Nonparametric Estimation Research Articles

Core Concepts in Pharmacoepidemiology: Time-To-Event Analysis Approaches in Pharmacoepidemiology.

This article provides an overview of time-to-event (TTE) analysis in pharmacoepidemiology. The key concept of censoring is reviewed, including right-, left-, interval- and informative censoring. Simple descriptive statistics are explained, including the nonparametric estimation of the TTE distribution as per Kaplan-Meier method, as well as more complex TTE regression approaches, including the parametric Accelerated Failure Time (AFT) model and the semi-parametric Cox Proportional Hazards and Restricted Mean Survival Time (RMST) models. Additional approaches and various TTE model extensions are presented as well. Finally, causal inference for TTE outcomes is addressed. A thorough review of the available concepts and methods outlines the immense variety of available and useful TTE models. There may be underused TTE concepts and methods, which are highlighted to raise awareness for researchers who aim to apply the most appropriate TTE approach for their study. This paper constitutes a modern summary of TTE analysis concepts and methods. A curated list of references is provided.

A Short-term PV Power Prediction and Uncertainty Analysis Model Based on CEEMDAN and AHA-BP

The stochastic and intermittent nature of photovoltaic (PV) generation brings a series of scheduling problems to the power system. An effective prediction of PV power is essential to minimize the impact of uncertainty. Therefore, this paper presents an integrated prediction model with complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), the artificial hummingbird algorithm (AHA), and the BP neural network (BPNN) for predicting power generation from PV power plants, and a methodology for uncertainty analysis by using the nonparametric kernel density estimation (NPKDE). First, one month of PV power is decomposed into an array of components using CEEMDAN. Then, the weights and thresholds of the BPNN are optimized by using AHA. These components are trained using the BPNN. Finally, the final prediction results are obtained by superimposing the components, and NPKDE is employed to compute the probability density and confidence interval of the prediction error. The proposed prediction method demonstrates superior predictive performance in comparison with other models. Also, the NPKDE approach better describes the accuracy of the probability density distribution.

Long-term outcome of diabetic patients after unprotected left main percutaneous coronary interventions

Abstract Background Diabetes mellitus (DM) represents an elevated risk in terms of percutaneous coronary intervention (PCI), especially in patients with significant left main (LM) disease. Purpose Our aims were to investigate the 60-month mortality and event-free survival of consecutive patients with DM undergoing unprotected LM PCI at our centre and sought to determine the independent predictors of event-free survival. Methods We included all patients undergoing unprotected LM PCI at our tertiary care centre between 1 January 2007 and 31 December 2014. The primary endpoint was the composite of all-cause mortality, myocardial infarction, and target lesion revascularization at 60 months. Survival curves were constructed using the Kaplan-Meier non-parametric estimator. ROC analysis was used to investigate the predictive power of conventional risk scores (SYNTAX, SYNTAX II, EuroSCORE II, additive and logistic EuroSCORE, ACEF, GRACE 2). Independent predictors were determined by univariate and multivariate analysis. Results A total of 513 patients (mean age 68 ± 12 years, 64% male) underwent unprotected LM PCI during this period, among these 310 (60%) were non-diabetic (non-DM) and 203 (40%) were diabetic (DM). In terms of indication, 157 (31%) elective and 356 (69%) acute LM PCI were performed. There was no significant difference between the non-DM and DM groups in terms of acute indication (218 (70%) vs. 138 (68%), p=0.574). Within the DM group, 135 (67%) were treated with oral antidiabetics (OAD) and 68 (33%) were treated with insulin (IDM). The mean survival (34.6 vs. 39.7 vs. 43.1 months, p=0.003) and event-free survival (29.3 vs. 34.7 vs. 39.3 months, p=0.001) were significantly lower in the IDM and OAD groups compared to non-DM, respectively. Of the risk scores, the SYNTAX score was the most predictive in diabetic patients (AUC=0.767). Based on the SYNTAX score, diabetic patients with a low SYNTAX score (<23) had less events (59% vs. 66%, p=0.043) than those having a moderate/high SYNTAX score (≥23). LVEF (HR 0.976; 95% CI, 0.965-0.987, p<0.001), right coronary artery occlusion (HR 2.031; 95% CI, 1.346-3.064, p=0.001), acute coronary syndrome (HR 1.861; 95% CI, 1.252-2.767, p=0.002), use of FFR (HR 0.481; 95% CI, 0.265-0.871, p=0.016), true bifurcation lesion (HR 1.559; 95% CI, 1.068-2.277, p=0.021) and newer DES generation (HR 0.706; 95% CI, 0.568-0.877, p=0.002) were predictors of event-free survival in diabetics by univariate analysis. Glomerular filtration rate (HR 0.982; 95% CI, 0.973-0.991, p<0.001) emerged as an independent predictor according to multivariate analysis. Conclusion Consecutive diabetic patients with significant unprotected LM stenosis have poor long-term outcome after LM PCI. Anatomical complexity of the lesions is a significant predictor of event-free survival. Careful intervention planning and the use of appropriate tools can improve the outcome in this high-risk population.

Quantitative Assessment of Ecological Flow in the Yellow River Under Changing Environments

ABSTRACTStudying the streamflow characteristics of the Yellow River mainstem under changing environmental conditions is crucial for the management and sustainable development of water resources within its basin. This research employs a long short‐term memory (LSTM) model to restore the flow characteristics of the Yellow River's mainstream under natural conditions. Additionally, the range of variation approach (RVA) and nonparametric kernel density estimation (KDE) method are integrated to quantitatively assess the impact of environmental changes on streamflow. The findings indicate that: (1) Hydrological variability in the Yellow River was observed in 1985, with a degree of variability ranging from 26% to 58%, classified as moderate. (2) The annual ecological flow value of the Yellow River is 560–1001 m3/s, and the average annual ecological flow assurance is 43%. (3) Based on LSTM simulation results (NSE > 0.7, R2 > 0.8), it is concluded that the ecological flow assurance under natural conditions in the Yellow River exceeds the measured values, primarily due to human activities, which contribute over 52% to this discrepancy. These results suggest that the river ecosystem of the Yellow River's mainstem is relatively unstable and requires further management.

An efficient surrogate model for system reliability with multiple failure modes

AbstractThe failure modes of complex systems are often highly dependent. Aiming at the reliability analysis of engineering systems with multiple failure modes, an efficient surrogate model for system reliability with multiple failure modes is proposed, namely, the Copula Adaptive Kriging surrogate model (CAKSM). First, the initial Kriging model is established based on the initial samples. In order to select more effective added samples to update the Kriging model, a new learning function, namely, Copula Unites with Expected Improvement Function (CUEIF), is established. The function can make a reasonable sample selection by considering the failure correlation. Then, based on the optimal Copula function, the reliability data of each failure mode are coupled and analyzed. In order to adapt to various computing scales, regularization is introduced to improve the prediction speed of the surrogate model, and the probability density function of each performance function is obtained by introducing nonparametric kernel density estimation. Finally, the effectiveness of the CAKSM method and the learning function CUEIF is verified through four examples.

Unified rules of renewable weighted sums for various online updating estimations

This paper establishes unified frameworks of renewable weighted sums (RWS) for various online updating estimations in the models with streaming data sets. The newly defined RWS lays the foundation of online updating likelihood, online updating loss function, online updating estimating equation and so on. The idea of RWS is intuitive and heuristic, and the algorithm is computationally simple. The RWS applies to various types of parametric, nonparametric and semiparametric estimators from likelihood, quasi-likelihood and least squares. The consistency and asymptotic normality of the proposed renewable estimator are established, and the oracle property is obtained. Moreover, these properties are always satisfied, without the familiar constraints on the number of data batches, which means that the new method is adaptive to the situation where streaming data sets arrive perpetually. The performance of the method is further illustrated by various numerical examples from simulation experiments and real data analysis.

Optimal configuration of dynamic VAR compensators considering uncertainty and correlation

AbstractThe transient voltage stability of modern power systems is challenged by the increasing uncertainty on source‐load dual sides. To cope with it, a robust optimal configuration method for dynamic VAR compensators (DVCs) is proposed. First, a series of power‐flow scenarios are generated with uncertainty and correlation considered, where nonparametric kernel density estimation is used to predict the marginal distribution of wind speeds and combined Copula function is employed to characterize correlations between nearby wind farms. Then, the variation‐of‐information indicator is introduced to assess the similarity among power‐flow (PF) scenarios, and representative PF (RPF) scenarios are screened with the help of Spectral clustering algorithm. Finally, locating and sizing of DVCs for RPF scenarios are achieved. By synthesizing the compensation schemes for RPF scenarios, the robust configuration scheme is suggested. Simulation studies in the modified New England 10‐machine 39‐bus system show the proposed method can ensure transient voltage security of the studied power system under source‐load uncertainty.

Deep regression learning with optimal loss function

In this paper, we develop a novel efficient and robust nonparametric regression estimator under a framework of a feedforward neural network (FNN). There are several interesting characteristics for the proposed estimator. First, the loss function is built upon an estimated maximum likelihood function, which integrates the information from observed data as well as the information from the data distribution. Consequently, the resulting estimator has desirable optimal properties, such as efficiency. Second, different from the traditional maximum likelihood estimation (MLE), the proposed method avoids the specification of the distribution, making it adaptable to various distributions such as heavy tails and multimodal or heterogeneous distributions. Third, the proposed loss function relies on probabilities rather than direct observations as in least square loss, contributing to the robustness of the proposed estimator. Finally, the proposed loss function involves a nonparametric regression function only. This enables the direct application of the existing packages, simplifying the computational and programming requirements. We establish the large sample property of the proposed estimator in terms of its excess risk and minimax near-optimal rate. The theoretical results demonstrate that the proposed estimator is equivalent to the true MLE where the density function is known in terms of excess risk. Our simulation studies show that the proposed estimator outperforms the existing methods based on prediction accuracy, efficiency and robustness. Particularly, it is comparable to the MLE with the known density and even gets slightly better as the sample size increases. This implies that the adaptive and data-driven loss function from the estimated density may offer an additional avenue for capturing valuable information. We further apply the proposed method to four real data examples, resulting in significantly reduced out-of-sample prediction errors compared to existing methods.

Residual Inaccuracy Extropy and its properties

Abstract In this paper, we introduce a novel concept of a dynamic residual inaccuracy measure based on extropy. We extend the traditional residual inaccuracy measure to its dynamic version, which allows us to measure the discrepancy between two residual life distributions. We study the properties of the proposed measure, including its discrimination principle and the proportional hazard rate model. We also investigate a characterization problem related to the extropy inaccuracy measure and propose some alternative expressions of the dynamic residual measure of inaccuracy. Furthermore, we establish upper and lower bounds and some inequalities concerning dynamic residual inaccuracy measures based on extropy. We demonstrate that the defined measure of inaccuracy is invariant under scale but not under location transformation. The given findings have important implications for statistical inference, estimation, and modeling. The proposed extropy-based dynamic residual inaccuracy measure provides a powerful tool for quantifying the discrepancy between two residual life distributions over time. At the end of the paper, we provide two non-parametric estimators for the proposed extropy measure of inaccuracy for both the non-censored (complete sample) and the right-censored scheme. The performances of these estimators are compared numerically based on their bias and MSE.

ANALYSIS OF PATH NONPARAMETRIC TRUNCATED SPLINE MAXIMUM CUBIC ORDER IN BANKING CREDIT OF RISK BEHAVIOR MODEL

Path analysis tests the relationship between variables through cause and effect. The assumption of linearity must be met before conducting further tests on path analysis. If the shape of the relationship is nonlinear and the shape of the curve is unknown, a nonparametric approach is used, one of which is a truncated spline. The purpose of this study is to estimate the function and obtain the best model on the nonparametric truncated spline path of linear, quadratic, and cubic orders with 1 and 2-knot points and determine the significance of the best function estimator in banking credit of risk behavior model through the jackknife resampling method. This study uses secondary data through questionnaires to KPR debtor consumers, as many as 100 respondents. Based on the results of the analysis, it is known that the best-truncated spline nonparametric path model is the quadratic order of 2 knots with a coefficient of determination of 85.50%; the significance of the best-truncated spline nonparametric path estimator shows that all exogenous variables have a significant effect on endogenous variables.

Nonparametric Modeling of Mutually Ambiguous Mappings

This paper considers the problem of approximating a function from observations in the case when the object under study contains mutually ambiguous characteristics in its description. This formulation is essential in identifying and controlling systems of the Wiener and Hammerstein class, in which nonlinear processes can be represented as a sequential connection of linear dynamic and nonlinear inertia-free blocks. Often elements such as hysteresis loop, backlash and others are used as nonlinear blocks. These elements are mutually ambiguous mappings. In connection with the transition to automated digital production, which is controlled in real time by intelligent systems rather than humans, nonlinear dynamic processes are found everywhere. The complexity of solving the problem lies in the lack of sufficient a priori information about the parametric structure of the model of the process under study. The paper proposes some modifications of the nonparametric estimation of the regression function, allowing for the modeling of mutually ambiguous mappings. Some fragments of numerical studies are presented that show acceptable results in terms of reconstruction accuracy.

Medium- and Long-Term Power System Planning Method Based on Source-Load Uncertainty Modeling

In order to consider the impact of source-load uncertainty on traditional power system planning methods, a medium- and long-term optimization planning method based on source-load uncertainty modeling and time-series production simulation is proposed. First, a new energy output probability model is developed using non-parametric kernel density estimation, and the spatial correlation of the new energy output is described using pair-copula theory to model the uncertainty analysis of the new energy output. Secondly, a large number of source-load scenarios are generated using the Markov chain Monte Carlo simulation method, and the optimal selection method for discrete state numbers is provided, and then the scenario reduction is carried out using the fast forward elimination technology. Finally, the typical time-series curves of the source-load uncertainty characteristics obtained are incorporated into the optimization planning method together with various flexible resources, such as the demand-side response and energy storage, and the rationality of the planning scheme is judged and optimized based on key indicators such as the cost, wind–light abandonment rate, and loss-of-load rate. Based on the above methods, this paper offers an example of the power supply planning scheme for a certain region in the next 30 years, providing effective guidance for the development of new energy in the region.

Statistical inference for Hicks–Moorsteen productivity indices

AbstractThe statistical framework for the Malmquist productivity index (MPI) is now well-developed and emphasizes the importance of developing such a framework for its alternatives. In this paper, we try to fill this gap in the literature for another popular measure, known as the Hicks–Moorsteen productivity index (HMPI). Unlike MPI, the HMPI has a total factor productivity interpretation in the sense of measuring productivity as the ratio of aggregated outputs to aggregated inputs and has other useful advantages over MPI. In this work, we develop a novel framework for statistical inference for HMPI in various contexts: when its components are known or when they are replaced with non-parametric envelopment estimators. This will be done for a particular firm’s HMPI as well as for the simple mean (unweighted) HMPI and the aggregate (weighted) HMPI. Our results further enrich the recent theoretical developments of nonparametric envelopment estimators for the various efficiency and productivity measures. We also examine the performance of these theoretical results for both the unweighted and weighted mean of HMPI for a finite sample, using Monte-Carlo simulations and also provide an empirical illustration along with the computation code.

On a nonparametric estimation of ℙ(X

Let θ = P ( X < Y < Z ) , where X ∼ N ( μ X , σ 2 ) , Z ∼ N ( μ Z , σ 2 ) and Y are independent random variables, with known constants μ X , μ Z ∈ R , σ > 0 . Suppose we observe a random sample Y 1 ′ , … , Y n ′ from the distribution of Y ′ = Y + ε . Here ε is a random error and distributed with a known continuous distribution. Our aim is to estimate θ based on the sample as well as on the complete knowledge about the distributions of X, Z and ε . We propose a nonparametric estimator of θ by applying the Fourier deconvolution method. Our estimator is shown to be mean consistent with respect to the mean squared error and strongly consistent. Under some regularity assumptions on the densities of Y and ε , some error estimates of the proposed estimator are derived. A simulation study is also conducted to illustrate the effectiveness of our method.

Score test for marks in Hawkes processes

AbstractA score statistic for detecting the impact of marks in a linear Hawkes self-exciting point process is proposed, with its asymptotic properties, finite sample performance, power properties using simulation and application to real data presented. A major advantage of the proposed inference procedure is that the Hawkes process can be fitted under the null hypothesis that marks do not impact the intensity process. Hence, for a given record of a point process, the intensity process is estimated once only and then assessed against any number of potential marks without refitting the joint likelihood each time. Marks can be multivariate and serially dependent. The score function for any given set of marks is easily constructed as the covariance of functions of future intensities fits the unmarked process with functions of the marks under assessment. The asymptotic distribution of the score statistic is a Chi-squared distribution, with degrees of freedom equal to the number of parameters required to specify the boost function. Model-based or nonparametric estimation of required features of the mark’s marginal moments and serial dependence can be used. Using sample moments of the marks in the test statistic construction does not impact the size and power properties.

Semiparametric estimation of a principal functional coefficient panel data model with cross-sectional dependence and its application to cigarette demand

In this paper, we consider the estimation of functional coefficient panel data models with cross-sectional dependence. Borrowing the principal component structure, the functional coefficient panel data models can be transformed into a semiparametric panel data model. Combining the local linear dummy variable technique and profile least squares method, we develop a semiparametric profile method to estimate the coefficient functions. A gradient-descent iterative algorithm is employed to enhance computation speed and estimation accuracy. The main results show that the resulting parameter estimator enjoys asymptotic normality with a NT convergence rate and the nonparametric estimator is asymptotically normal with a nonparametric convergence rate NTh when both the number of cross-sectional units N and the length of time series T go to infinity, under some regularity conditions. Monte Carlo simulations are carried out to evaluate the proposed methods, and an application to cigarette demand is investigated for illustration.

Nonparametric regression estimator of multivariable Fourier Series for categorical data

In recent years, Fourier Series estimators in nonparametric regression for quantitative data have received significant attention. However, in reality, there is often a relationship between response and predictor, where the response is categorical data. Some methods developed today to address the case of qualitative response data use only certain approaches. No Fourier Series estimator can handle categorical response data. This paper introduces a new method that uses response variable in the form of categorical data. This study aimed to develop a multivariable Fourier Series nonparametric regression estimator for categorical data. The research methods used are literature and theoretical studies. To apply this method, we used two application data. The results obtained indicate that the nonparametric regression of the Fourier Series provides significantly better estimation results and accuracy for both data applications, due to the small deviance value and larger AUC and Press'Q values. The highlights of this research are summarized below.•The Fourier Series method for categorical data assumes a relationship between the logit function and predictor variables that has a repeating pattern.•The estimator was obtained through Maximum Likelihood Estimation and Newton–Raphson method.•The Fourier Series nonparametric regression method provides better estimation than binary logistic regression.

Identifying the number of latent factors of stochastic volatility models

AbstractWe provide a procedure to identify the number of latent factors of stochastic volatility models. The methodology relies on the non-parametric Fourier estimation method introduced by Malliavin and Mancino (Finance Stoch 4:49–61, 2002) and applies to high-frequency data. Based on the Fourier analysis, we first estimate the latent volatility process and then the volatilities and covariances of the processes that are gradually identified, such as volatility of volatility and leverage. The analysis of the eigenvalue spectrum of the Gram matrix can reveal information about the actual number of factors driving the process at hand. We corroborate our analysis by numerical simulations on single and multi factor models. Finally, we apply our methodology to intraday prices from the S &amp;P 500 index futures.

Rapid acquisition of battery impedance across multiple scenarios using DRT analysis

Quick and accurate electrochemical impedance spectroscopy (EIS) measurement has always been challenging. This paper proposes a reliable and fast measurement method, which, based on battery characteristics, utilizes a distribution of relaxation times (DRT) extraction algorithm to construct a characteristic spectrum and map it to a binary sequence. The proposed method for constructing characteristic sequences is applicable to battery measurements in multiple scenarioes. The paper additionally introduces a hybrid reconstruction filtering (HRF) method that amalgamates the DRT reconstruction technique and non-parametric estimation techniques. The filtering method does not require preset parameters, resulting in high accuracy and applicability. Simultaneously, combining the characteristic sequence with HRF ultimately obtains a smooth and complete EIS curve under varying states of charges (SOCs), temperatures, and capacities. The proposed testing framework obtains impedance from 0.1 Hz to 2000 Hz <13.2 s. The overall measurement error for batteries with different internal resistances does not exceed 2 %. This work provides a reliable characteristic optimization sequence for large-scale battery impedance measurements, offering a method that is both simple and highly versatile.

Estimation of vessel link-level travel time distribution: A directed network-driven approach

Accurate vessel travel time estimation is essential for operational efficiency and route optimization. Despite the prevalent use of the automatic identification system (AIS) in garnering multifaceted real-time data, ambiguities and inaccuracies in travel time predictions persist. It leads to planning uncertainties, inefficient resource allocations, and heightened operational costs in maritime logistics. To addresses these issues, this paper proposed a nuanced method to enhance the precision and reliability of vessel travel time estimations. Firstly, a directed maritime network is constructed by extracting essential information from AIS-based historical vessel trajectories. This lays the foundation for the subsequent analytical processes. Secondly, the non-parametric kernel density estimation (KDE) is applied to this constructed network, enabling the estimation of vessel travel time distributions across various network links. The non-parametric KDE is used in combination with AIS data, which improves the specificity and accuracy of the travel time estimations at the link level. Finally, this paper employs cellular automata (CA) simulations to validate the accuracy of the KDE-based estimations. Comparison between the simulation results and real-world data reveals a high degree of accuracy in the proposed method, confirming its applicability and effectiveness in estimating vessel travel times.