Nonparametric Component Research Articles

Distributed Least Product Relative Error estimation for semi-parametric multiplicative regression with massive data

Distributed systems has been widely used for massive data analysis, but few studies focus on multiplicative regression models. We consider a communication-efficient surrogate likelihood method using the Least Product Relative Error criterion for semi-parametric multiplicative models on massive datasets. The non-parametric component is efficiently handled via B-spline approximation. We derive the asymptotic properties for both parametric and non-parametric components, while the SCAD and adaptive Lasso penalty functions are developed and their oracle properties for variable selection are validated. Simulation studies and an application to an energy prediction dataset are used to demonstrate the effectiveness and practical utility of the proposed method.

Double robust semiparametric weighted M-estimators of a zero-inflated Poisson regression with missing data in covariates

Frequently, the covariates in the linear predictors of a zero-inflated Poisson regression model are prone to missingness. When the missing data process is at random, the naive estimator and the inverse probability weighted estimator of the model parameter are known to be biased or less efficient. Hence, we propose four different semiparametric double robust weighting M-estimators of a zero-inflated Poisson model. In particular, these estimators differ in term of the nature and the combination of the nuisance components in the estimating equation. The Nadaraya kernel and the generalized additive models are the two smoothing approaches used to estimate the nuisance parameters in step 1. Each estimator in step 2 is a solution to a specific M-estimating equation which requires two distinct nonparametric nuisance components including the selection probability and the augmentation term. The resulting semiparametric weighted M-estimators are double robust and relatively more efficient than their parametric counterpart and related inverse probability weighted estimators. We examine the performance of the proposed estimators by conducting a simulation study and exploring a road traffic dataset. Overall, the performance of the proposed estimators is satisfactory and potential for various extensions.

Unified specification tests in partially linear time series models

Based on a residual marked empirical process, Cramér–von Mises and Kolmogorov–Smirnov tests are proposed for the correct specification of the nonparametric components in partially linear time series models. The tests are unified in the sense that the asymptotic distribution of residual marked empirical process is invariant across different nν-consistent estimators in calculating residuals (where ν>1/4) under the null. In addition, the residual marked empirical process has the same power property under the sequence of local alternatives regardless of the estimators used. Achieved through a projection method, these features also enable using a computationally convenient multiplier bootstrap to approximate the unified null distributions of the test statistics. Simulations show satisfactory finite-sample performance of the proposed method. The application to validate the parametric form of conditional variance in the ARCH-X model is also highlighted, along with an empirical analysis of the conditional variance of the FTSE 100 index return series.

MODELING STUNTING PREVALENCE IN INDONESIA USING SPLINE TRUNCATED SEMIPARAMETRIC REGRESSION

Semiparametric regression combines parametric and nonparametric regression approaches. It is employed when the relationship pattern of the response variable is known with some predictors, while for other predictors, the relationship pattern is uncertain. The parametric regression component in this study is linear regression, while the nonparametric component utilizes a spline truncated estimator, resulting in a semiparametric spline truncated regression model. The case study focuses on the prevalence of stunting across 34 provinces in Indonesia in 2022, revealing a relatively high prevalence of 21.60%. The research aims to determine the optimal number of knots, the best model, and factors influencing stunting prevalence in Indonesia. The findings indicate that the optimal three-knot model with a GCV of 9.30 yields an RMSE of 1.70 and R2 of 92.71%. Significance tests for simultaneous and partial parameters reveal that all predictor variables significantly influence stunting prevalence.

Double penalized variable selection for high-dimensional partial linear mixed effects models

In this study, we address the selection of both fixed and random effects in partial linear mixed effects models. By combining B-spline and QR decomposition techniques, we propose a double-penalized likelihood procedure for both estimating and selecting these effects. Furthermore, we introduce an orthogonality-based method to estimate the non-parametric component, ensuring that the fixed and random effects are separated without any mutual interference. The asymptotic properties of the resulting estimators are investigated under mild conditions. Simulation studies are conducted to evaluate the finite sample performance of the proposed method. Finally, we demonstrate the practical applicability of our methodology by analyzing a real data.

Comparison of Some Robust Methods of Difference Based Ridge Estimator in Semiparametric Regression Model

The semiparametric regression models have received a lot of attention from researchers recently because it combines parametric and nonparametric methods, it is one of the advanced topics in data analysis for various studies, which aims to find the best capabilities and a high level of efficiency. One of the most important semiparametric regression models is the partial linear regression model (PLM), which consists of a parametric component and a nonparametric component, for the purpose of estimating the parametric component, the difference method will be used to remove the nonparametric component. When the analysis hypotheses of the parametric component are not fulfilled, it will suffer from several problems, the most important of which is the problem of complete multicollinearity, besides the multicollinearity, there are also outliers in the data. In this research, the problems of multicollinearity and outliers of the semiparametric regression model were addressed, where simulation was used to generate data with different sample sizes and for different correlations and outlier ratios and for different methods such as [Difference Ridge based M robust with Nadaraya – Watson (DRMNW), Difference Ridge based S robust with Nadaraya – Watson (DRSNW), Difference Ridge based M robust with Smoothing spline (DRMSP), Difference Ridge based S robust with Smoothing spline (DRSSP)], the results showed that method Difference Ridge based M robust with Smoothing spline (DRMSP) is the best estimator.

Locally linear method for fixed effects panel interval-valued data model

The literature on fixed effects panel interval-valued data models has been established. However, less attention has been given to models that simultaneously, consider the interval information of panel data and explore the nonlinear relationship between interval variables. To deal with this issue, this paper formulates a nonparametric fixed effects panel interval-valued data model. To estimate the fixed effects and nonparametric component, we propose a locally linear method based on the profile least squares framework. Later, experiment results on synthetic and real data sets illustrate the advantages of our proposed model.

A one-covariate-at-a-time multiple testing approach to variable selection in additive models

. This article proposes a One-Covariate-at-a-time Multiple Testing (OCMT) approach to choose significant variables in high-dimensional nonparametric additive regression models. Similarly to Chudik, Kapetanios, and Pesaran, we consider the statistical significance of individual nonparametric additive components one at a time and take into account the multiple testing nature of the problem. Both one-stage and multiple-stage procedures are considered. The former works well in terms of the true positive rate only if the net effects of all signals are strong enough; the latter helps to pick up hidden signals that have weak net effects. Simulations demonstrate the good finite-sample performance of the proposed procedures. As an empirical illustration, we apply the OCMT procedure to a dataset extracted from the Longitudinal Survey on Rural Urban Migration in China. We find that our procedure works well in terms of out-of-sample root mean square forecast errors, compared with competing methods such as adaptive group Lasso (AGLASSO).

The Simons Observatory: Pipeline comparison and validation for large-scale B-modes

Context. The upcoming Simons Observatory Small Aperture Telescopes aim at achieving a constraint on the primordial tensor-to-scalar ratio r at the level of σ(r = 0)≲0.003, observing the polarized CMB in the presence of partial sky coverage, cosmic variance, inhomogeneous non-white noise, and Galactic foregrounds. Aims. We present three different analysis pipelines able to constrain r given the latest available instrument performance, and compare their predictions on a set of sky simulations that allow us to explore a number of Galactic foreground models and elements of instrumental noise, relevant for the Simons Observatory. Methods. The three pipelines employ different combinations of parametric and non-parametric component separation at the map and power spectrum levels, and use B-mode purification to estimate the CMB B-mode power spectrum. We applied them to a common set of simulated realistic frequency maps, and compared and validated them with focus on their ability to extract robust constraints on the tensor-to-scalar ratio r. We evaluated their performance in terms of bias and statistical uncertainty on this parameter. Results. In most of the scenarios the three methodologies achieve similar performance. Nevertheless, several simulations with complex foreground signals lead to a > 2σ bias on r if analyzed with the default versions of these pipelines, highlighting the need for more sophisticated pipeline components that marginalize over foreground residuals. We show two such extensions, using power-spectrum-based and map-based methods, that are able to fully reduce the bias on r below the statistical uncertainties in all foreground models explored, at a moderate cost in terms of σ(r).

Local linear-$k$NN smoothing for semi-functional partial linear regression

The aim of this paper is to study a semi-functional partial linear regression model. The estimators are constructed by $k$-nearest neighbors local linear method. Some asymptotic results are established for an i.i.d sample under certain conditions, including asymptotic normality of the parametric component and the almost certain convergence (with rate) of the non-parametric component. Lastly, using cross-validation, the performances of our estimation method are presented on simulated data and on real data by comparing them with other known approaches for semi-functional partial linear regression models.

Non-parametric quantile regression-based modelling of additive effects to solar irradiation in Southern Africa

Modelling of solar irradiation is paramount to renewable energy management. This warrants the inclusion of additive effects to predict solar irradiation. Modelling of additive effects to solar irradiation can improve the forecasting accuracy of prediction frameworks. To help develop the frameworks, this current study modelled the additive effects using non-parametric quantile regression (QR). The approach applies quantile splines to approximate non-parametric components when finding the best relationships between covariates and the response variable. However, some additive effects are perceived as linear. Thus, the study included the partial linearly additive quantile regression model (PLAQR) in the quest to find how best the additive effects can be modelled. As a result, a comparative investigation on the forecasting performances of the PLAQR, an additive quantile regression (AQR) model and the new quantile generalised additive model (QGAM) using out-of-sample and probabilistic forecasting metric evaluations was done. Forecasted density plots, Murphy diagrams and results from the Diebold–Mariano (DM) hypothesis test were also analysed. The density plot, the curves on the Murphy diagram and most metric scores computed for the QGAM were slightly better than for the PLAQR and AQR models. That is, even though the DM test indicates that the PLAQR and AQR models are less accurate than the QGAM, we could not conclude an outright greater forecasting performance of the QGAM than the PLAQR or AQR models. However, in situations of probabilistic forecasting metric preferences, each model can be prioritised to be applied to the metric where it performed slightly the best. The three models performed differently in different locations, but the location was not a significant factor in their performances. In contrast, forecasting horizon and sample size influenced model performance differently in the three additive models. The performance variations also depended on the metric being evaluated. Therefore, the study has established the best forecasting horizons and sample sizes for the different metrics. It was finally concluded that a 20% forecasting horizon and a minimum sample size of 10000 data points are ideal when modelling additive effects of solar irradiation using non-parametric QR.

Pemodelan Regresi Semiparametrik B Spline (Studi Kasus: Pengaruh Harga Emas dan Minyak Mentah Dunia Terhadap Indeks Harga Saham Gabungan)

<p dir="ltr"><span>The increases of the world gold and crude oil prices have a big role as a main factor that effect composite stock price index, the effect can make investors to buy stock from Bursa Efek Indonesia. Regression semiparametric used in this research for a purpose to get combined parametric and nonparametric with B Spline approach. B Spline is a development of spline to overcome weaknesses in making singular matrix at a high order spline with many knot points and close together. Variable parametric component is composite stock price index with crude oil price, and variable nonparametric component is composite stock price index with gold price that got obtained from January 2015 until December 2022. The result from this research is best regression semiparametric B-Spline modelling can be obtained using some combination of order and knot points. The optimal point is obtained on 2nd order using 4 knot point (1.135;1.319,15;1.320,75;1.323,25) with a minimum GCV value is 100.227,8. The best measure of goodness with a coefficient of determination value (R-Square) obtained a value 78,8%, because the value is more than 67% make it as a strong model. MAPE value is 3,37% that has a value less than 10 %, make this model have a perfect forecasting ability.</span></p><p><span id="docs-internal-guid-09fba3ae-7fff-a25a-8197-7dd90ea8b1e1"><span>Keywords: </span><span>Gold; Crude Oil; Composite Stock Price Index; Semiparametric B Spline; GCV</span></span></p>

Point-Sim: A Lightweight Network for 3D Point Cloud Classification

Analyzing point clouds with neural networks is a current research hotspot. In order to analyze the 3D geometric features of point clouds, most neural networks improve the network performance by adding local geometric operators and trainable parameters. However, deep learning usually requires a large amount of computational resources for training and inference, which poses challenges to hardware devices and energy consumption. Therefore, some researches have started to try to use a nonparametric approach to extract features. Point-NN combines nonparametric modules to build a nonparametric network for 3D point cloud analysis, and the nonparametric components include operations such as trigonometric embedding, farthest point sampling (FPS), k-nearest neighbor (k-NN), and pooling. However, Point-NN has some blindness in feature embedding using the trigonometric function during feature extraction. To eliminate this blindness as much as possible, we utilize a nonparametric energy function-based attention mechanism (ResSimAM). The embedded features are enhanced by calculating the energy of the features by the energy function, and then the ResSimAM is used to enhance the weights of the embedded features by the energy to enhance the features without adding any parameters to the original network; Point-NN needs to compute the similarity between each feature at the naive feature similarity matching stage; however, the magnitude difference of the features in vector space during the feature extraction stage may affect the final matching result. We use the Squash operation to squeeze the features. This nonlinear operation can make the features squeeze to a certain range without changing the original direction in the vector space, thus eliminating the effect of feature magnitude, and we can ultimately better complete the naive feature matching in the vector space. We inserted these modules into the network and build a nonparametric network, Point-Sim, which performs well in 3D classification tasks. Based on this, we extend the lightweight neural network Point-SimP by adding some trainable parameters for the point cloud classification task, which requires only 0.8 M parameters for high performance analysis. Experimental results demonstrate the effectiveness of our proposed algorithm in the point cloud shape classification task. The corresponding results on ModelNet40 and ScanObjectNN are 83.9% and 66.3% for 0 M parameters—without any training—and 93.3% and 86.6% for 0.8 M parameters. The Point-SimP reaches a test speed of 962 samples per second on the ModelNet40 dataset. The experimental results show that our proposed method effectively improves the performance on point cloud classification networks.

Estimating the size of a closed population by modeling latent and observed heterogeneity.

The paper extends the empirical likelihood (EL) approach of Liu etal. to a new and very flexible family of latent class models for capture-recapture data also allowing for serial dependence on previous capture history, conditionally on latent type and covariates. The EL approach allows to estimate the overall population size directly rather than by adding estimates conditional to covariate configurations. A Fisher-scoring algorithm for maximum likelihood estimation is proposed and a more efficient alternative to the traditional EL approach for estimating the non-parametric component is introduced; this allows us to show that the mapping between the non-parametric distribution of the covariates and the probabilities of being never captured is one-to-one and strictly increasing. Asymptotic results are outlined, and a procedure for constructing profile likelihood confidence intervals for the population size is presented. Two examples based on real data are used to illustrate the proposed approach and a simulation study indicates that, when estimating the overall undercount, the method proposed here is substantially more efficient than the one based on conditional maximum likelihood estimation, especially when the sample size is not sufficiently large.

Uncertainty Quantification in Heterogeneous Treatment Effect Estimation with Gaussian-Process-Based Partially Linear Model

Estimating heterogeneous treatment effects across individuals has attracted growing attention as a statistical tool for performing critical decision-making. We propose a Bayesian inference framework that quantifies the uncertainty in treatment effect estimation to support decision-making in a relatively small sample size setting. Our proposed model places Gaussian process priors on the nonparametric components of a semiparametric model called a partially linear model. This model formulation has three advantages. First, we can analytically compute the posterior distribution of a treatment effect without relying on the computationally demanding posterior approximation. Second, we can guarantee that the posterior distribution concentrates around the true one as the sample size goes to infinity. Third, we can incorporate prior knowledge about a treatment effect into the prior distribution, improving the estimation efficiency. Our experimental results show that even in the small sample size setting, our method can accurately estimate the heterogeneous treatment effects and effectively quantify its estimation uncertainty.

On an asymmetric functional-coefficient ARCH-M model

This paper proposes an asymmetric functional-coefficient autoregressive conditional heteroscedasticity in mean (ARCH-M) model, which allows for asymmetry in the volatility. The profile likelihood approach is applied to estimate the parametric and nonparametric components. Under some regularity assumptions, we derive asymptotic behavior of the proposed estimator. To avoid model misspecification, the Wald, quasi-likelihood ratio test statistic and generalized likelihood ratio test statistic are put forward to detect ARCH effect, asymmetric effect and goodness-of-fit, respectively. Moreover, their asymptotic distributions are established under both null and alternative hypotheses. Some Monte Carlo simulations are conducted to evaluate the finite sample performance of the proposed estimation methodology and testing procedure. Also, real data sets are analyzed to demonstrate the applications of the proposed model.

Inference on Conditional Quantile Processes in Partially Linear Models with Applications to the Impact of Unemployment Benefits

Abstract We propose methods to estimate and make inferences on conditional quantile processes for models with both nonparametric and (locally or globally) linear components. We derive their asymptotic properties, optimal bandwidths, and uniform confidence bands over quantiles allowing for robust bias correction. Our framework covers the sharp regression discontinuity design, which is used to study the effects of unemployment insurance benefits extensions, focusing on heterogeneity over quantiles and covariates. We show economically strong effects in the tails of the outcome distribution. They reduce the within-group inequality, but can be viewed as enhancing between-group inequality, although they help to bridge the gender gap.

Double sparsity garrotized kernel machine in high-dimensional partially linear model

Obtaining excellent prediction accuracy in the high-dimensional partially linear model is particularly important. However, it is difficult to achieve due to the complex relationship between nonparametric covariates and the response. Irrelevant covariates and unimportant data also commonly attenuate the prediction performance of the model. Further, high-dimensional data analysis is challenging for modern statistical studies. To overcome these difficulties, we propose the Double Sparsity Garrotized Kernel Machine (DSGKM) method with an efficient algorithm and its adjusted version for prediction. Specifically, we estimate the nonparametric components using the kernel machine technique, and impose L 1 -norm penalties simultaneously to select relevant covariates and retain the representative data in the final model. Besides, the convergence analysis of the adjusted algorithm is conducted. The advantages of our method are: (i) to sufficiently capture the complex relationship between nonparametric covariates and the response; (ii) to identify relevant covariates and select representative data; and (iii) to achieve higher computational efficiency, especially the situations when both parametric and nonparametric components are high-dimensional. Results on both simulated and real data show that the proposed method outperforms existing methods, even when outliers exist.

Impaired 24-h activity patterns are associated with an increased risk of Alzheimer’s disease, Parkinson’s disease, and cognitive decline

BackgroundSleep-wake regulating circuits are affected during prodromal stages in the pathological progression of both Alzheimer’s disease (AD) and Parkinson’s disease (PD), and this disturbance can be measured passively using wearable devices. Our objective was to determine whether accelerometer-based measures of 24-h activity are associated with subsequent development of AD, PD, and cognitive decline.MethodsThis study obtained UK Biobank data from 82,829 individuals with wrist-worn accelerometer data aged 40 to 79 years with a mean (± SD) follow-up of 6.8 (± 0.9) years. Outcomes were accelerometer-derived measures of 24-h activity (derived by cosinor, nonparametric, and functional principal component methods), incident AD and PD diagnosis (obtained through hospitalization or primary care records), and prospective longitudinal cognitive testing.ResultsOne hundred eighty-seven individuals progressed to AD and 265 to PD. Interdaily stability (a measure of regularity, hazard ratio [HR] per SD increase 1.25, 95% confidence interval [CI] 1.05–1.48), diurnal amplitude (HR 0.79, CI 0.65–0.96), mesor (mean activity; HR 0.77, CI 0.59–0.998), and activity during most active 10 h (HR 0.75, CI 0.61–0.94), were associated with risk of AD. Diurnal amplitude (HR 0.28, CI 0.23–0.34), mesor (HR 0.13, CI 0.10–0.16), activity during least active 5 h (HR 0.24, CI 0.08–0.69), and activity during most active 10 h (HR 0.20, CI 0.16–0.25) were associated with risk of PD. Several measures were additionally predictive of longitudinal cognitive test performance.ConclusionsIn this community-based longitudinal study, accelerometer-derived metrics were associated with elevated risk of AD, PD, and accelerated cognitive decline. These findings suggest 24-h rhythm integrity, as measured by affordable, non-invasive wearable devices, may serve as a scalable early marker of neurodegenerative disease.

Regression analysis of group-tested current status data

Summary Group testing is an effective way to reduce the time and cost associated with conducting large-scale screening for infectious diseases. Benefits are realized through testing pools formed by combining specimens, such as blood or urine, from different individuals. In some studies, individuals are assessed only once and a time-to-event endpoint is recorded, for example, the time until infection. Combining group testing with this type of endpoint results in group-tested current status data (Petito & Jewell, 2016). To analyse these complex data, we propose methods that estimate a proportional hazard regression model based on test outcomes from measuring the pools. A sieve maximum likelihood estimation approach is developed that approximates the cumulative baseline hazard function with a piecewise constant function. To identify the sieve estimator, a computationally efficient expectation-maximization algorithm is derived by using data augmentation. Asymptotic properties of both the parametric and nonparametric components of the sieve estimator are then established by applying modern empirical process theory. Numerical results from simulation studies show that our proposed method performs nominally and has advantages over the corresponding estimation method based on individual testing results. We illustrate our work by analysing a chlamydia dataset collected by the State Hygienic Laboratory at the University of Iowa.