Weighted Maximum Likelihood Estimation Research Articles

Inverse probability of treatment weighting with generalized linear outcome models for doubly robust estimation.

There are now many options for doubly robust estimation; however, there is a concerning trend in the applied literature to believe that the combination of a propensity score and an adjusted outcome model automatically results in a doubly robust estimator and/or to misuse more complex established doubly robust estimators. A simple alternative, canonical link generalized linear models (GLM) fit via inverse probability of treatment (propensity score) weighted maximum likelihood estimation followed by standardization (the -formula) for the average causal effect, is a doubly robust estimation method. Our aim is for the reader not just to be able to use this method, which we refer to as IPTW GLM, for doubly robust estimation, but to fully understand why it has the doubly robust property. For this reason, we define clearly, and in multiple ways, all concepts needed to understand the method and why it is doubly robust. In addition, we want to make very clear that the mere combination of propensity score weighting and an adjusted outcome model does not generally result in a doubly robust estimator. Finally, we hope to dispel the misconception that one can adjust for residual confounding remaining after propensity score weighting by adjusting in the outcome model for what remains 'unbalanced' even when using doubly robust estimators. We provide R code for our simulations and real open-source data examples that can be followed step-by-step to use and hopefully understand the IPTW GLM method. We also compare to a much better-known but still simple doubly robust estimator.

A new approach for semi-parametric regression analysis of bivariate interval-censored outcomes from case-cohort studies

Interval-censored failure time data frequently occur in many areas and a great deal of literature on their analyses has been established. In this article, we discuss the situation where one faces bivariate interval-censored data arising from case-cohort studies, which are commonly used as a tool to save costs when disease incidence is low and covariates are difficult to obtain. For this problem, a class of copula-based semi-parametric models is presented and for estimation, a sieve weighted maximum likelihood estimation procedure is developed. The resulting estimators of regression parameters are shown to be strongly consistent and asymptotically normal. Furthermore, the proposed method is generalized to the situation of non rare diseases. A simulation study is conducted to assess the finite sample performance of the proposed method and suggests that it performs well in practice.

Bayesian improved cross entropy method for network reliability assessment

We identify the zero count problem (or overfitting) of cross-entropy-based methods in the context of network reliability assessment, and propose a consistent Bayesian estimator that mitigates this issue. Thereby, we derive the posterior predictive distribution of importance sampling distribution parameters that replaces the weighted maximum likelihood estimation employed in the standard cross entropy optimization. For rare event estimation, we embed the Bayesian estimator into the improved cross entropy (iCE) method and provide theoretical insights into the adaptive selection of intermediate target distributions in the iCE. The modified version of the iCE, termed the Bayesian iCE (BiCE), is proved to be unbiased. By contrast, even with higher computational cost, the standard iCE method is often significantly biased when solving network reliability problems. Our numerical investigations indicate that a uniform prior in the proposed BiCE method performs suboptimally, and an informative symmetric Dirichlet prior is suggested.

Spatial dynamic panel models with missing data

Missing data are a common problem that researchers face in practice. In this article, we focus on the missing response problem for a spatial dynamic panel data (SDPD) model, which allows for both spatial and temporal dependencies. A logistic regression with a set of prespecified covariates is used to model the missingness mechanism, which is assumed to be missing at random (MAR). A weighted maximum likelihood estimator (WMLE) is proposed for parameter estimation in the presence of incomplete data. The associated asymptotic properties are investigated. Thereafter, we develop a novel imputation method, which makes use of the information from spatial dependence, temporal dependence and exogenous regression covariates. Lastly, the performance of WMLE and the proposed imputation method are demonstrated by both simulation studies and a real data example.

Estimation Curve of Mixed Spline Truncated and Fourier Series Estimator for Geographically Weighted Nonparametric Regression

Geographically Weighted Regression (GWR) is the development of multiple linear regression models used in spatial data. The assumption of spatial heterogeneity results in each location having different characteristics and allows the relationships between the response variable and each predictor variable to be unknown, hence nonparametric regression becomes one of the alternatives that can be used. In addition, regression functions are not always the same between predictor variables. This study aims to use the Geographically Weighted Nonparametric Regression (GWNR) model with a mixed estimator of truncated spline and Fourier series. Both estimators are expected to overcome unknown data patterns in spatial data. The mixed GWNR model estimator is then determined using the Weighted Maximum Likelihood Estimator (WMLE) technique. The estimator’s characteristics are then determined. The results of the study found that the estimator of the mixed GWNR model is an estimator that is not biased and linear to the response variable y.

A comparative study for parameter estimation of the Weibull distribution in a small sample size: An application to spring fatigue failure data

The Weibull distribution is the most widely applied model in reliability analysis. The main objective of this paper is to present a simple method called the minimum discrepancy method that is applicable to both complete and censored data for the parameter estimation of the Weibull distribution and a detailed comparison in a small sample size of thirteen methods in terms of several criteria by a simulation study. Additionally, parameter estimation methods are applied to the spring fatigue failure data. By extensive simulations and comparisons, the generalized least square 1, the weighted least square 1, the weighted Maximum likelihood estimation and the minimum discrepancy method are recommended for parameter estimation with small samples.

A Modified PGA for Spaceborne SAR Scintillation Compensation Based on the Weighted Maximum Likelihood Estimator and Data Division

The P-band spaceborne synthetic aperture radar (SAR) is significantly affected by ionospheric scintillation. Although the traditional phase gradient autofocus (PGA) can estimate and compensate the scintillation phase of the single polarization SAR data, the quality of the refocused image will degrade at the scene edge. In this paper, a modified PGA based on the weighted maximum likelihood (WML) estimator and data division is proposed for full-scene image refocusing. First, a data division strategy for scintillation corrupted image is introduced, which is based on the prior scintillation information including its power spectral density (PSD) and autocorrelation function (ACF). Then, some pre-processing steps including data selection, circular shifting and windowing are performed for suppressing the noise and clutter. Finally, the scintillation phase is estimated by the WML estimator with fewer iterations, and after the scintillation phase of all data blocks are obtained, the distorted full-scene image is refocused. Using the generated wide-band ionospheric scintillation model (WBMOD) phase screen, numerical simulations based on point targets and scenes derived from real spaceborne SAR data are carried out. The evaluation results about resolution, peak side-lobe ratio (PSLR), integral side-lobe ratio (ISLR), correlation coefficient and image entropy demonstrate the effectiveness of the proposed algorithm.

Weighted Maximum Likelihood Correlation Coefficient to Handle Missing Values and Outliers in Data Set

The proposed estimator, namely weighted maximum likelihood (WML) correlation coefficient, for measuring the relationship between two variables to concern about missing values and outliers in the dataset is presented. This estimator is proven by applying the conditional probability function to take care of some missing values and pay more attention to values near the center. However, outliers in the dataset are assigned a slight weight. These using techniques will give the robust proposed method when the preliminary assumptions are not met data analysis. To inspect about the quality of the proposed estimator, the six methods—WML, Pearson, median, percentage bend, biweight mid, and composite correlation coefficients—are compared the properties in two criteria, i.e. the bias and mean squared error, via the simulation study. The results of generated data are illustrated that the WML estimator seems to have the best performance to withstand the missing values and outliers in dataset, especially for the tiny sample size and large percentage of outliers regardless of missing data levels. However, for the massive sample size, the median correlation coefficient seems to have the good estimator when linear relationship levels between two variables are approximately over 0.4 irrespective of outliers and missing data levels

A novel PSO-KELM based soil liquefaction potential evaluation system using CPT and Vs measurements

Evaluation of soil liquefaction potential is an essential step in geotechnical engineering design. This study presents a novel soil liquefaction potential evaluation system using cone penetration test (CPT) and shear wave velocity test (Vs) measurements. To this end, a new hybrid machine learning model called PSO-KELM model that combines the kernel extreme learning machine (KELM) with particle swarm optimization (PSO) is developed to assess soil liquefaction potential. Then, the PSO-KELM based searching technique is adopted to search the nonlinear relationship between CRR and CPT along with Vs measurements. Finally, a new probabilistic model is developed by considering the model uncertainty and sampling bias based on weighted maximum likelihood estimation. Results demonstrate that the performance of PSO-KELM model is significantly better than that of many other machine learning methods. The cyclic stress ratio, equivalent clean sand normalized cone tip resistance, normalized friction ratio, fines content, and soil behavior type are the recommended input variables for PSO-KELM model. The combined use of CPT and Vs measurements can significantly improve the prediction accuracy since it can more fully reflect soil liquefaction phenomenon. The proposed evaluation system can improve the performance of seismic CPT (SCPT) in soil liquefaction potential evaluation.

Penerapan Model Geographically Weighted Logistic Regression Pada Data Status Kesejahteraan Masyarakat di Kalimantan Tahun 2017

Geographically Weighted Logistic Regression (GWLR) model is a regression model developed from logistic regression which is applied to spatial data. The aims of research is a GWLR model determination on dichotomous data of community welfare status based on the Human Development Index (HDI) and to find the factors influencing the probability of high welfare status of each Regency/City on Kalimantan Island in 2017. Parameters estimation of the GWLR model was done at each observation location using a weighted Maximum Likelihood Estimation (MLE) method and maximum likelihood estimator was obtained by Newton Raphson iterative method. Spatial weighting on parameter estimation was determined using Adaptive Gaussian weighting function and optimum bandwidth was determined using Generalized Cross-Validation (GCV) criterion. Based on the result of GWLR parameter testing, it was concluded that the factors influencing the probability of high welfare status of Regency/City on Kalimantan Island in 2017 were school enrollment rates (senior high school), the number of health workers, real per capita income and the open unemployment rate.

Robust ENF Estimation Based on Harmonic Enhancement and Maximum Weight Clique

We present a framework for robust electric network frequency (ENF) extraction from real-world audio recordings, featuring multi-tone ENF harmonic enhancement and graph-based optimal harmonic selection. Specifically, We first extend the recently developed single-tone ENF signal enhancement method to the multi-tone scenario and propose a harmonic robust filtering algorithm (HRFA). It can respectively enhance each harmonic component without cross-component interference, thus further alleviating the effects of unwanted noise and audio content on the much weaker ENF signal. In addition, considering the fact that some harmonic components could be severely corrupted even after enhancement, disturbing rather than facilitating ENF estimation, we propose a graph-based harmonic selection algorithm (GHSA), which finds the optimal combination of harmonic components for more accurate ENF estimation. Noticeably, the harmonic selection problem is equivalently formulated as a maximum weight clique (MWC) problem in graph theory, and the Bron-Kerbosch algorithm (BKA) is adopted in the GHSA. With the enhanced and optimally selected harmonic components, both the existing maximum likelihood estimator (MLE) and weighted MLE (WMLE) are incorporated to yield the final ENF estimation results. The proposed framework is extensively evaluated using both synthetic signals and our ENF-WHU dataset consisting of $130$ real-world audio recordings, demonstrating substantially improved capability of extracting the ENF from realistically noisy observations over the existing single- and multi-tone competitors. This work further improves the applicability of the ENF as a forensic criterion in real-world situations.

Autoregressive Model With Spatial Dependence and Missing Data

We study herein an autoregressive model with spatially correlated error terms and missing data. A logistic regression model with completely observed covariates is used to model the missingness mechanism. An autoregressive model is used to accommodate time series dependence, and a spatial error model is used to capture spatial dependence. To estimate the model, a weighted least squares estimator is developed for the temporal component, and a weighted maximum likelihood estimator is developed for the spatial component. The asymptotic properties for both estimators are investigated. The finite sample performance is assessed through extensive simulation studies. A real data example about Beijing’s PM level data is illustrated.

Testing validity inferences of science motivation questionnaire (SMQ-II) instrument: Rasch-based analysis with Indonesian secondary students

Examining science motivation is essential for science learning in the classroom, even more, science motivation is often related to students’ achievement and performance. The test of science motivation has broadly employed and some of the instrument has been translated into a local language where the instrument used. The current study explores the validity evidence of Science Motivation Questionnaire II (SMQ-II) by IRT-Rasch based analysis using Test Analysis Models ‘TAM’ Package v. 3.1-45 in R software from Indonesian context. This study reveals construct validity of SMQ-II instrument based on The Standards for Educational and Psychological Testing using Messick’s (1989) validity theories and construct validity. The data collected from 984 Indonesian middle and high school students. As result, the current study had SMQ-II validity evidence which includes (1) Dimensionality of the instrument using Exploratory Factor Analysis and Rasch-analysis likelihood ratio approach, (2) Expected A Posteriori (EAP) reliability and Weighted Maximum Likelihood Estimation (WLE) reliability, (3) Item fit and item properties, (4) Wright Map using Rasch modeling. The result of construct analysis shows that the instrument was appropriate with a theory where the construct was categorized into five dimensions, all the items of SMQ-II fit the rasch modelling, and the internal reliability of each dimension is categorized as good. In general, the current study suggests that SMQ-II instrument of Indonesian version is adequate to be implemented in Indonesia.

A Gaussian Estimation of Distribution Algorithm With Random Walk Strategies and Its Application in Optimal Missile Guidance Handover for Multi-UCAV in Over-the-Horizon Air Combat

To overcome the premature convergence caused by the ill-distribution of solutions in the basic Gaussian estimation of distribution algorithm (GEDA), this paper explores a novel GEDA variant with random walk strategies, namely RW-GEDA. In RW-GEDA, the weighted maximum likelihood estimation method is used to estimate the Gaussian distribution. The new candidates are sampled using a shifted mean to enhance exploration performance. When the algorithm stagnates, two random walk strategies, namely, Gaussian random walk and Levy walk, are activated to enrich the population diversity. Moreover, RW-GEDA is executed in an Eigen coordinate framework to promote the evolution towards the dominant region. The performance of RW-GEDA is evaluated by using the CEC 2014 test suite and compared with other top algorithms from different communities as well as promising GEDA extensions. The statistical results demonstrate the competitive performance of our proposed RW-GEDA in terms of efficiency and accuracy. In addition, RW-GEDA is applied to solve the optimal missile guidance handover problem. To fill the gap in solving this problem, a novel missile guidance advantage model is established, and the optimal missile guidance handover is determined by optimizing the control variables of unmanned combat aerial vehicles. The validity and practicability of the problem model as well as the accuracy and efficiency of RW-GEDA are demonstrated by the experimental results.

Target Speaker Localization Based on the Complex Watson Mixture Model and Time-Frequency Selection Neural Network

Common sound source localization algorithms focus on localizing all the active sources in the environment. While the source identities are generally unknown, retrieving the location of a speaker of interest requires extra effort. This paper addresses the problem of localizing a speaker of interest from a novel perspective by first performing time-frequency selection before localization. The speaker of interest, namely the target speaker, is assumed to be sparsely active in the signal spectra. The target speaker-dominant time-frequency regions are separated by a speaker-aware Long Short-Term Memory (LSTM) neural network, and they are sufficient to determine the Direction of Arrival (DoA) of the target speaker. Speaker-awareness is achieved by utilizing a short target utterance to adapt the hidden layer outputs of the neural network. The instantaneous DoA estimator is based on the probabilistic complex Watson Mixture Model (cWMM), and a weighted maximum likelihood estimation of the model parameters is accordingly derived. Simulative experiments show that the proposed algorithm works well in various noisy conditions and remains robust when the signal-to-noise ratio is low and when a competing speaker exists.

Does Lending by banks and non-banks differ? Evidence from small business financing

Non-bank loans to corporate businesses have shown a dramatic increase compared to bank loans. Despite the increasing importance of non-bank lending, the differences between loans made by different types of lenders are mostly unknown. To uncover the distinctions, the author investigates whether bank and non-bank financial institutions deal differently with information scarcity of small firms by introducing lender-borrower distance as a proxy for information availability. Using the National Survey of Small Business Finances (NSSBF) provided by the Federal Reserve Board, estimate the loan approval probability models after controlling for various borrower characteristics. The NSSBF data is collected by using stratified sampling to ensure sufficient numbers of observations for minority-owned firms. To circumvent potential bias due to the sampling method, the author follows the approach suggested by Wooldridge (1999) and estimates a weighted maximum likelihood estimation to adjust for sampling design. This paper establishes novel evidence supporting the notion that banks and non-bank financial institutions are different in their ability to deal with information scarcity. Bank loan approval probability decreases as distance to their borrowers increases, while its effect on non-bank loan approval probability is statistically insignificant, supporting the notion that non-bank lending is different from bank lending in dealing with information asymmetry.

IoT Network에서 위치 인식을 위한 가중치 방식의 최대우도방법을 이용한 하드웨어 위치인식엔진 개발 연구

IoT Network에서 위치 인식을 위한 가중치 방식의 최대우도방법을 이용한 하드웨어 위치인식엔진 개발 연구

Simplified weighting function for high dynamic range video frame formation.

High dynamic range imagery has matured from a laboratory demonstration to an integrated capability in consumer-level cameras. However, high dynamic range video has lagged in development despite the introduction of several different frame formation methodologies and system architectures. The most common formation methodology involves the calculation of a high dynamic range image from a series of rapidly bracketed frames at varying exposure levels, then through the use of a radiometric calibration, recombined utilizing a weighted maximum likelihood estimator. The ideal weighting scheme to minimize the error on final image formation has been investigated by several authors. A new nonrecursive, simplified weighting scheme is proposed that utilized only knowledge of the optical attenuation, integration time, and sensor gain. A method is developed to test the various weighting schemes for their resilience to error with limited available exposures over a wide range of exposure value offsets, a common scenario for multi-imager-based high dynamic range video systems.

Real-time online learning of Gaussian mixture model for opacity mapping

Rendering volumetric scattering in real-time is a challenge due to the complex interactions between the light and the particles in the participating media. Assuming that a ray leaving the emitter is scattered only once along its path to the sensor, we propose to represent the extinction coefficient by a Gaussian mixture model. Then the model is trained with a large number of particles colliding that ray in an online way. A low-cost updating function based on the weighted maximum likelihood estimation is derived for the weighted stepwise expectation–maximization algorithm, which is fitted into the graphics pipeline as a stage of learning. This enables all those particles to contribute to the extinction on the fly without storing and sorting them together with respect to the emitter in a geometry pass. Our approach is able to accurately reconstruct the per-pixel transmittance of the opacity map for optically thick heterogeneous media in real-time but operate in bounded memory, using the recently introduced fragment shader critical section feature of the graphics processing unit.

Weighted maximum likelihood for dynamic factor analysis and forecasting with mixed frequency data

For the purpose of forecasting key macroeconomic or financial variables from a panel of time series variables, we adopt the dynamic factor model and propose a weighted likelihood-based method for parameter estimation. The loglikelihood function is split into two parts that are weighted differently. The first part is associated with the key variables while the second part is associated with the related variables which may contribute to the forecasting of key variables. We derive asymptotic properties, including consistency and asymptotic normality, of the weighted maximum likelihood estimator. We show that this estimator outperforms the standard likelihood-based estimator in approximating the true unknown distribution of the data as well as in out-of-sample forecasting accuracy. We verify the new estimation method in a Monte Carlo study and investigate the role of different weights in different settings. In the context of forecasting gross domestic product growth, this key variable is typically observed at a low (quarterly) frequency while the supporting variables are observed at a high (monthly) frequency. We adopt a low frequency representation of the mixed frequency dynamic factor model and discuss the computational efficiencies of this approach. In our empirical study for the U.S. economy, we present improvements in nowcasting and forecasting accuracy when the weighted likelihood-based estimation procedure is adopted.