain approximation is derived to efficiently split suboptimizations for image and kinetic parameter separately, which can simplify suboptimizations including the nonlinear fitting of the two-tissue compartment model (2-TCM). In addition, we further investigate the feasibility of image-driven input function extraction by comparing with the standard blood sampling. We evaluated the performance of the proposed method using simulation and patient study with [18F]MK6240 tau scan data of two subjects, and results are compared with the conventional method and the Logan graphical model. We demonstrate that the proposed method outperforms the conventional parametric imaging methods.

On Partially Linear Single-Index Models with Missing Response and Error-in-Variable Predictors

In this paper, we consider a partially linear single-index model when missing responses and nonlinear regressors with measurement error are taken into account. Utilizing data imputation for missing values and regression calibration for error-prone regressors, we not only estimate the parameters in the linear part as well as the single-index part, but also estimate the nonpara-metric link function by local linear fit. Under normalization, all the proposed estimators for the regression coefficients and the link function are proven to be asymptotically normal, and some illustrative simulations are provided to justify our methods.

Regularized S‐map for inference and forecasting with noisy ecological time series

AbstractIt is well known that fluctuations of species abundances observed in ecological time series emerge from an interplay between deterministic nonlinear dynamics and stochastic forces. Importantly, nonlinearity and stochasticity introduce significant challenges to the analysis of ecological time series, such as the inference of the effect of species interactions on community dynamics and forecasting of species abundances.Local linear fits with state‐space‐dependent kernel functions, known as S‐maps, provide an efficient method to infer Jacobian coefficients (a proxy for the local effect of species interactions) and to make reliable forecasts from nonlinear time series. Yet, while it has been shown that the S‐map outperforms existing methods for nonparametric inference and forecasting, the methodology is sensitive to process noise. To overcome this limitation, we integrate the S‐map with different regularization schemes.To validate our approach, we test our methodology against different levels of noise and nonlinearity using three standard population dynamics models. We show that an appropriate choice of the regularization scheme, alongside an accurate choice of the kernel functions, can significantly improve the in‐sample inference of Jacobian coefficients and the out‐of‐sample forecast of species abundances in the presence of process noise. We further validate our methodology using two empirical time series of marine microbial communities.Our results illustrate that the regularized S‐map is an efficient method for nonparametric inference and forecasting from noisy, nonlinear, ecological time series. Yet, attention must be paid on the regularization scheme and the structure of the kernel for whether inference or forecasting is the ultimate goal of a research study.

Penalized PET Reconstruction Using Deep Learning Prior and Local Linear Fitting

Motivated by the great potential of deep learning in medical imaging, we propose an iterative positron emission tomography reconstruction framework using a deep learning-based prior. We utilized the denoising convolutional neural network (DnCNN) method and trained the network using full-dose images as the ground truth and low dose images reconstructed from downsampled data by Poisson thinning as input. Since most published deep networks are trained at a predetermined noise level, the noise level disparity of training and testing data is a major problem for their applicability as a generalized prior. In particular, the noise level significantly changes in each iteration, which can potentially degrade the overall performance of iterative reconstruction. Due to insufficient existing studies, we conducted simulations and evaluated the degradation of performance at various noise conditions. Our findings indicated that DnCNN produces additional bias induced by the disparity of noise levels. To address this issue, we propose a local linear fitting function incorporated with the DnCNN prior to improve the image quality by preventing unwanted bias. We demonstrate that the resultant method is robust against noise level disparities despite the network being trained at a predetermined noise level. By means of bias and standard deviation studies via both simulations and clinical experiments, we show that the proposed method outperforms conventional methods based on total variation and non-local means penalties. We thereby confirm that the proposed method improves the reconstruction result both quantitatively and qualitatively.

Semiparametric jump-preserving estimation for single-index models

ABSTRACTEstimation of the single-index model with a discontinuous unknown link function is considered in this paper. Existed refined minimum average variance estimation (rMAVE) method can estimate the single-index parameter and unknown link function simultaneously by minimising the average pointwise conditional variance, where the conditional variance can be estimated using the local linear fit method with centred kernel function. When there are jumps in the link function, big biases around jumps can appear. For this reason, we embed the jump-preserving technique in the rMAVE method, then propose an adaptive jump-preserving estimation procedure for the single-index model. Concretely speaking, the conditional variance is obtained by the one among local linear fits with centred, left-sided and right-sided kernel functions who has minimum weighted residual mean squares. The resulting estimators can preserve the jumps well and also give smooth estimates of the continuity parts. Asymptotic properties are established under some mild conditions. Simulations and real data analysis show the proposed method works well.

Partially linear transformation model for length-biased and right-censored data

In this paper, we consider a partially linear transformation model for data subject to length-biasedness and right-censoring which frequently arise simultaneously in biometrics and other fields. The partially linear transformation model can account for nonlinear covariate effects in addition to linear effects on survival time, and thus reconciles a major disadvantage of the popular semiparamnetric linear transformation model. We adopt local linear fitting technique and develop an unbiased global and local estimating equations approach for the estimation of unknown covariate effects. We provide an asymptotic justification for the proposed procedure, and develop an iterative computational algorithm for its practical implementation, and a bootstrap resampling procedure for estimating the standard errors of the estimator. A simulation study shows that the proposed method performs well in finite samples, and the proposed estimator is applied to analyse the Oscar data.

Bias Reduction for Nonparametric and Semiparametric Regression Models

Nonparametric and semiparametric regression models are useful statistical regression models to discover nonlinear relationships between the response variable and predictor variables. However, optimal efficient estimators for the nonparametric components in the models are biased which hinders the development of methods for further statistical inference. In this paper, based on the local linear fitting, we propose a simple bias reduction approach for the estimation of the nonparametric regression model. Our approach does not need to use higher-order local polynomial regression to estimate the bias, and hence avoids the double bandwidth selection and design sparsity problems suffered by higher-order local polynomial fitting. It also does not inflate the variance. Hence it can be easily applied to complex statistical inference problems. We extend our approach to varying coefficient models, to estimate the variance function, and to construct simultaneous confidence band for the nonparametric regression function. Simulations are carried out for comparisons with existing methods, and a data example is used to investigate the performance of the proposed method.

Measuring the transient airflow rates of the infiltration through the doorway of the cold store by using a local air velocity linear fitting method

The measurement of the infiltration airflow rates can support the calculation of the infiltration cooling load for the better understanding and optimizing the energy consumption of cold stores. However, the large temperature difference and the intense transient features make it difficult and complex to measure the airflow rates accurately. In this paper, a simple and practical method to measure the transient infiltration airflow rates is developed by using the local air velocity linear fitting. The proposed method is validated by the measurement results of the tracer gas decay method. It is concluded that the proposed method shows a good performance on the transient infiltration airflow rates measurement. The measurement errors are between ±10%. To enhance the application of this method, the layout of the measuring points of the air velocities are analyzed. The results show that, along the vertical layout direction, air velocity measuring points around the neutral level (where the cold and the warm air separate, about the middle height of the door) are not preferred when using this method. What’s more, the calculation of the infiltration cooling load by using this measuring method is also discussed.

Characterizing Speech Intelligibility in Noise After Wide Dynamic Range Compression.

The effects of nonlinear signal processing on speech intelligibility in noise are difficult to evaluate. Often, the effects are examined by comparing speech intelligibility scores with and without processing measured at fixed signal to noise ratios (SNRs) or by comparing the adaptive measured speech reception thresholds corresponding to 50% intelligibility (SRT50) with and without processing. These outcome measures might not be optimal. Measuring at fixed SNRs can be affected by ceiling or floor effects, because the range of relevant SNRs is not know in advance. The SRT50 is less time consuming, has a fixed performance level (i.e., 50% correct), but the SRT50 could give a limited view, because we hypothesize that the effect of most nonlinear signal processing algorithms at the SRT50 cannot be generalized to other points of the psychometric function. In this article, we tested the value of estimating the entire psychometric function. We studied the effect of wide dynamic range compression (WDRC) on speech intelligibility in stationary, and interrupted speech-shaped noise in normal-hearing subjects, using a fast method-based local linear fitting approach and by two adaptive procedures. The measured performance differences for conditions with and without WDRC for the psychometric functions in stationary noise and interrupted speech-shaped noise show that the effects of WDRC on speech intelligibility are SNR dependent. We conclude that favorable and unfavorable effects of WDRC on speech intelligibility can be missed if the results are presented in terms of SRT50 values only.

Local linear smoothers using inverse Gaussian regression

Local linear fitting has been widely used for estimating the univariate regression function, it has numerous fantastic properties like minimax efficiency and boundary correction. The asymmetric kernel functions match the support of the explanatory variables, and we discover the inverse Gaussian (IG) kernel function is identical to the normal kernel with variable bandwidth. Based on these, this paper proposes a new local linear estimation procedure with the IG kernel when the covariates are supported on \((0,\infty )\). Asymptotic theories of the proposed estimator are systematically studied, including the conditional mean squared error, the asymptotic normality and the uniform almost sure convergence. A simulation study and a data example indicate that the proposed estimator works efficiently.

Parametrically guided local quasi-likelihood with censored data

It is widely pointed out in the literature that misspecification of a parametric model can lead to inconsistent estimators and wrong inference. However, even a misspecified model can provide some valuable information about the phenomena under study. This is the main idea behind the development of an approach known, in the literature, as para- metrically guided nonparametric estimation. Due to its promising bias reduction property, this approach has been investigated in different frameworks such as density estimation, least squares regression and local quasi-likelihood. Our contribution is concerned with parametrically guided local quasi-likelihood estimation adapted to randomly right cen- sored data. The generalization to censored data involves synthetic data and local linear fitting. The asymptotic properties of the guided estimator as well as its finite sample performance are studied and compared with the unguided local quasi-likelihood estima- tor. The results confirm the bias reduction property and show that, using an appropriate guide and an appropriate bandwidth, the proposed estimator outperforms the classical local quasi-likelihood estimator.

Semi-parametric inference for semi-varying coefficient panel data model with individual effects

We study a semi-varying coefficient panel data model with unobserved individual effects, where all the covariates are high-dimensional variables. Based on multivariate local linear fitting, the transformation technique and the profile likelihood method, we establish semi-parametric fixed effects estimators, semi-parametric random effects estimators, and their asymptotic properties. We also introduce a test for discriminating between a semi-varying coefficient random effects panel data model and a semi-varying coefficient fixed effects panel data model. The critical values are estimated by a bootstrap procedure. Monte Carlo studies exhibit the finite-sample performance of the proposed estimators and test statistics. Simulation results show that the methods perform well for moderate sample sizes. Finally, we analyze the cigarette consumption panel data from 46 American states covering the period 1963–1992.

Detecting Terrain Stoniness From Airborne Laser Scanning Data †

Three methods to estimate the presence of ground surface stones from publicly available Airborne Laser Scanning (ALS) point clouds are presented. The first method approximates the local curvature by local linear multi-scale fitting, and the second method uses Discrete-Differential Gaussian curvature based on the ground surface triangulation. The third baseline method applies Laplace filtering to Digital Elevation Model (DEM) in a 2 m regular grid data. All methods produce an approximate Gaussian curvature distribution which is then vectorized and classified by logistic regression. Two training data sets consisted of 88 and 674 polygons of mass-flow deposits, respectively. The locality of the polygon samples is a sparse canopy boreal forest, where the density of ALS ground returns is sufficiently high to reveal information about terrain micro-topography. The surface stoniness of each polygon sample was categorized for supervised learning by expert observation on the site. The leave-pair-out (L2O) cross-validation of the local linear fit method results in the area under curve A U C = 0 . 74 and A U C = 0 . 85 on two data sets, respectively. This performance can be expected to suit real world applications such as detecting coarse-grained sediments for infrastructure construction. A wall-to-wall predictor based on the study was demonstrated.

Local linear double and asymmetric kernel estimation of conditional quantiles

In this work, we propose and investigate a family of non parametric quantile regression estimates. The proposed estimates combine local linear fitting and double kernel approaches. More precisely, we use a Beta kernel when covariate’s support is compact and Gamma kernel for left-bounded supports. Finite sample properties together with asymptotic behavior of the proposed estimators are presented. It is also shown that these estimates enjoy the property of having finite variance and resistance to sparse design.

Semiparametric smooth coefficient quantile estimation of the production profile

In this paper, quantile regression models are suggested as an alternative description of a production technology. The quantile of continuous order defines the production profile and the quantile-based individual technical efficiency relative to the quantile order. Quantile-based production frontier and efficiency are easy to derive and estimate and do not envelop all sample observation points. A quantile-based production frontier is more robust to extreme observations than DEA or FDH. Furthermore, quantile regression does not make a distribution assumption. It is more robust to the misspecification of error structure than DFA or SFA. In this paper, the quantile regression methods are extended to semiparametric smooth coefficient models. A local linear fitting scheme to estimate the smooth coefficients is proposed in the quantile framework. An empirical application of the model to the Taiwan manufacturing industry demonstrates the potential for the estimation of production technology and efficiency measures.

Robust estimation for varying index coefficient models

Varying index coefficient models (VICMs) proposed by Ma and Song (J Am Stat Assoc, 2014. doi:10.1080/01621459.2014.903185) are a new class of semiparametric models, which encompass most of the existing semiparametric models. So far, only the profile least squares method and local linear fitting were developed for the VICM, which are very sensitive to the outliers and will lose efficiency for the heavy tailed error distributions. In this paper, we propose an efficient and robust estimation procedure for the VICM based on modal regression which depends on a bandwidth. We establish the consistency and asymptotic normality of proposed estimators for index coefficients by utilizing profile spline modal regression method. The oracle property of estimators for the nonparametric functions is also established by utilizing a two-step spline backfitted local linear modal regression approach. In addition, we discuss the bandwidth selection for achieving better robustness and efficiency and propose a modified expectation---maximization-type algorithm for the proposed estimation procedure. Finally, simulation studies and a real data analysis are carried out to assess the finite sample performance of the proposed method.

Goodness-of-fit testing of error distribution in nonparametric ARCH(1) models

This paper discusses the goodness-of-fit testing of an error distribution in a nonparametric autoregressive conditionally heteroscedastic model of order one. The test is based on a weighted empirical distribution function of the residuals, where the residuals are obtained from a local linear fit for the autoregressive and heteroscedasticity functions, and the weights are chosen to adjust for the undesirable behavior of these nonparametric estimators in the tails of their domains. An asymptotically distribution free test is obtained via the Khmaladze martingale transformation. A simulation study is included to assess the finite sample level and power behavior of this test. It exhibits some superiority of this test compared to the classical Kolmogorov–Smirnov and Cramér–von Mises tests in terms of the finite sample level and power.