Popular Estimation Research Articles

Improved Variance Estimation From Trimmed Samples

ABSTRACTSeveral methods for the robust estimation of the variance of a normal random variable are based on trimming. For example, the popular estimator is based on trimming the pairs of samples with the largest absolute distance. Another example is least trimmed squares regression, where all unusually large residuals are removed before the estimation of the variance. Here, in this work, we propose two new classes of estimators that use an optimal linear combination of the trimmed samples to achieve a lower mean squared error (MSE). The first class guarantees the smallest variance among all unbiased estimators that are based on linear combinations, while the second class of estimators guarantees the smallest MSE at the cost of some small bias. Through simulations, we demonstrate that our proposed estimators can have considerably smaller MSE than other robust estimators both in the presence and absence of outliers.

On robust inference in time series regression

Abstract Least squares regression with heteroskedasticity consistent standard errors (“OLS-HC regression”) has proved very useful in cross section environments. However, several major difficulties, which are generally overlooked, must be confronted when transferring the HC technology to time series environments via heteroskedasticity and autocorrelation consistent standard errors (“OLS-HAC regression”). First, in plausible time-series environments, OLS parameter estimates can be inconsistent, so that OLS-HAC inference fails even asymptotically. Second, most economic time series have autocorrelation, which renders OLS parameter estimates inefficient. Third, autocorrelation similarly renders conditional predictions based on OLS parameter estimates inefficient. Finally, the structure of popular HAC covariance matrix estimators is ill-suited for capturing the autoregressive autocorrelation typically present in economic time series, which produces large size distortions and reduced power in HAC-based hypothesis testing, in all but the largest samples. We show that all four problems are largely avoided by the use of a simple and easily-implemented dynamic regression procedure, which we call DURBIN. We demonstrate the advantages of DURBIN with detailed simulations covering a range of practical issues.

Effect of sensor noise characteristics and calibration errors on the choice of IMU-sensor fusion algorithms

This paper focuses on accurate and precise orientation estimation with consumer-grade MEMS-IMUs for ‘slow’ orientation change and ‘short’-time applications. A simulation platform is developed to predict a suitable algorithm for a MEMS-IMU of known noise specifications, improving similar works. Experimentally measured noise characteristics of two commercial grade IMUs (MPU9250 and BNO055) are used in the simulation platform to generate simulated data and evaluate some popular orientation estimation algorithms along with two new Kalman filter-based algorithms. Real experiments are conducted with the same IMUs using an electromagnetic tracker as reference sensor. The output orientation results for two new improved algorithms are compared with other algorithms in simulations and real experiments. We show that the choice of the ‘best’ algorithm varies with the noise characteristics of individual sensors within the sensor module. The two new best-performing algorithms tested achieve<1˚ RMS angle error for the two low-cost consumer-grade IMUs.

A lightweight color and geometry feature extraction and fusion module for end-to-end 6D pose estimation

Although advancements in red–green–blue-depth (RGB-D)-based six degree-of-freedom (6D) pose estimation methods, severe occlusion remains challenging. Addressing this issue, we propose a novel feature fusion module that can efficiently leverage the color and geometry information in RGB-D images. Unlike prior fusion methods, our method employs a two-stage fusion process. Initially, we extract color features from RGB images and integrate them into a point cloud. Subsequently, an anisotropic separable set abstraction network-like network is utilized to process the fused point cloud, extracting both local and global features, which are then combined to generate the final fusion features. Furthermore, we introduce a lightweight color feature extraction network to reduce model complexity. Extensive experiments conducted on the LineMOD, Occlusion LineMOD, and YCB-Video datasets conclusively demonstrate that our method significantly enhances prediction accuracy, reduces training time, and exhibits robustness to occlusion. Further experiments show that our model is significantly smaller than the latest popular 6D pose estimation models, which indicates that our model is easier to deploy on mobile platforms.

Addressing Autocorrelation, Multicollinearity, and Heavy-Tail Errors in the Linear Regression Model

The most popular estimator for estimating parameters of linear regression models is the Ordinary Least Squares (OLS) Estimator. The OLS is considered the best linear unbiased estimator when certain assumptions are not violated. However, when autocorrelation, multicollinearity, and heavy-tail error are jointly present in the dataset, the OLS estimator is inefficient and imprecise. In this paper, we developed an estimator of linear regression model parameters that jointly handle multicollinearity, autocorrelation, and heavy tail errors. The new estimator, LADHLKL, was derived by combining the Hildreth-Lu (HL), the Kibria Lukman (KL), and the Least Absolute Deviation (LAD) estimators. The LADHLKL poses both the characteristics of the LAD, HL, and KL estimators which makes it resistant to both problems. We examined the properties of the proposed estimator and compared its performance with other existing estimators in terms of mean square error. An application to real-life data and simulation study revealed that the proposed estimator dominates other estimators in all the considered conditions in terms of mean square error.

A novel sequential estimation framework for battery state of health and remaining useful life based on sparse and limited data

Battery State of Health (SOH) estimation and Remaining Useful Life (RUL) prediction are significant for battery management systems in both electric vehicles and energy storage systems. Various battery Health Indicators (HIs) and abundant health information are generally utilized for SOH and RUL estimation. However, HIs and health information may not be available for various reasons such as sensor installation limitations, computational burden and communication delay of the system. To overcome the issue of sparse and limited data acquisition in real applications, this study proposed a novel battery SOH and RUL sequential estimation framework only utilizing sparse segments of time series voltage data. The Extreme Learning Machine (ELM) and Long Short Term Memory (LSTM) network are applied for SOH estimation and RUL prediction respectively. Locally Weighted Scatterplot Smoothing (LOWESS) is used for both data smoothing and sparse data reconstruction. Three common battery datasets are fully investigated for validation. The experiment results show well estimation accuracies in both battery SOH and RUL, demonstrating the effectiveness of the framework in limited data prediction. Several popular SOH and RUL estimation algorithms and two state-of-the-art works are compared to further elaborate the superiority of the proposed framework.

Unbiased news recommendation model combining time and content

The influence of popularity bias on news recommendation systems is substantial, as it increased the exposure of popular news and their being pushes to irrelevant users frequently, leading to less-than-ideal performance of the system. Existing popularity debiasing methods aim to optimize the fairness of recommendations so that unpopular news have more chances to be recommended. However, they ignore the timeliness that characterizes news, and some outdated news are recommended to users due to their low popularity. Unfortunately, users are not interested in outdated news. In addition, existing debiasing methods use content-independent popularity computation, which cannot accurately capture the dynamic changes in news popularity, thus reducing the effectiveness of debiasing. In this research, we introduce an innovative method named Time and Content-aware Causal Model, referred to as TCCM, which mitigates the popularity bias using current causal inference techniques that work well. The difference is that, first, we design a novel causal graph to analyze user interaction considering that news is timeliness. Based on this causal graph, TCCM models the influences of three factors on user interaction, namely, the timeliness of news, the popularity of news, and the matching between the content of news and the interest of the user, in order to solve the problem of recommending outdated news to users after de-biasing. Second, we consider the influences of news content on popularity and propose a new popularity estimation method. In TCCM, we improve the debiasing effect by combining news content (entity and word popularity) to obtain more accurate news popularity. Extensive experiments conducted on widely recognized benchmark datasets show that TCCM surpasses several cutting-edge approaches.

On the effect of the Kaplan-Meier estimator’s assumed tail behavior on goodness-of-fit testing

When analyzing lifetime data in the presence of censoring one is often required to estimate the distribution function of the lifetimes non-parametrically. The most popular estimator used for this purpose is the Kaplan-Meier estimator. Interestingly, in its initial formulation this estimator is only defined up to the observed sample maximum. For values larger than the sample maximum two different assumptions are commonly used in the statistical literature. The first is to set the value of the estimate to one while the second is to use the value of the estimate at the sample maximum when estimating the tail of the distribution function. This paper illustrates the profound effect of these assumptions on the sizes and powers of goodness-of-fit tests for three classes of distributions often used in survival analysis. These differences are illustrated using observed remission time data. The considered classes of distributions are the exponential, Weibull and gamma. As a result of independent interest, we amend two classes of tests developed for the gamma distribution in the full sample case for use with censored data.

SE(3) Synchronization by eigenvectors of dual quaternion matrices

Abstract In synchronization problems, the goal is to estimate elements of a group from noisy measurements of their ratios. A popular estimation method for synchronization is the spectral method. It extracts the group elements from eigenvectors of a block matrix formed from the measurements. The eigenvectors must be projected, or ‘rounded’, onto the group. The rounding procedures are constructed ad hoc and increasingly so when applied to synchronization problems over non-compact groups. In this paper, we develop a spectral approach to synchronization over the non-compact group $\mathrm{SE}(3)$, the group of rigid motions of $\mathbb{R}^{3}$. We based our method on embedding $\mathrm{SE}(3)$ into the algebra of dual quaternions, which has deep algebraic connections with the group $\mathrm{SE}(3)$. These connections suggest a natural rounding procedure considerably more straightforward than the current state of the art for spectral $\mathrm{SE}(3)$ synchronization, which uses a matrix embedding of $\mathrm{SE}(3)$. We show by numerical experiments that our approach yields comparable results with the current state of the art in $\mathrm{SE}(3)$ synchronization via the spectral method. Thus, our approach reaps the benefits of the dual quaternion embedding of $\mathrm{SE}(3)$ while yielding estimators of similar quality.

PCKRF: Point Cloud Completion and Keypoint Refinement With Fusion Data for 6D Pose Estimation.

Some robust point cloud registration approaches with controllable pose refinement magnitude, such as ICP and its variants, are commonly used to improve 6D pose estimation accuracy. However, the effectiveness of these methods gradually diminishes with the advancement of deep learning techniques and the enhancement of initial pose accuracy, primarily due to their lack of specific design for pose refinement. In this paper, we propose Point Cloud Completion and Keypoint Refinement with Fusion Data (PCKRF), a new pose refinement pipeline for 6D pose estimation. The pipeline consists of two steps. First, it completes the input point clouds via a novel pose-sensitive point completion network. The network uses both local and global features with pose information during point completion. Then, it registers the completed object point cloud with the corresponding target point cloud by our proposed Color supported Iterative KeyPoint (CIKP) method. The CIKP method introduces color information into registration and registers a point cloud around each keypoint to increase stability. The PCKRF pipeline can be integrated with existing popular 6D pose estimation methods, such as the full flow bidirectional fusion network, to further improve their pose estimation accuracy. Experiments demonstrate that our method exhibits superior stability compared to existing approaches when optimizing initial poses with relatively high precision. Notably, the results indicate that our method effectively complements most existing pose estimation techniques, leading to improved performance in most cases. Furthermore, our method achieves promising results even in challenging scenarios involving textureless and symmetrical objects. Our source code is available at https://github.com/zhanhz/KRF.

Flexible control of the median of the false discovery proportion

Abstract We introduce a multiple testing procedure that controls the median of the proportion of false discoveries in a flexible way. The procedure only requires a vector of p-values as input and is comparable to the Benjamini–Hochberg method, which controls the mean of the proportion of false discoveries. Our method allows free choice of one or several values of alpha after seeing the data, unlike the Benjamini–Hochberg procedure, which can be very anti-conservative when alpha is chosen post hoc. We prove these claims and illustrate them with simulations. Our procedure is inspired by a popular estimator of the total number of true hypotheses. We adapt this estimator to provide simultaneously median unbiased estimators of the proportion of false discoveries, valid for finite samples. This simultaneity allows for the claimed flexibility. Our approach does not assume independence. The time complexity of our method is linear in the number of hypotheses, after sorting the p-values.

A Note on Simultaneous Confidence Intervals for Direct, Indirect and Synthetic Estimators

Direct, indirect and synthetic estimators have a long history in official statistics. While model-based or model-assisted approaches have become very popular, direct and indirect estimators remain the predominant standard and are therefore important tools in practice. This is mainly due to their simplicity, including low data requirements, assumptions and straightforward inference. With the increasing use of domain estimates in policy, the demands on these tools have also increased. Today, they are frequently used for comparative statistics. This requires appropriate tools for simultaneous inference. We study devices for constructing simultaneous confidence intervals and show that simple tools like the Bonferroni correction can easily fail. In contrast, uniform inference based on max-type statistics in combination with bootstrap methods, appropriate for finite populations, work reasonably well. We illustrate our methods with frequently applied estimators of totals and means.

Minimum density power divergence estimation for the generalized exponential distribution

Statistical modeling of rainfall data is an active research area in agro-meteorology. The most common models fitted to such datasets are exponential, gamma, log-normal, and Weibull distributions. As an alternative to some of these models, the generalized exponential (GE) distribution was proposed by Gupta and Kundu (2001a). Rainfall (specifically for short periods) datasets often include outliers, and thus, a proper robust parameter estimation procedure is necessary. Here, we use the popular minimum density power divergence estimation (MDPDE) procedure developed by Basu et al. (1998) for estimating the GE parameters. We derive the analytical expressions for the estimating equations and asymptotic distributions. We analytically compare MDPDE with maximum likelihood estimation in terms of robustness, through an influence function analysis. Besides, we study the asymptotic relative efficiency of MDPDE analytically for different parameter settings. We apply the proposed technique to some simulated datasets and two rainfall datasets from Texas, United States. The results indicate superior performance of MDPDE compared to the other existing estimation techniques in most of the scenarios.

Should Humans Lie to Machines? The Incentive Compatibility of Lasso and GLM Structured Sparsity Estimators

We consider situations where a user feeds her attributes to a machine learning method that tries to predict her best option based on a random sample of other users. The predictor is incentive-compatible if the user has no incentive to misreport her covariates. Focusing on the popular Lasso estimation technique, we borrow tools from high-dimensional statistics to characterize sufficient conditions that ensure that Lasso is incentive compatible in the asymptotic case. We extend our results to a new nonlinear machine learning technique, Generalized Linear Model Structured Sparsity estimators. Our results show that incentive compatibility is achieved if the tuning parameter is kept above some threshold in the case of asymptotics.

MODELING OPEN UNEMPLOYMENT RATE IN KALIMANTAN ISLAND USING NONPARAMETRIC REGRESSION WITH FOURIER SERIES ESTIMATOR

Nonparametric regression is a regression approach that is used to determine the relationship between the response variable and the predictor variable if the shape of the regression curve is unknown. One of the popular estimators used in nonparametric regression is the Fourier series estimator. Fourier series nonparametric regression is generally used when the pattern of the investigated data is unknown and there is a tendency for the pattern to repeat. The purpose of this study is to estimate nonparametric regression using the Fourier series approach and to find out the factors that influence the open unemployment rate on the island of Borneo in 2021. The criteria for the goodness of the model used Generalized Cross Validation (GCV) and the coefficient of determination ( ). Based on the results, it was found that the best nonparametric regression model for the Fourier series was the model with 5 oscillations which indicated a minimum GCV of 10.47 and an of 74.22%. Furthermore, based on the results of parameter significance testing either simultaneously or partially, it shows that all predictor variables have a significant effect on the open unemployment rate. The predictor variables include the labor force participation rate, the average length of schooling, the percentage of poor people, economic growth rate, and total population.

High-dimensional and permutation invariant anomaly detection

Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable properties such as permutation invariance and variable-length inputs becomes difficult within popular density estimation methods. In this work, we introduce a permutation-invariant density estimator for particle physics data based on diffusion models, specifically designed to handle variable-length inputs. We demonstrate the efficacy of our methodology by utilizing the learned density as a permutation-invariant anomaly detection score, effectively identifying jets with low likelihood under the background-only hypothesis. To validate our density estimation method, we investigate the ratio of learned densities and compare to those obtained by a supervised classification algorithm.

G.ridge: An R Package for Generalized Ridge Regression for Sparse and High-Dimensional Linear Models

Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested that involved generalizing the uniform shrinkage of ridge regression to non-uniform shrinkage; this was shown to perform well in sparse and high-dimensional linear models. In this paper, we introduce our newly developed R package “g.ridge” (first version published on 7 December 2023) that implements both the ridge estimator and generalized ridge estimator. The package is equipped with generalized cross-validation for the automatic estimation of shrinkage parameters. The package also includes a convenient tool for generating a design matrix. By simulations, we test the performance of the R package under sparse and high-dimensional settings with normal and skew-normal error distributions. From the simulation results, we conclude that the generalized ridge estimator is superior to the benchmark ridge estimator based on the R package “glmnet”. Hence the generalized ridge estimator may be the most recommended estimator for sparse and high-dimensional models. We demonstrate the package using intracerebral hemorrhage data.

Observations and Estimates of Wet-Bulb Globe Temperature in Varied Microclimates

Abstract Wet-bulb globe temperature (WBGT) is used to assess environmental heat stress and accounts for the influences of air temperature, humidity, wind speed, and radiation on heat stress. Measurements of WBGT are highly sensitive to slight changes in environmental conditions and can vary several degrees Celsius across small distances (tens to hundreds of meters). Relative to observations with an International Organization for Standardization (ISO)-compliant WBGT meter, this work assesses the accuracy of WBGT measurements made with a popular handheld meter (the Kestrel 5400 Heat Stress Tracker) and WBGT estimates. Measurements were made during the summers of 2019–21 in a variety of suburban and urban environments in North Carolina, including three high school campuses. WBGT can be estimated from standard weather station variables, and many of these stations report cloud cover in lieu of solar radiation. Therefore, this work also evaluates the accuracy of clear-sky radiation estimates and adjustments to those estimates based on cloud cover. WBGT estimated with the method from Liljegren et al. from a weather station were on average 0.2°C warmer than Observed WBGT, while the Kestrel 5400 WBGT was 0.7°C warmer. Large variations in WBGT were observed across surfaces and shade conditions, with differences of 0.9°C (0.3°–1.4°C) between a tennis court and a neighboring grass field. The method for estimating clear-sky radiation in Ryan and Stolzenbach was most accurate and the clear-sky radiation modified by percentage cloud cover was found to be within 75 W m−2of observations on average. Significance Statement Wet-bulb globe temperature (WBGT) is a heat stress index that accounts for the effects of air temperature, humidity, wind, and radiation on humans. However, WBGT is not routinely measured at weather stations. This work demonstrated the accuracy of estimating WBGT with methods from Liljegren et al. (2008), finding it to be more accurate than measurements from a popular handheld meter, the Kestrel 5400 Heat Stress Tracker. Variations in WBGT that result in different danger levels were found between measurements over a tennis court and a neighboring grass field, and between sun and shade conditions. Understanding the magnitude of these differences and the biases with WBGT estimates and measurements can inform the planning of outdoor activity to robustly safeguard health.

Dollo-CDP: a polynomial-time algorithm for the clade-constrained large Dollo parsimony problem

The last decade of phylogenetics has seen the development of many methods that leverage constraints plus dynamic programming. The goal of this algorithmic technique is to produce a phylogeny that is optimal with respect to some objective function and that lies within a constrained version of tree space. The popular species tree estimation method ASTRAL, for example, returns a tree that (1) maximizes the quartet score computed with respect to the input gene trees and that (2) draws its branches (bipartitions) from the input constraint set. This technique has yet to be used for parsimony problems where the input are binary characters, sometimes with missing values. Here, we introduce the clade-constrained character parsimony problem and present an algorithm that solves this problem for the Dollo criterion score in O(|Sigma |^{3.726}(n+k) + |Sigma |^{1.726}nk) time, where n is the number of leaves, k is the number of characters, and Sigma is the set of clades used as constraints. Dollo parsimony, which requires traits/mutations to be gained at most once but allows them to be lost any number of times, is widely used for tumor phylogenetics as well as species phylogenetics, for example analyses of low-homoplasy retroelement insertions across the vertebrate tree of life. This motivated us to implement our algorithm in a software package, called Dollo-CDP, and evaluate its utility for analyzing retroelement insertion presence / absence patterns for bats, birds, toothed whales as well as simulated data. Our results show that Dollo-CDP can improve upon heuristic search from a single starting tree, often recovering a better scoring tree. Moreover, Dollo-CDP scales to data sets with much larger numbers of taxa than branch-and-bound while still having an optimality guarantee, albeit a more restricted one. Lastly, we show that our algorithm for Dollo parsimony can easily be adapted to Camin-Sokal parsimony but not Fitch parsimony.

Tenets and Methods of Fractal Analysis (1/f Noise).

This chapter deals with the methodical challenges confronting researchers of the fractal phenomenon known as pink or 1/f noise. This chapter introduces concepts and statistical techniques for identifying fractal patterns in empirical time series. It defines some basic statistical terms, describes two essential characteristics of pink noise (self-similarity and long memory), and outlines four parameters representing the theoretical properties of fractal processes: the Hurst coefficient (H), the scaling exponent (α), the power exponent (β), and the fractional differencing parameter (d) of the ARFIMA (autoregressive fractionally integrated moving average) method. Then, it compares and evaluates different approaches to estimating fractal parameters from observed data and outlines the advantages, disadvantages, and constraints of some popular estimators. The final section of this chapter answers the questions: Which strategy is appropriate for the identification of fractal noise in empirical settings and how can it be applied to the data?