Traditional Maximum Likelihood Research Articles

Optimal Subsampling for Functional Quasi-Mode Regression with Big Data

We propose investigating optimal subsampling for functional regression with massive datasets based on the mode value, which is referred to as functional quasi-mode regression, to reduce data volume and alleviate computational burden. Utilizing data-adaptive weights derived from regression residuals, the suggested regression offers enhanced robustness against non-normal errors compared to traditional least squares or maximum likelihood estimation methods. To estimate the model, we employ B-spline basis functions to approximate the functional coefficient and include a penalty term in the objective function for enforcing smoothness in the resulting estimator. We adopt a computationally efficient mode-expectation-maximization algorithm, augmented by a Gaussian kernel, for numerical estimation. Under mild regularity conditions, we derive the asymptotic distributions of both full data and subsample quasi-mode estimators. The optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under A- and L-optimality criteria are identified. These optimal probabilities rely on the full data estimate, prompting the development of a two-step algorithm to approximate the optimal subsampling procedure. The resultant algorithm is processing-efficient and can significantly reduce computational time compared to the full data approach. We also establish the asymptotic normality of the quasi-mode estimator obtained through this two-step algorithm. To assess finite sample performance, we conduct Monte Carlo simulations and analyze air quality data, showcasing the effectiveness of the developed estimator. Supplemental materials for this paper are available online.

HBMIRT: A SAS macro for estimating uni- and multidimensional 1- and 2-parameter item response models in small (and large!) samples

Item response theory (IRT) has evolved as a standard psychometric approach in recent years, in particular for test construction based on dichotomous (i.e., true/false) items. Unfortunately, large samples are typically needed for item refinement in unidimensional models and even more so in the multidimensional case. However, Bayesian IRT approaches with hierarchical priors have recently been shown to be promising for estimating even complex models in small samples. Still, it may be challenging for applied researchers to set up such IRT models in general purpose or specialized statistical computer programs. Therefore, we developed a user-friendly tool – a SAS macro called HBMIRT – that allows to estimate uni- and multidimensional IRT models with dichotomous items. We explain the capabilities and features of the macro and demonstrate the particular advantages of the implemented hierarchical priors in rather small samples over weakly informative priors and traditional maximum likelihood estimation with the help of a simulation study. The macro can also be used with the online version of SAS OnDemand for Academics that is freely accessible for academic researchers.

Assessing forest cover changes in Dak Lak province (Central Highlands of Vietnam) from multi-temporal Landsat data and machine learning techniques

Dak Lak is a province in the Central Highlands region of Vietnam, with a large area of forests and forestry land. However, the forest cover has changed dramatically in recent times due to the influence of human activities and climate change. This article presents the results of assessing forest cover changes in Dak Lak province from Landsat satellite image data for the period 2000 – 2020. Three Landsat satellite image scenes, including Landsat 5 TM images taken in March 2000 and February 2010 and Landsat 8 OLI image taken in February 2020 are used to classify forest cover. Three common machine learning techniques, including Random Forest (RF), Support Vector Machine (SVM), Classification and Regression Tree (CART) and the traditional maximum likelihood classification algorithm are used to classify forest cover in the study area, thereby choosing the method with the highest accuracy. The results show that the RF algorithm has the highest accuracy in classifying forest cover from multi-temporal Landsat images by comparing the overall accuracy value and the Kappa coefficient. The obtained results are used to build forest cover change maps in the period 2000 - 2010, 2010 - 2020 and 2000 - 2020. The results received in the study provide information to help managers in monitoring and protecting forest resources.

Joint estimation model for FSO channel parameters and performance evaluation based on CNNs.

Free space optical (FSO) communication systems experience turbulence-induced fading. As a possible solution, adaptive transmission, which adjusts transmitter parameters based on instantaneous channel state information (CSI), can be used. Most of the existing channel estimation methods ignore the impact of detection noise at the receiver, which will lead to additional estimation errors. In this paper, a joint estimation model based on convolutional neural networks (CNNs) is proposed to estimate detection noise and turbulence fading parameters. We obtained turbulence channel simulation data sets considering the background of detection noise based on the edge probability distribution function of the receive signal. The training of the CNN estimator is carried out through maximum pooling, adaptive learning rate, and regularization, ultimately accurately estimating channel characteristics based on the optimal output results of the network. The simulation results show that the proposed CNN joint estimator performs better in high-detection-noise environments compared with traditional maximum likelihood estimators, and it has better generalization ability in different real atmospheric environments.

A Novel OFDM-Based Time Domain Quadrature GSM for Visible Light Communication System

In order to improve the spectral efficiency (SE) as well as the receiver performance of band-limited visible light communications (VLCs), two orthogonal frequency division multiplexing (OFDM)-based quadrature generalized multiple-input multiple-output (QG-MIMO) transmission schemes, including time domain (TD) quadrature generalized spatial modulation (TD-QGSM) and TD quadrature generalized spatial multiplexing (TD-QGSMP), are proposed in this paper. Firstly, the constellation symbols in the frequency domain are split into in-phase and quadrature components to perform the OFDM modulation separately. Then, the corresponding time domain signal is spatially mapped on different light emitting diodes (LEDs) for achieving the diversity or multiplexing. In addition, we also propose an illegal vector correction (IVC)-based orthogonal matching pursuit (OMP) detection algorithm to deal with the error propagation and noise amplification effect, where a novel correction criterion is involved for assisting the index vectors estimation and thus for improving the demodulation performance. The simulation results demonstrate that the SE can be significantly improved by the proposed schemes as compared with the existing OFDM-based generalized MIMO schemes, with the TD-QGSM increasing by at least 56.5% and the TD-QGSMP increasing by at least 72.3%. Moreover, the bit error rate (BER) performance can be further improved when applying the proposed IVC-OMP detection method, which outperforms the traditional maximum-likelihood and maximum ratio combining (ML-MRC) detection by at least 62.5%.

Comparison of accuracy and reliability of random forest, support vector machine, artificial neural network and maximum likelihood method in land use/cover classification of urban setting

Accurate land use and land cover (LULC) is crucial for sustainable urban planning and for many scientific researches. However, the demand for accurate LULC maps is increasing; it is required to compare the classification algorithms to choose the best one. Though, machine and deep learning algorithms are widely used across the world their application is limited in Bangladesh. Accurate urban LULC mapping is challenging because urban heterogeneity affects image classification models in specific feature extraction. In this research, the accuracy of machine learning algorithms (MLA) of RF (Random Forest), SVM (Support Vector Machine), deep learning algorithm (DLA) of ANN (Artificial Neural Network) and traditional Maximum Likelihood (MaxL) method was compared in LULC classification of Dhaka city. Model accuracy of MLA and DLA was tested by statistical indices of sensitivity, specificity, precision, recall F1 etc. There is a high correlation between SVM and ANN models were found. The overall accuracy of the maps was 0.93, 0.94, 0.91 and 0.95 and kappa was 0.89, 0.91, 0.86 and 0.93 for the MaxL, RF, SVM and ANN models respectively. The user accuracy and producer accuracy largely varied according to LULC classes in the applied models. The lowest accuracy of the models was found for bare land classification followed by built-up and vegetation. The high mixture of LULC classes affects the accuracy of built up and bare land classification which produces the lowest accuracy in the MaxL model. The findings indicate that the most accurate and reliable model for urban LULC classification was the ANN model.

Iteratively Reweighted Least Squares Method for Estimating Polyserial and Polychoric Correlation Coefficients

An iteratively reweighted least squares (IRLS) method is proposed for the estimation of polyserial and polychoric correlation coefficients in this article. It calculates the slopes in a series of weighted linear regression models fitting on conditional expected values. For polyserial correlation, conditional expectations of the latent predictor is derived from the observed ordinal categorical variable, and the regression coefficient is obtained with the weighted least squares method. In estimating polychoric correlation coefficient, conditional expectations of the response variable and the predictor are updated in turns. Standard errors of the estimators are obtained using the delta method based on data summaries instead of the whole data. Conditional univariate normal distribution is exploited and a single integral is numerically evaluated in the proposed algorithm, comparing to the double integral computed numerically based on the bivariate normal distribution in the traditional maximum likelihood (ML) approaches. This renders the new algorithm very fast in the estimation of both polyserial and polychoric correlation coefficients. Thorough simulation studies are conducted to compare the performances of the proposed method with the classical ML methods. Real data analyses illustrate the advantage of the new method in computing speed. Supplementary materials for this article are available online.

A simulation study on the insurance claims distribution using Weibull distribution

<p style="text-align:justify"><span style="font-size:10.5pt"><span style="font-family:等线"><span dir="ltr" lang="EN-US" style="font-family:"Cambria",serif"><span style="color:black">The Weibull distribution is extensively useful in the field of finance, insurance and natural disasters. Recently, It has been considered as one of the most frequently used statistical distributions in modelling and analyzing stock pricing movement and uncertain prediction in financial and investment data sets, such as insurance claims distribution. It is well known that the Bayes estimators of the two-parameter Weibull distribution do not have a compact form and the closed-form expression of the Bayes estimators cannot be obtained. In this paper and the Bayesian setting, it is assumed that the scale parameter of the Weibull model has a gamma prior under the assumption that its shape parameter is known. A simulation study is performed using random claims amount to compare the performance of the Bayesian approach with traditional maximum likelihood estimators in terms of Root Mean Square Errors (RMSE) and Mean Absolute Error (MAE) for different sample sizes, with specific values of the scale parameter and shape parameters. The results have been compared with the estimated result via the maximum likelihood method. The result revealed that the Bayesian approach behaves similarly to the maximum likelihood method when the sample size is small. Nevertheless, in all cases for both methods, the RMSE and MAE decrease as the sample size increases. Finally, applications of the proposed model to the insurance claim data set have been presented.</span></span></span></span></p>

A k-mer-Based Approach for Phylogenetic Classification of Taxa in Environmental Genomic Data.

In the age of genome sequencing, whole-genome data is readily and frequently generated, leading to a wealth of new information that can be used to advance various fields of research. New approaches, such as alignment-free phylogenetic methods that utilize k-mer-based distance scoring, are becoming increasingly popular given their ability to rapidly generate phylogenetic information from whole-genome data. However, these methods have not yet been tested using environmental data, which often tends to be highly fragmented and incomplete. Here, we compare the results of one alignment-free approach (which utilizes the D2 statistic) to traditional multi-gene maximum likelihood trees in 3 algal groups that have high-quality genome data available. In addition, we simulate lower-quality, fragmented genome data using these algae to test method robustness to genome quality and completeness. Finally, we apply the alignment-free approach to environmental metagenome assembled genome data of unclassified Saccharibacteria and Trebouxiophyte algae, and single-cell amplified data from uncultured marine stramenopiles to demonstrate its utility with real datasets. We find that in all instances, the alignment-free method produces phylogenies that are comparable, and often more informative, than those created using the traditional multi-gene approach. The k-mer-based method performs well even when there are significant missing data that include marker genes traditionally used for tree reconstruction. Our results demonstrate the value of alignment-free approaches for classifying novel, often cryptic or rare, species, that may not be culturable or are difficult to access using single-cell methods, but fill important gaps in the tree of life.

Parameter estimation of a model using maximum likelihood function and Bayesian analysis through moment of order statistics

Due to advancements in Bayesian modeling, the likelihood-free posterior estimate is now feasible. These estimation methods are crucial for a deeper understanding of simulation-based systems since it might be difficult, if not impossible, to estimate probability values. This compares the effectiveness of such updated estimate approaches to earlier maximum likelihood forecasting models and offers some adjustments to maximum likelihood estimation for estimating the parameters of the Bayesian analysis in this work. Recent improvements in Bayesian modeling have made it feasible to obtain the likelihood-free posterior estimate. These estimate methods are essential for evaluating simulation-based theories since it might be difficult, if not impossible, to determine probability values. Simulation-based concepts such as the Leaky Competing Accumulator (LCA) theory and Feed-Forward Inhibition (FFI) theory have not yet benefited from Bayesian techniques. As assessment criteria, total relative deviation (TRD), total mean square error (TMSE), and Stein Loss Function (SLF) are used. Maximum likelihood (ML) estimates are modified because the original statistic's Cumulative Distribution Function (CDF) is better than traditional ML estimations and other modified estimators emphasize average and coefficient variability. Prior estimator performance was unaffected by response rate or real parameter settings. These systems have not been formally evaluated by the Bayesian factor.

Recurrent neural network based parameter estimation of Hawkes model on high-frequency financial data

This study examines the use of a recurrent neural network for estimating the parameters of a Hawkes model based on high-frequency financial data, and subsequently, for computing volatility. Neural networks have shown promising results in various fields, and interest in finance is also growing. Our approach demonstrates significantly faster computational performance compared to traditional maximum likelihood estimation methods while yielding comparable accuracy in both simulation and empirical studies. Furthermore, we demonstrate the application of this method for real-time volatility measurement, enabling the continuous estimation of financial volatility as new price data keeps coming from the market.

A Computationally Efficient Direct Position Determination Algorithm Based on OFDM System

Based on the orthogonal frequency division multiplexing (OFDM) system, a computationally attractive implementation for the traditional single source maximum likelihood (SML) direct position determination (DPD) algorithm is proposed. The proposed algorithm implements fast Fourier transform (FFT) to the received frequency-domain signals after deconvolution. Then, the cost function for all points can be obtained from the same FFT output set. As a consequence, some repeated calculation in the traditional SML DPD algorithm is avoided. Simulation results demonstrate that the proposed modified SML DPD algorithm can achieve a comparable performance to traditional SML-DPD while significantly reducing the computational complexity.

On Fitting the Lomax Distribution: A Comparison between Minimum Distance Estimators and Other Estimation Techniques

In this paper, we investigate the performance of a variety of frequentist estimation techniques for the scale and shape parameters of the Lomax distribution. These methods include traditional methods such as the maximum likelihood estimator and the method of moments estimator. A version of the maximum likelihood estimator adjusted for bias is included as well. Furthermore, an alternative moment-based estimation technique, the L-moment estimator, is included, along with three different minimum distance estimators. The finite sample performances of each of these estimators are compared in an extensive Monte Carlo study. We find that no single estimator outperforms its competitors uniformly. We recommend one of the minimum distance estimators for use with smaller samples, while a bias-reduced version of maximum likelihood estimation is recommended for use with larger samples. In addition, the desirable asymptotic properties of traditional maximum likelihood estimators make them appealing for larger samples. We include a practical application demonstrating the use of the described techniques on observed data.

New Cure Rate Survival Models Generated by Poisson Distribution and Different Regression Structures with Applications to Cancer Data Set

A new cure rate model is presented by assuming that, conditional on η , the number of competing causes of the event of interest follows the Poisson distribution, where η is assumed a random variable with gamma and generalized exponential distributions. For the time-to-event of the concurrent causes, we assumed the recently introduced truncated Nadarajah–Haghighi model. The model is parameterized directly in terms of the cure term, and then different symmetric and asymmetric link functions are used to assess the effects of covariates, such as logit, probit, log-log, Cauchit, Aranda-Ordaz, skewed probit, and skewed logit. Parameters estimation for the model is approached based on the traditional maximum likelihood estimation method. We achieve a simulation study in order to investigate the performance of these estimators under different scenarios. Finally, the model is illustrated in data sets related to two kinds of cancers (melanoma and colon cancer).

Hierarchical Covariance Estimation Approach to Meta-Analytic Structural Equation Modeling

We present a fully Bayesian approach to meta-analytic SEM based on hierarchical modeling of sample covariance matrices. The approach allows for flexible models that would not be identified under a traditional maximum likelihood approach. The approach allows for the inclusion of moderators, produces a global fit index, and permits the investigation of local misspecification. Simulation-based calibration studies show that the Bayesian computation procedure produces valid inferences for commonplace meta-analytic SEM applications. We demonstrate the approach with diverse data analysis examples and provide accompanying R code to support adoption and additional study of the approach. Finally, we lay out proposals that have the potential to extend the approach to accommodate the wide variety of analyses and data conditions that comprise meta-analytic SEM applications.

Application of Discriminative Training Algorithm Based on Intelligent Computing in English Translation Evaluation

Abstract Aiming at the higher correlation between the objective evaluation of computer English speech and the subjective evaluation of experts, an acoustic model based on discriminative training is proposed to improve the confidence score of objective evaluation. First, the process of obtaining the pronunciation quality evaluation score of the speech vector by the forced matching algorithm is introduced, and then the mathematical theory of hypothesis testing is used to prove that the acoustic model trained based on the discriminative algorithm ‘minimum phoneme error’ is more effective than the acoustic model based on the traditional maximum likelihood algorithm. Confidence scores close to subjective assessments are obtained. By calculating the correlation coefficient of the subjective and objective evaluation results, the experiment verifies that the speech evaluation system using the discriminative acoustic model can give a higher confidence score and proposes a data selection method based on dynamic weighting, which is applied to continuous speech recognition in the discriminative training of the acoustic model. This method combines the posterior probability and the phoneme accuracy rate to select the data. First, the Beam algorithm of the posterior probability is used to trim the word graph. On this basis, according to the error rate of the candidate path where the candidate word is located, the probability dynamically assigns different weights to the candidate words; second, by calculating the confusion degree between the phoneme pairs, different penalty weights is dynamically added to the easily confused phoneme pairs to calculate the phoneme accuracy; finally, the expected accuracy of the obtained arc is calculated on the basis of the probability distribution. The Gaussian function is used to softly weight the expected phoneme accuracy of all competing arcs. The experimental results show that compared with the minimum phoneme error criterion, the dynamic weighting method has higher recognition accuracy and can effectively reduce the training time.

Age- and sex-specific survivorship of the Southern Hemisphere long-finned pilot whale (Globicephala melas edwardii).

Biodiversity loss is a major global challenge of the 21st century. Ultimately, extinctions of species are determined by birth and death rates; thus, conservation management of at-risk species is dependent on robust demographic data. In this study, data gathered from 381 (227 females, 154 males) long-finned pilot whales (Globicephala melas edwardii) that died in 14 stranding events on the New Zealand coast between 2006 and 2017 were used to construct the first age- and sex-specific life tables for the subspecies. Survivorship curves were fitted to these data using (1) a traditional maximum likelihood approach, and (2) Siler's competing-risk model. Life table construction and subsequent survival curves revealed distinct differences in the age- and sex-specific survival rates, with females outliving males. Both sexes revealed slightly elevated rates of mortality among the youngest age-classes (<2 years) with postweaning mortality rates decreasing and remaining relatively low until the average life expectancy is reached; 11.3 years for males and 14.7 years for females. Overall (total) mortality is estimated to be 8.8% and 6.8% per annum for males and females, respectively. The mortality curve resembles that of other large mammals, with high calf mortality, lower postweaning mortality, and an exponentially increasing risk of senescent mortality. An accelerated mortality rate was observed in mature females, in contrast to the closely related short-finned pilot whale (G. macrorhynchus), which selects for an extension to the postreproductive life span. The reason for the observed differences in the mortality rate acceleration and postreproductive life span between the two pilot whale species have not been established and warrant further investigation. Obtaining robust information on the life history of long-lived species is challenging, but essential to improve our understanding of population dynamics and help predict how future pressures may impact populations. This study illustrates how demographic data from cetacean stranding events can improve knowledge of species survival rates, thus providing essential information for conservation management.

Comparing Four Machine Learning Algorithms for Land Cover Classification in Gold Mining: A Case Study of Kyaukpahto Gold Mine, Northern Myanmar

Numerous studies have been undertaken to determine the optimal land use/cover classification algorithm. However, there have not been many studies that have compared and evaluated the performance of maximum likelihood (ML), random forest (RF), support vector machine (SVM), and classification and regression trees (CART) using ASTER imagery, especially in a mining district. Therefore, this study aims to investigate land use/cover (LULC) change over three decades (1990–2020), comparing the performance of the ML, RF, SVM, and CART machine learning algorithms. The Landsat and ASTER data were retrieved using Google Earth Engine (GEE). Traditional ML classification was performed on ArcGIS 10.2 software while RF, SVM, and CART classification were undertaken on GEE. Then, thematic accuracy assessments were conducted for the four algorithms and their performances were compared. The results showed that the largest changes in area occurred in forest cover that decreased from 37.8 to 27.3 km2 during the three decades. The remarkable expansion of gold mining occurred during 2005–2010 with the increases of 1.6%. The mining land rose by 2.9% during the study period whereas agricultural land increased significantly by 10.7% between 1990 and 2020. When comparing the four algorithms, the RF algorithm gives the highest accuracy with an overall accuracy of 95.85% while SVM follows RF with 91.69%. This study proved that RF is the best choice for optimal land use/cover classification, particularly in the mining district.

Risk preferences, gender effects and Bayesian econometrics

Gender differences in decision making is a topic that has attracted much attention in the literature and the debate seems to be inconclusive. A method that is often used in the economics literature to account for gender effects is by estimating econometric structural models and testing the significance of the estimated parameters. In this paper we focus on estimations of preference models and we show how omitting to account for behavioural heterogeneity can lead to failures in identifying potential differences. Using data from risky choice experiments, we compare the traditional representative agent Maximum Likelihood Estimation approach against two more flexible inference methods that allow for heterogeneity at the individual level, the Maximum Simulated Likelihood Estimation, and the Hierarchical Bayesian modelling. We show how ignoring heterogeneity may lead to failures capturing gender differences and we suggest the use of Bayesian modelling to effectively estimate the underlying parameters.

Bootstrap-based inferential improvements to the simplex nonlinear regression model.

In this paper we evaluate the performance of point and interval estimators based on the maximum likelihood(ML) method for the nonlinear simplex regression model. Inferences based on traditional maximum likelihood estimation have good asymptotic properties, but their performance in small samples may not be satisfactory. At out set we consider the maximum likelihood estimation for the parameters of the nonlinear simplex regression model, and so we introduced a bootstrap-based correction for such estimators of this model. We also develop the percentile and bootstrapt confidence intervals for those parameters as competitors to the traditional approximate confidence interval based on the asymptotic normality of the maximum likelihood estimators (MLEs). We then numerically evaluate the performance of these different methods for estimating the simplex regression model. The numerical evidence favors inference based on the bootstrap method, in special the bootstrapt interval, which was decisive in an application to real data.