Nonparametric Estimation Research Articles

Study on the distribution of average wind speeds at a mountainous bridge site for structural durability design

Conventional wind speed distribution methods (e.g., Rayleigh distribution and Weibull distribution) may not adequately capture complex characteristics of wind fields in mountainous areas. To address this problem, this study proposes a semi-parametric mix method for modeling the distribution of average wind speeds based on the combination of nonparametric Kernel Density Estimation (KDE) and Generalized Pareto Distribution (GPD). In the proposed method, KDE focuses on capturing the distribution in the main part of average wind speeds, while GPD aims at performing the distribution in terms of those in the extreme part. The segment point (i.e., the threshold) between KDE and GPD distributions is determined based on the combination of conditional mean excesses criterion and empirical rule. Meanwhile, the selection of modeling parameters should ensure that the mix distribution model is continuous and differentiable at the identified threshold point. Then, the commonly-used conditional probability model is further introduced to describe the wind direction distribution. Finally, a case study based on the measured 10-min average wind speeds at a mountainous bridge site is employed to demonstrate the effectiveness of the proposed method. The results indicate that: (1) the distribution of omnidirectional average wind speeds in the mountainous bridge site exhibits an obviously single-peak characteristic, while those considering wind directionality present a certain bimodal characteristic; (2) the proposed method can effectively describe wind speed distributions with different statistical characteristics, and the fitting accuracy outperforms the frequently-employed Weibull distribution model.

Big data analytics for quality variation over work shifts in manufacturing systems

ABSTRACT In the manufacturing industry, mass production enables manufacturers to produce parts with high precision and lower costs. Multiple shifts operate production processes to maximize efficiency. Several researches have been conducted on the impact of shift work on labor’s health and habits. However, there have been few studies on the influence of shift work on the consistency of product quality. This paper provides a methodology to analyze the impact of different work shifts in a real electronic board manufacturing industry. The study uses big data and analytics to assess product quality from data. Non-parametric kernel density estimation is used to approximate the distribution of good products in each work slot. Then several metrics are used to measure the dissimilarity between the estimated densities. The approach can be leveraged in various problems related to process performance and quality. The obtained results show that there is no significant difference in terms of product quality between work shifts. These prove the consistency of the manufacturing processes and the homogeneity of performance across work shifts in the studied factory. Compared to the literature, the paper presents the first quantitative analysis to compare production process performance and product quality over shift works.

Estimators for Topic-Sampling Designs

Abstract When researchers design an experiment, they usually hold potentially relevant features of the experiment constant. We call these details the “topic” of the experiment. For example, researchers studying the impact of party cues on attitudes must inform respondents of the parties’ positions on a particular policy. In doing so, researchers implement just one of many possible designs . Clifford, Leeper, and Rainey (2023. “Generalizing Survey Experiments Using Topic Sampling: An Application to Party Cues.” Forthcoming in Political Behavior. https://doi.org/10.1007/s11109-023-09870-1) argue that researchers should implement many of the possible designs in parallel—what they call “topic sampling”—to generalize to a larger population of topics. We describe two estimators for topic-sampling designs: First, we describe a nonparametric estimator of the typical effect that is unbiased under the assumptions of the design; and second, we describe a hierarchical model that researchers can use to describe the heterogeneity. We suggest describing the heterogeneity across topics in three ways: (1) the standard deviation in treatment effects across topics, (2) the treatment effects for particular topics, and (3) how the treatment effects for particular topics vary with topic-level predictors. We evaluate the performance of the hierarchical model using the Strengthening Democracy Challenge megastudy and show that the hierarchical model works well.

Sample-Based Distance-Approximation for Subsequence-Freeness

AbstractIn this work, we study the problem of approximating the distance to subsequence-freeness in the sample-based distribution-free model. For a given subsequence (word) $$w = w_1 \ldots w_k$$ w = w 1 … w k , a sequence (text) $$T = t_1 \ldots t_n$$ T = t 1 … t n is said to contain w if there exist indices $$1 \le i_1< \cdots < i_k \le n$$ 1 ≤ i 1 < ⋯ < i k ≤ n such that $$t_{i_{j}} = w_j$$ t i j = w j for every $$1 \le j \le k$$ 1 ≤ j ≤ k . Otherwise, T is w-free. Ron and Rosin (ACM Trans Comput Theory 14(4):1–31, 2022) showed that the number of samples both necessary and sufficient for one-sided error testing of subsequence-freeness in the sample-based distribution-free model is $$\Theta (k/\epsilon )$$ Θ ( k / ϵ ) . Denoting by $$\Delta (T,w,p)$$ Δ ( T , w , p ) the distance of T to w-freeness under a distribution $$p:[n]\rightarrow [0,1]$$ p : [ n ] → [ 0 , 1 ] , we are interested in obtaining an estimate $$\widehat{\Delta }$$ Δ ^ , such that $$|\widehat{\Delta }- \Delta (T,w,p)| \le \delta $$ | Δ ^ - Δ ( T , w , p ) | ≤ δ with probability at least 2/3, for a given error parameter $$\delta $$ δ . Our main result is a sample-based distribution-free algorithm whose sample complexity is $$\tilde{O}(k^2/\delta ^2)$$ O ~ ( k 2 / δ 2 ) . We first present an algorithm that works when the underlying distribution p is uniform, and then show how it can be modified to work for any (unknown) distribution p. We also show that a quadratic dependence on $$1/\delta $$ 1 / δ is necessary.

Towards optimal model evaluation: enhancing active testing with actively improved estimators

With rapid advancements in machine learning and statistical models, ensuring the reliability of these models through accurate evaluation has become imperative. Traditional evaluation methods often rely on fully labeled test data, a requirement that is becoming increasingly impractical due to the growing size of datasets. In this work, we address this issue by extending existing work on active testing (AT) methods which are designed to sequentially sample and label data for evaluating pre-trained models. We propose two novel estimators: the Actively Improved Levelled Unbiased Risk (AILUR) and the Actively Improved Inverse Probability Weighting (AIIPW) estimators which are derived from nonparametric smoothing estimation. In addition, a model recalibration process is designed for the AIIPW estimator to optimize the sampling probability within the AT framework. We evaluate the proposed estimators on four real-world datasets and demonstrate that they consistently outperform existing AT methods. Our study also shows that the proposed methods are robust to changes in subsample sizes, and effective at reducing labeling costs.

An Aerial Robotic Missing-Person Search in Urban Settings—A Probabilistic Approach

Autonomous robotic teams have been proposed for a variety of lost-person searches in wilderness and urban settings. In the latter scenarios, for missing persons, the application of such teams, however, is more challenging than it would be in the wilderness. This paper, specifically, examines the application of an autonomous team of unmanned aerial vehicles (UAVs) to perform a sparse, mobile-target search in an urban setting. A novel multi-UAV search-trajectory planning method, which relies on the prediction of the missing-person’s motion, given a known map of the search environment, is the primary focus. The proposed method incorporates periodic updates of the estimates of where the lost/missing person may be, allowing for intelligent re-coverage of previously searched areas. Additional significant contributions of this work include a behavior-based motion-prediction method for missing persons and a novel non-parametric estimator for iso-probability-based (missing-person-location) curves. Simulated experiments are presented to illustrate the effectiveness of the proposed search-planning method, demonstrating higher rates of missing-person detection and in shorter times compared to other methods.

Volatility estimation of hidden Markov processes and adaptive filtration

The partially observed linear Gaussian system of stochastic differential equations with low noise in observations is considered. The coefficients of this system are supposed to depend on some unknown parameter. The problem of estimation of these parameters is considered and the possibility of the approximation of the filtering equations is discussed. An estimators are used for estimation of the quadratic variation of the derivative of the limit of the observed process. Then this estimator is used for nonparametric estimation of the integral of the square of volatility of unobservable component. This estimator is also used for construction of method of moments estimators in the case where the drift in observable component and the volatility of the state component depend on some unknown parameter. Then this method of moments estimator and Fisher-score device allow us to introduce the One-step MLE-process and adaptive Kalman–Bucy filter. The asymptotic efficiency of the proposed filter is discussed.

Summary statistics for spatio-temporal point processes on linear networks

We propose novel second/higher-order summary statistics for inhomogeneous spatio-temporal point processes when the spatial locations are limited to a linear network. More specifically, letting the spatial distance between events be measured by a regular distance metric, appropriate forms of K- and J-functions are introduced, and their theoretical relationships are studied. The theoretical forms of our proposed summary statistics are investigated under homogeneity, Poissonness, and independent thinning. Moreover, non-parametric estimators are derived, facilitating the use of our proposed summary statistics to study the spatio-temporal dependence between events. Through simulation studies, we demonstrate that our proposed J-function effectively identifies spatio-temporal clustering, inhibition, and randomness. Finally, we examine spatio-temporal dependencies for street crimes in Valencia, Spain, and traffic accidents in New York, USA.

Pointwise Nonparametric Estimation of Odds Ratio Curves with R: Introducing the flexOR Package

The analysis of odds ratio curves is a valuable tool in understanding the relationship between continuous predictors and binary outcomes. Traditional parametric regression approaches often assume specific functional forms, limiting their flexibility and applicability to complex data. To address this limitation and introduce more flexibility, several smoothing methods may be applied, and approaches based on splines are the most frequently considered in this context. To better understand the effects that each continuous covariate has on the outcome, results can be expressed in terms of splines-based odds ratio (OR) curves, taking a specific covariate value as reference. In this paper, we introduce an R package, flexOR, which provides a comprehensive framework for pointwise nonparametric estimation of odds ratio curves for continuous predictors. The package can be used to estimate odds ratio curves without imposing rigid assumptions about their underlying functional form while considering a reference value for the continuous covariate. The package offers various options for automatically choosing the degrees of freedom in multivariable models. It also includes visualization functions to aid in the interpretation and presentation of the estimated odds ratio curves. flexOR offers a user-friendly interface, making it accessible to researchers and practitioners without extensive statistical backgrounds.

On Binscatter

Binscatter is a popular method for visualizing bivariate relationships and conducting informal specification testing. We study the properties of this method formally and develop enhanced visualization and econometric binscatter tools. These include estimating conditional means with optimal binning and quantifying uncertainty. We also highlight a methodological problem related to covariate adjustment that can yield incorrect conclusions. We revisit two applications using our methodology and find substantially different results relative to those obtained using prior informal binscatter methods. General purpose software in Python, R, and Stata is provided. Our technical work is of independent interest for the nonparametric partition-based estimation literature. (JEL C13, C14, C18, C51, O31, R32)

Formula: see text]-[Formula: see text]: A Nonparametric Model for Neural Power Spectra Decomposition.

The power spectra estimated from the brain recordings are the mixed representation of aperiodic transient activity and periodic oscillations, i.e., aperiodic component (AC) and periodic component (PC). Quantitative neurophysiology requires precise decomposition preceding parameterizing each component. However, the shape, statistical distribution, scale, and mixing mechanism of AC and PCs are unclear, challenging the effectiveness of current popular parametric models such as FOOOF, IRASA, BOSC, etc. Here, ξ- π was proposed to decompose the neural spectra by embedding the nonparametric spectra estimation with penalized Whittle likelihood and the shape language modeling into the expectation maximization framework. ξ- π was validated on the synthesized spectra with loss statistics and on the sleep EEG and the large sample iEEG with evaluation metrics and neurophysiological evidence. Compared to FOOOF, both the simulation presenting shape irregularities and the batch simulation with multiple isolated peaks indicated that ξ- π improved the fit of AC and PCs with less loss and higher F1-score in recognizing the centering frequencies and the number of peaks; the sleep EEG revealed that ξ- π produced more distinguishable AC exponents and improved the sleep state classification accuracy; the iEEG showed that ξ- π approached the clinical findings in peak discovery. Overall, ξ- π offered good performance in the spectra decomposition, which allows flexible parameterization using descriptive statistics or kernel functions. ξ- π is a seminal tool for brain signal decoding in fields such as cognitive neuroscience, brain-computer interface, neurofeedback, and brain diseases.

Nonparametric estimation of the copula function with bivariate twice censored data

In this work, we are interested in the nonparametric estimation of the copula function in the presence of bivariate twice censored data. Assuming that the copula functions of the right and the left censoring variables are known, we propose an estimator of the joint distribution function of the variables of interest, then we derive an estimator of their copula function. Using a representation of the proposed estimator of the joint distribution function as a sum of independent and identically distributed variables, we establish the weak convergence of the empirical copula that we introduce.

Nonparametric estimation of conditional incremental effects

Abstract Conditional effect estimation has great scientific and policy importance because interventions may impact subjects differently depending on their characteristics. Most research has focused on estimating the conditional average treatment effect (CATE). However, identification of the CATE requires that all subjects have a non-zero probability of receiving treatment, or positivity, which may be unrealistic in practice. Instead, we propose conditional effects based on incremental propensity score interventions, which are stochastic interventions where the odds of treatment are multiplied by some factor. These effects do not require positivity for identification and can be better suited for modeling scenarios in which people cannot be forced into treatment. We develop a projection approach and a flexible nonparametric estimator that can each estimate all the conditional effects we propose and derive model-agnostic error guarantees showing that both estimators satisfy a form of double robustness. Further, we propose a summary of treatment effect heterogeneity and a test for any effect heterogeneity based on the variance of a conditional derivative effect and derive a nonparametric estimator that also satisfies a form of double robustness. Finally, we demonstrate our estimators by analyzing the effect of intensive care unit admission on mortality using a dataset from the (SPOT)light study.

Simple analytical models for estimating the queue lengths from probe vehicles at traffic signals: A combinatorial approach for nonparametric models

This study develops a combinatorial approach for nonparametric short-term queue length estimation in terms of cycle-by-cycle partially observed queues from probe vehicles (PV). The method does not assume random arrivals and does not assume any primary parameters or estimation of any parameters but uses simple algebraic expressions that only depend on signal timing. For an approach lane at a traffic intersection, the conditional queue lengths given probe vehicle location, count, time, and analysis interval (e.g., at the end of the red signal phase) are represented by a Negative Hypergeometric distribution. The simple analytical estimators obtained are compared with parametric methods from literature and highway capacity manual methods using field test data and simulation data involving probe vehicles. The analysis indicates that the nonparametric models presented in this paper match the accuracy of the parametric ones used in the field test and simulated data for estimating queue lengths.

Tests for equal forecast accuracy under heteroskedasticity

SummaryHeteroskedasticity is a common feature in empirical time series analysis, and in this paper, we consider the effects of heteroskedasticity on statistical tests for equal forecast accuracy. In such a context, we propose two new Diebold–Mariano‐type tests for equal accuracy that employ nonparametric estimation of the loss differential variance function. We demonstrate that these tests have the potential to achieve power improvements relative to the original Diebold–Mariano test in the presence of heteroskedasticity, for a quite general class of loss differential series. The size validity and potential power superiority of our new tests are studied theoretically and in Monte Carlo simulations. We apply our new tests to competing forecasts of changes in the dollar/sterling exchange rate and find the new tests provide greater evidence of differences in forecast accuracy than the original Diebold–Mariano test, illustrating the value of these new procedures for practitioners.

Stock market prices and Dividends in the US: Bubbles or Long-run equilibria relationships?

This paper presents a novel approach to identifying potential bubbles in the US stock market by employing alternative time series methods based on long memory, including fractional integration and cointegration, as well as duration dependence non-parametric models. To test for duration dependence, the paper employs a unique non-parametric hazard function estimation method, using monotonic P-splines, which enables the estimation of a coherent and sophisticated Bayesian confidence interval for the function. By analyzing historical data of real US stock index from January 1871 to November 2022, the results reveal strong evidence of bubbles in the US stock market. It is worth noting that this is the first time a fractional integration approach and a novel non-parametric hazard function have been utilized to test for rational speculative bubbles in the US stock market, making this paper a significant contribution to the field.

Selection and Aggregation of Conformal Prediction Sets

Conformal prediction is a generic methodology for finite-sample valid distribution-free prediction. This technique has garnered a lot of attention in the literature partly because it can be applied with any machine learning algorithm that provides point predictions to yield valid prediction regions. Of course, the efficiency (width/volume) of the resulting prediction region depends on the performance of the machine learning algorithm. In the context of point prediction, several techniques (such as cross-validation) exist to select one of many machine learning algorithms for better performance. In contrast, such selection techniques are seldom discussed in the context of set prediction (or prediction regions). In this paper, we consider the problem of obtaining the smallest conformal prediction region given a family of machine learning algorithms. We provide two general-purpose selection algorithms and consider coverage as well as width properties of the final prediction region. The first selection method yields the smallest width prediction region among the family of conformal prediction regions for all sample sizes but only has an approximate coverage guarantee. The second selection method has a finite sample coverage guarantee but only attains close to the smallest width. The approximate optimal width property of the second method is quantified via an oracle inequality. As an illustration, we consider the use of aggregation of non-parametric regression estimators in the split conformal method with the absolute residual conformal score.

Partial-linear single-index transformation models with censored data.

In studies with time-to-event outcomes, multiple, inter-correlated, and time-varying covariates are commonly observed. It is of great interest to model their joint effects by allowing a flexible functional form and to delineate their relative contributions to survival risk. A class of semiparametric transformation (ST) models offers flexible specifications of the intensity function and can be a general framework to accommodate nonlinear covariate effects. In this paper, we propose a partial-linear single-index (PLSI) transformation model that reduces the dimensionality of multiple covariates into a single index and provides interpretable estimates of the covariate effects. We develop an iterative algorithm using the regression spline technique to model the nonparametric single-index function for possibly nonlinear joint effects, followed by nonparametric maximum likelihood estimation. We also propose a nonparametric testing procedure to formally examine the linearity of covariate effects. We conduct Monte Carlo simulation studies to compare the PLSI transformation model with the standard ST model and apply it to NYU Langone Health de-identified electronic health record data on COVID-19 hospitalized patients' mortality and a Veteran's Administration lung cancer trial.

The effects of manager sentiment in financial disclosure: Perspectives of operational efficiency and market reaction

This study constructs a measure of managerial optimism using textual and nonparametric estimation methods, exploring its impact on company operational efficiency and market reactions. Findings indicate that managerial optimism positively influences stock price returns over the subsequent year by enhancing internal operational efficiency and reducing analyst forecast dispersion, with a more pronounced effect in state-owned enterprises. Utilizing information from the MD&A (Manager Discussion and Analysis) section of annual reports, this research demonstrates the role of managerial optimism in company operations and market reactions, offering empirical evidence for corporate behavioral finance research and practical implications for management practice.

Identification and Estimation of Discrete Choice Models with Unobserved Choice Sets*

We propose a framework for nonparametric identification and estimation of discrete choice models with unobserved choice sets. We recover the joint distribution of choice sets and preferences from a cross-section of repeated choices. We assume that either the latent choice sets are sparse or that the number of repeated choices is sufficiently large. Sparsity requires the number of possible choice sets to be relatively small. It is satisfied, for instance, when the choice sets are nested or when they form a partition. Our estimation procedure is computationally fast and uses mixed-integer programming to recover the sparse support of choice sets. Analyzing the ready-to-eat cereal industry using a household scanner dataset, we find that ignoring the unobservability of choice sets can lead to incorrect estimates of preferences.