Variance Estimation Method Research Articles

Robust high-dimensional regression for data with anomalous responses

The accuracy of response variables is crucially important to train regression models. In some situations, including the high-dimensional case, response observations tend to be inaccurate, which would lead to biased estimators by directly fitting a conventional model. For analyzing data with anomalous responses in the high-dimensional case, in this work, we adopt γ-divergence to conduct variable selection and estimation methods. The proposed method possesses good robustness to anomalous responses, and the proportion of abnormal data does not need to be modeled. It is implemented by an efficient coordinate descent algorithm. In the setting where the dimensionality p can grow exponentially fast with the sample size n, we rigorously establish variable selection consistency and estimation bounds. Numerical simulations and an application on real data are presented to demonstrate the performance of the proposed method.

Summarizing causal differences in survival curves in the presence of unmeasured confounding.

Proportional hazard Cox regression models are frequently used to analyze the impact of different factors on time-to-event outcomes. Most practitioners are familiar with and interpret research results in terms of hazard ratios. Direct differences in survival curves are, however, easier to understand for the general population of users and to visualize graphically. Analyzing the difference among the survival curves for the population at risk allows easy interpretation of the impact of a therapy over the follow-up. When the available information is obtained from observational studies, the observed results are potentially subject to a plethora of measured and unmeasured confounders. Although there are procedures to adjust survival curves for measured covariates, the case of unmeasured confounders has not yet been considered in the literature. In this article we provide a semi-parametric procedure for adjusting survival curves for measured and unmeasured confounders. The method augments our novel instrumental variable estimation method for survival time data in the presence of unmeasured confounding with a procedure for mapping estimates onto the survival probability and the expected survival time scales.

Efficient DOA Estimation Method Using Bias-Compensated Adaptive Filtering

We consider the DOA estimation problem by using adaptive nulling antenna technology and bias-compensated adaptive filtering framework. The adaptive nulling antenna array consists of one reference antenna element and multiple auxiliary antenna elements, which forms nulls in certain directions. By defining the reciprocal of array pattern as the spatial spectrum, the DOA estimation problem is considered as the peak searching for it. In this paper, we present an efficient bias-compensated adaptive filtering algorithm for DOA estimation based on the adaptive nulling array. First of all, a new noise-free mean square error (NF-MSE) cost function associated with the adaptive nulling array is provided. Secondly, the proposed algorithm, called variable step-size bias-compensated least mean square (VSS-BC-LMS) algorithm, can be derived by minimizing the NF-MSE. Due to the bias compensation, the bias of the estimated weight vector caused by noises is canceled. More importantly, in order to resist the unsatisfactory DOA estimation performance when using the fixed step-size, a variable step size scheme is introduced. And then, its mean stability, steady state mean square performance and computational complexity are discussed. Additionally, we also explore a noise variance estimation method for calculating the bias term. Simulation results indicate that the proposed algorithm achieves an improved DOA estimation performance compared with other adaptive methods.

Estimating outcome-specific effects in meta-analyses of multiple outcomes: A simulation study.

In meta-analysis, primary studies often include multiple, dependent effect sizes. Several methods address this dependency, such as the multivariate approach, three-level models, and the robust variance estimation (RVE) method. As for today, most simulation studies that explore the performance of these methods have focused on the estimation of the overall effect size. However, researchers are sometimes interested in obtaining separate effect size estimates for different types of outcomes. A recent simulation study (Park & Beretvas, 2019) has compared the performance of the three-level approach and the RVE method in estimating outcome-specific effects when several effect sizes are reported for different types of outcomes within studies. The goal of this paper is to extend that study by incorporating additional simulation conditions and by exploring the performance of additional models, such as the multivariate model, a three-level model that specifies different study-effects for each type of outcome, a three-level model that specifies a common study-effect for all outcomes, and separate three-level models for each type of outcome. Additionally, we also tested whether the a posteriori application of the RV correction improves the standard error estimates and the 95% confidence intervals. Results show that the application of separate three-level models for each type of outcome is the only approach that consistently gives adequate standard error estimates. Also, the a posteriori application of the RV correction results in correct 95% confidence intervals in all models, even if they are misspecified, meaning that Type I error rate is adequate when the RV correction is implemented.

Estimation in single-index varying-coefficient panel data model

In this paper, we study the single-index varying-coefficient panel data model. Combining the refined minimum average variance estimation (RMAVE) method with the local linear regression, we estimate the parameters in single index and link function, and explain the steps of the iterative algorithm. Under certain regularity conditions, the asymptotic properties of the estimators of the parameters and link functions are derived. Finally, numerical simulations are presented and our model is shown to perform better than the single-index panel data model in a real-data example.

Statistical properties and different methods of estimation for extended weighted inverted Rayleigh distribution

Abstract The aim of this paper is to introduce a new weighted probability distribution to model the non-monotone failure rate pattern for survival data. The proposed distribution is generalized by considering inverted Rayleigh distribution as a baseline distribution called an extended weighted inverted Rayleigh distribution. Different statistical properties such as moment, quantile function, moment generating function, entropy measurement, Bonferroni and Lorenz curve, stochastic ordering and order statistics have been derived. Different estimation procedures have also been discussed to estimate the unknown parameters of the proposed probability distribution. The Monte Carlo simulation study has been conducted to compare the performances of the proposed estimators obtained through various methods of estimation. Finally, two real data sets have been used to show the applicability of the proposed model in a real-life scenario.

DEqMS: A Method for Accurate Variance Estimation in Differential Protein Expression Analysis

Quantitative proteomics by mass spectrometry is widely used in biomarker research and basic biology research for investigation of phenotype level cellular events. Despite the wide application, the methodology for statistical analysis of differentially expressed proteins has not been unified. Various methods such as t test, linear model and mixed effect models are used to define changes in proteomics experiments. However, none of these methods consider the specific structure of MS-data. Choices between methods, often originally developed for other types of data, are based on compromises between features such as statistical power, general applicability and user friendliness. Furthermore, whether to include proteins identified with one peptide in statistical analysis of differential protein expression varies between studies. Here we present DEqMS, a robust statistical method developed specifically for differential protein expression analysis in mass spectrometry data. In all data sets investigated there is a clear dependence of variance on the number of PSMs or peptides used for protein quantification. DEqMS takes this feature into account when assessing differential protein expression. This allows for a more accurate data-dependent estimation of protein variance and inclusion of single peptide identifications without increasing false discoveries. The method was tested in several data sets including E. coli proteome spike-in data, using both label-free and TMT-labeled quantification. Compared with previous statistical methods used in quantitative proteomics, DEqMS showed consistently better accuracy in detecting altered protein levels compared with other statistical methods in both label-free and labeled quantitative proteomics data. DEqMS is available as an R package in Bioconductor.

Variance Estimation With Complex Data and Finite Population Correction—A Paradigm for Comparing Jackknife and Formula‐Based Methods for Variance Estimation

The finite population correction (FPC) factor is often used to adjust variance estimators for survey data sampled from a finite population without replacement. As a replicated resampling approach, the jackknife approach is usually implemented without the FPC factor incorporated in its variance estimates. A paradigm is proposed to compare the jackknifed variance estimates with those yielded by the delta method because the delta method has the effect of the FPC factor implicitly integrated. The goal is to examine whether the grouped jackknife approach properly estimates the variance of complex samples without incorporating the FPC effect, in particular for data sampled from a finite population with a high sampling rate. The investigation focuses on the data drawn by two‐stage sampling with probability proportional to size of schools and with simple random sampling of students. Moreover, the Hájek approximation of the joint probabilities is used in the delta method for a Horvitz–Thompson (H–T) estimator. Samples of the National Assessment of Educational Progress (NAEP) state science assessments are used in the analysis.

Chronic Spinal Pain and Financial Worries in the US Adult Population.

Epidemiological study based on cross-sectional data of a representative sample. To determine whether financial worries are associated with chronic spinal pain in the US adult population. This study used data from the US 2015 National Health Interview Survey. The sample size was 33,672 and the study population is defined as aged 18 to 85 years. To account for the complex sampling design, the Taylor linearized variance estimation method was used. Spinal pain was defined in two ways: chronic low back pain and neck pain, chronic low back pain and/or neck pain. Eight types of financial worries were assessed: paying monthly bills, maintaining standard of living, credit card payments, paying rent/mortgage/housing costs, medical costs for healthcare, money for retirement, medical costs of illness/accident, and paying for children's college. Different types of financial worries were significantly associated with chronic spinal pain, controlling for demographic characteristics and socioeconomic status. These worries included paying monthly bills (odds ratio [OR] 2.5), maintaining standard of living (OR 2.5), credit card payments (OR 2.2), paying rent/mortgage/housing costs (OR 2.2), medical costs for healthcare (OR 2.2), money for retirement, (OR 2.3), medical costs of illness/accident (OR 2.2), and paying for children's college (OR 1.4). This study shows that financial worries were significantly associated with chronic spinal pain. Financial worries may be important to be taken into consideration by clinicians managing patients with spinal pain. More future research is needed to explore the association between financial worries and spinal pain. 3.

Weight fused functional sliced average variance estimation

Selecting the number of slice is a key step for the implement of the sliced average variance estimation (SAVE) method. To our knowledge, there is no widely accepted method for it in a practical application. And an incorrect number of the slice may leads to an inaccurate conclusion. In traditional multivariate sufficient dimension reduction procedure, it is usually to adopt the fuze approach which combined the kernel operators of SAVE with various numbers of slices to solve this problem. Due to the infinite dimension in functional data, the fuze approach can not be directly applied to functional SAVE (FSAVE). Hence we propose a novel fused approach which based on a weighted kernel operator of FSAVE that named as the approach weight fused FSAVE (WFFSAVE). Simulation studies show that the WFFSAVE method performs better than FSAVE. And we also apply this new method to the Tecator data set.

Semiparametric Estimation in Continuous-Time: Asymptotics for Integrated Volatility Functionals with Small and Large Bandwidths

This article studies the estimation of integrated volatility functionals, which is a semiparametric two-step estimation problem in the nonstationary continuous-time setting. We generalize the asymptotic normality results of Jacod and Rosenbaum to a wider range of bandwidths. Moreover, we employ matrix calculus to obtain a new analytical bias correction and variance estimation method. The proposed method gives more succinct expressions than the element-by-element analytical method of the above cited article. In addition, it has a computational advantage over the jackknife/simulation-based method proposed by Li, Liu, and Xiu. Comprehensive simulation studies demonstrate that our method has good finite sample performance for a variety of volatility functionals, including quadraticity, determinant, continuous beta, and eigenvalues.

Robust filtering employing bias compensated M‐estimate affine‐projection‐like algorithm

This Letter presents a bias compensated M-estimate affine-projection-like algorithm for robust adaptive filtering in case of noisy input signal and impulsive noise interference. In order to mitigate the effect of bias introduced due to noisy input signal, a bias compensation vector is derived along with robust cost function minimisation employing M-estimate and accordingly the weight update learning process of the adaptive filter has been improved. In conjunction with this, a new input noise variance estimation method is introduced using the median filter. The proposed algorithm is evaluated for acoustic echo cancellation application and compared with other existing methods. Simulation results demonstrate its effectiveness in terms of enhanced convergence and better steady-state performance in case of impulsive environment and input signal contaminated with noise.

Variable selection and estimation for high‐dimensional spatial autoregressive models

AbstractSpatial regression models are important tools for many scientific disciplines including economics, business, and social science. In this article, we investigate postmodel selection estimators that apply least squares estimation to the model selected by penalized estimation in high‐dimensional regression models with spatial autoregressive errors. We show that by separating the model selection and estimation process, the postmodel selection estimator performs at least as well as the simultaneous variable selection and estimation method in terms of the rate of convergence. Moreover, under perfect model selection, the ℓ2 rate of convergence is the oracle rate of , compared with the convergence rate of in the general case. Here, n is the sample size and p, s are the model dimension and number of significant covariates, respectively. We further provide the convergence rate of the estimation error in the form of norm, and ideally the rate can reach as fast as .

Joint adjustment by CPIII precision trigonometric elevation control network assisted with precision levelling observation

Using the precision trigonometric elevation instead of the precision levelling to build a CPⅢ elevation control network will greatly increase the speed of CPⅢ control network construction. However, the accuracy of CPIII precision trigonometric elevation control network is still difficult to reach the level of CPⅢ precision levelling network. Based on the existing parameter method, this paper introduces some precision levelling for joint adjustment, and uses Helmert’s variance estimation method to perform strict weight determination. Our experiments show that when the number of precision levelling participating in the joint adjustment exceeds 1/3 of the total number of CPⅢ precision levelling network observations, the accuracy of the CPIII precision trigonometric elevation control network can be effectively improved.

Financial development and health care expenditure in Sub Saharan Africa Countries

The study aimed to examine the relationship between financial development and health care expenditure in 46 Sub Saharan Africa (SSA) countries. The paper argues that health care expenditure is a key transmission mechanism through which financial development influences better health outcomes. The study used random and fixed effects as well as instrumental variable estimation methods using data from 1995 to 2014. The results showed that financial development leads to increased health care expenditure. In terms of policy implications, the findings underscore the need to foster financial development in SSA economies to assist with domestic resource mobilisation to finance health care expenditure.

Estructura interna de una medida breve de inteligencia emocional en estudiantes mexicanos de ciencias de la salud

ObjectiveTo obtain evidence on the internal structure of a brief emotional intelligence scale in Mexican health sciences students. MethodA total of 221 students (66.1% women) from 4 health sciences degrees were evaluated with the EQ-i-M20. An exploratory structural equation modeling was carried out, with the weighted least square mean and variance (WLSMV) estimation method and geomin rotation. The reliability of the construct was evaluated using the omega coefficient. ResultsThe original structure of 5 factors obtained satisfactory fit indices, as well as an expected grouping of the items in their theoretical factors. Similarly, adequate reliability coefficients were obtained. ConclusionThe structure of the EQ-i-M20 is favourably replicated in Mexican university students. The practical implications of the findings are discussed.

Safety surveillance and the estimation of risk in select populations: Flexible methods to control for confounding while targeting marginal comparisons via standardization.

We consider the critical problem of pharmacosurveillance for adverse events once a drug or medical product is incorporated into routine clinical care. When making inference on comparative safety using large-scale electronic health records, we often encounter an extremely rare binary adverse outcome with a large number of potential confounders. In this context, it is challenging to offer flexible methods to adjust for high-dimensional confounders, whereas use of the propensity score (PS) can help address this challenge by providing both confounding control and dimension reduction. Among PS methods, regression adjustment using the PS as a covariate in an outcome model has been incompletely studied and potentially misused. Previous studies have suggested that simple linear adjustment may not provide sufficient control of confounding. Moreover, no formal representation of the statistical procedure and associated inference has been detailed. In this paper, we characterize a three-step procedure, which performs flexible regression adjustment of the estimated PS followed by standardization to estimate the causal effect in a select population. We also propose a simple variance estimation method for performing inference. Through a realistic simulation mimicking data from the Food and Drugs Administration's Sentinel Initiative comparing the effect of angiotensin-converting enzyme inhibitors and beta blockers on incidence of angioedema, we show that flexible regression on the PS resulted in less bias without loss of efficiency, and can outperform other methods when the PS model is correctly specified. In addition, the direct variance estimation method is a computationally fast and reliable approach for inference.

Long-term trends in the ionospheric response to solar extreme-ultraviolet variations

Abstract. The thermosphere–ionosphere system shows high complexity due to its interaction with the continuously varying solar radiation flux. We investigate the temporal and spatial response of the ionosphere to solar activity using 18 years (1999–2017) of total electron content (TEC) maps provided by the international global navigation satellite systems service and 12 solar proxies (F10.7, F1.8, F3.2, F8, F15, F30, He II, Mg II index, Ly-α, Ca II K, daily sunspot area (SSA), and sunspot number (SSN)). Cross-wavelet and Lomb–Scargle periodogram (LSP) analyses are used to evaluate the different solar proxies with respect to their impact on the global mean TEC (GTEC), which is important for improved ionosphere modeling and forecasts. A 16 to 32 d periodicity in all the solar proxies and GTEC has been identified. The maximum correlation at this timescale is observed between the He II, Mg II, and F30 indices and GTEC, with an effective time delay of about 1 d. The LSP analysis shows that the most dominant period is 27 d, which is owing to the mean solar rotation, followed by a 45 d periodicity. In addition, a semi-annual and an annual variation were observed in GTEC, with the strongest correlation near the equatorial region where a time delay of about 1–2 d exists. The wavelet variance estimation method is used to find the variance of GTEC and F10.7 during the maxima of the solar cycles SC 23 and SC 24. Wavelet variance estimation suggests that the GTEC variance is highest for the seasonal timescale (32 to 64 d period) followed by the 16 to 32 d period, similar to the F10.7 index. The variance during SC 23 is larger than during SC 24. The most suitable proxy to represent solar activity at the timescales of 16 to 32 d and 32 to 64 d is He II. The Mg II index, Ly-α, and F30 may be placed second as these indices show the strongest correlation with GTEC, but there are some differences in correlation during solar maximum and minimum years, as the behavior of proxies is not always the same. The indices F1.8 and daily SSA are of limited use to represent the solar impact on GTEC. The empirical orthogonal function (EOF) analysis of the TEC data shows that the first EOF component captures more than 86 % of the variance, and the first three EOF components explain 99 % of the total variance. EOF analysis suggests that the first component is associated with the solar flux and the third EOF component captures the geomagnetic activity as well as the remaining part of EOF1. The EOF2 captures 11 % of the total variability and demonstrates the hemispheric asymmetry.

Improving GPS positioning accuracy using weighted Kalman Filter and variance estimation methods

Accurate positioning plays a crucial role in the navigation of moving objects. This paper introduces a new, fast, and accurate GPS positioning algorithm using weighting Kalman Filter (KF) based on the variance estimation method. The proposed method is evaluated using three different motion scenarios, including straight movement in the air with a velocity of 90 m/s and circular movement with velocities of 100 m/s and 500 m/s. The experimental results demonstrate that using the suggested method, the positioning accuracy for all three scenarios increases up to 30 percent as compared to two predominant methods (i.e., recursive least squares and KF).

Financial Development and Health Outcomes in Sub-Saharan African Countries

Sub-Saharan African (SSA) countries are faced with health human capital challenges that include high child mortality rates, low life expectancy and disease burden due to challenges in health care financing among other factors. The study sought to determine the effect of financial development on child health outcomes and life expectancy in Sub-Saharan Africa (SSA) countries. It posits that financial development leads to improved health outcomes through several causal channels that include income, education, credit access and risk management. The financial development variables used in the study aimed to capture access and depth dimensions of a financial sector and understand their respective impact on health outcomes. Financial access was measured using the number of ATMS and commercial bank branches per 100 000 people. Broad money and bank credit to private sector to GDP ratios were used to measure financial depth. In addition to the financial development variables, the study controlled for the effects of access to basic infrastructure, real GDP per capita, education level and health system financing mechanisms among other variables using a health production function approach. The study used random and fixed effects as well instrumental variable estimation methods. The regression analysis was carried out using data from 1995 to 2014 for 46 SSA countries. The results of both the random and fixed effects as well as the 2SLS estimation approaches confirmed our hypothesis that financial development leads to better health outcomes. The results showed that financial development leads to a reduction in under-five years' mortality rate as well as increasing life expectancy. Other variables which are statistically significant include real GDP per capita, level of education, access to basic infrastructure and health financing mechanism. These findings imply that policy makers must craft and implement policies that promote financial development in order improve national health outcomes. The policies must aim at both deepening and widening of the financial sector to ensure inclusive financial development. Other policies must aim at promoting economic growth, infrastructure and promoting prepaid health financing systems.