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Abstract.This study considers excess distribution estimation in iid settings. There are two ways for the estimation; the fitting to the generalized Pareto distribution and the fully non parametric estimation. The fitting estimator is justified by the approximation proven in the extreme value theory; however, the accuracy depends on how extremely large the target is. The non parametric estimator does not need an approximation and has the advantage of wide applicability. This study conducts both theoretical and numerical comparative study on excess distribution estimation. Asymptotic convergence rates of two estimators are obtained, and the mean integrated squared errors are numerically surveyed by simulation study. An illustrative example of Abisko rainfall amount is presented. [ABSTRACT FROM AUTHOR]

The Homotopy Analysis Method (HAM) is an effective technique to achieve the analytical solution of a broad range of problems, mainly with nonlinear governing equations. The solution of Pennes' bioheat equation in nonlinear form arising from the linear temperature-dependent nature of specific heat capacity of a biological tissue using the Homotopy Analysis Method has been obtained analytically and validated with the numerical results obtained from the Finite Difference Method (FDM) the first time in this study. The analysis demonstrated that considering the various values of the convergence parameter and computing the Mean Squared Error (MSR) to achieve the optimum values ensures accurate results even at the low-order approximations of the solution. Investigating the effect of the nonlinear term's magnitude on the solution indicated a direct relationship; However, the effect was not remarkable even at the major values, thus it is possible to consider the specific heat capacity of a living tissue, a constant value through thermal simulations. According to this research, the Homotopy Analysis Method can be a proper method to derive the analytical solution of either the linear or nonlinear form of Pennes' bioheat equation. [ABSTRACT FROM AUTHOR]

This article addresses the problem of estimating the population distribution function for stratified random sampling in the presence of non-response. We suggest a generalized class of estimators for estimating the finite cumulative distribution function using the auxiliary information. Expressions for bias and mean squared error are derived up to the first order of approximation. The performance of the estimators are compared both theoretically and numerically. A real data set is used to support the theoretical findings. [ABSTRACT FROM AUTHOR]

Summary Multicollinearity results in inflation in the variance of the ordinary least squares estimators due to the correlation between two or more independent variables (including the constant term). A widely applied solution is to estimate with penalised estimators such as the ridge estimator, which trade off some bias in the estimators to gain a reduction in the variance of these estimators. Although the variance diminishes with these procedures, all seem to indicate that the inference and goodness of fit are controversial. Alternatively, the raise regression allows mitigation of the problems associated with multicollinearity without the loss of inference or the coefficient of determination. This paper completely formalises the raise estimator. For the first time, the norm of the estimator, the behaviour of the individual and joint significance, the behaviour of the mean squared error and the coefficient of variation are analysed. We also present the generalisation of the estimation and the relation between the raise and the residualisation estimators. To have a better understanding of raise regression, previous contributions are also summarised: its mean squared error, the variance inflation factor, the condition number, adequate selection of the variable to be raised, the successive raising, and the relation between the raise and the ridge estimator. The usefulness of the raise regression as an alternative to mitigate multicollinearity is illustrated with two empirical applications. [ABSTRACT FROM AUTHOR]

In this research, a logarithmic-type estimator was formulated for estimating the finite population variance in stratified random sampling. By ensuring that the sampling process is symmetrically conducted across the population, biases can be minimized, and the sample is more likely to be representative of the population as a whole. We conducted a comprehensive numerical study and simulation study to evaluate the performance of the proposed estimator. The mean squared error values were computed for both our proposed estimator and several existing ones, including the standard unbiased variance estimator, difference-type estimator, and other considered estimators. The results of the numerical study and simulation study demonstrated that the proposed log-type estimator outperforms the other considered estimators in terms of MSE and percentage relative efficiency. Graphical representations of the results are also provided to illustrate the efficiency of the proposed estimator. Based on the findings of this study, we conclude that the proposed log-type estimator is a valuable addition to the existing literature on variance estimation in stratified random sampling. It provides a more efficient and accurate estimate of the population variance, which can be beneficial for various statistical applications. [ABSTRACT FROM AUTHOR]

The varying coefficient model is a potent dimension reduction tool for nonparametric modeling and has received extensive attention from researchers. Most existing methods for fitting this model use polynomial splines with equidistant knots and treat the number of knots as a hyperparameter. However, imposing equidistant knots tends to be overly rigid, and systematically determining the optimal number of knots is also challenging. In this article, we address these challenges by employing polynomial splines with adaptively selected and predictor-specific knots to fit the varying coefficients in the model. We propose an efficient dynamic programming algorithm to find the optimal solution. Numerical results demonstrate that our new method achieves significantly smaller mean squared errors for coefficient estimations compared to the equidistant spline fitting method. An implementation of our method in R is available at . Proofs of the theorems are provided in the . [ABSTRACT FROM AUTHOR]

Cryptography is required while interacting through an insecure media, such as internet. Unauthorised individuals have the ability to view and alter data as it is being transferred from one location to other. Cryptography is important in the realm of security of data. Cryptographic methods are being utilized to protect information against attackers in various areas. Symmetric key encryption employs a single key for encryption and decryption, and is a famously used cryptosystem. In this manuscript, improved elliptical curve cryptography and chaotic mapping with fruitfly optimization algorithm is proposed for Secure Data Transmission (IECC-CMFOA-SDT). Here, cryptography and steganography are consolidated to enhance the data security. Initially, input is the plain text from the sender and compression is done to decrease the size of input data. Then data obfuscation is carried out over the compressed data file with the aid of binary conversion, 2's complement, decimal conversion, and ASCII conversion. By utilizing the improved elliptical curve cryptography (IECC) algorithm, obfuscated data is encrypted. Encrypted data is embedded with the support of Chaotic mapping based fruitfly optimization algorithm (CMFOA), which conceals the data by jumbling the pixels in the image. Hence the secret data is diversified. CMFOA picks the superior values of pixels to root the encrypted data. The receiver acquires the stego image with embedded concealed data, which chooses the optimum pixels points to extract the concealed data from the image. Original data is acquired by decrypting, deobfuscating and decompressing the extracted data. The proposed approach is executed in CloudSim Plus. The performance metrics, like obfuscation time, deobfuscation time, encryption time, decryption time, MSE and PSNR are analysed. Performance of IECC-CMFOA-SDT model gives 39.01%, 28.34%, and 37.45% lower encryption time and 17.12%, 24.12% and 32.07 higher PSNR compared with the existing methods, like optimal users based secure data transmission with lightweight block ciphers (CRT-HTLBO-SDT), Secure data transmission employing a hybrid of a bit mask oriented genetic algorithm, encryption and steganography (BMOGA-DWT-SDT) and cryptanalysis of an encryption method based on a compound coupled logistic map and an anti-codifying technique for secure data transmission (CCLM-ACT-SDT). [ABSTRACT FROM AUTHOR]

Background: Farmers need information regarding soil fertility at every location of their fields to attain a higher level of precision in nutrient management. Nonetheless, the acquisition and processing of soil samples are labor‐intensive and time‐utilizing, and the related cost remains high‐priced to farmers. Artificial intelligence is the most speedily growing area combined into approximately all aspects of human life. Soil macronutrients like nitrogen (N), phosphorous (P), and potassium (K) have a significant role in precision agriculture. There is a huge need for powerful and rapid measurement systems to measure accurately the macronutrients in the soil for optimal crop productivity, especially in site‐specific crop management system, where the application of fertilizer can be regulated spatially with respect to crop demand. Nevertheless, it can present a research direction to design an advanced scheme in order to predict the properties of soil. A portable sensor device is a basic need of an agriculture system for the accurate and rapid monitoring of soil macronutrients. Aim: In this research, the soil nutrients identified from the collected soil samples using optical sensors are evaluated for their accuracy using a deep learning approach. Methods: A deep residual network is exploited for the soil nutrient prediction after augmenting the gathered soil data. Finally, various performance evaluation measures, like mean squared error (MSE), mean absolute error (MAE), and root mean squared error (RMSE), are calculated to detect how accurately the sensor predicted the soil nutrients. Results: From the experimental analysis, it is stated that the proposed model attained low MSE value of 4.59 e−09, the low RMSE value of 6.78 e−05, and the low MAE value of 4.66 e−05 for N prediction. Likewise, the proposed model attained the least MSE value of 1.41 e−05, the least RMSE value of 0.0003, and the least MAE value of 0.0001 for P prediction. Conclusion: Finally, for K prediction, the proposed model achieved the least MSE value of 1.54 e−06, least RMSE value of 1.24 e−03, and the least MAE value of 1.38 e−05. [ABSTRACT FROM AUTHOR]

Effective machine learning regression models are useful toolsets for managing and planning energy in PV grid-connected systems. Machine learning regression models, however, have been crucial in the analysis, forecasting, and prediction of numerous parameters that support the efficient management of the production and distribution of green energy. This article proposes multiple regression models for power prediction using the Sharda University PV dataset (2022 Edition). The proposed regression model is inspired by a unique data pre-processing technique for forecasting PV power generation. Performance metrics, namely mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), R2-score, and predicted vs. actual value plots, have been used to compare the performance of the different regression. Simulation results show that the multilayer perceptron regressor outperforms the other algorithms, with an RMSE of 17.870 and an R2 score of 0.9377. Feature importance analysis has been performed to determine the most significant features that influence PV power generation. [ABSTRACT FROM AUTHOR]

Multicollinearity among independent variables is one of the most common problems in regression models. The aftereffects of this problem, such as ill-conditioning, instability of estimators, and inflating mean squared error of ordinary least squares estimator (OLS), in the multivariate linear regression model (MLRM) are the same that of linear regression models. To combat multicollinearity, several approaches have been presented in the literature. Liu estimator (LE), as a well known estimator in this connection, has been used in linear, generalized linear, and nonlinear regression models by researchers in recent years. In this paper, for the first time, LE and jackknifed Liu estimator (JLE) are investigated in MLRM. To improve estimators in the sense of mean squared error, two known resampling methods, i.e., jackknife and bootstrap, are used. Finally, OLS, LE, and JLE are compared by a simulation study and also using a real data set, by resampling methods in MLRM. [ABSTRACT FROM AUTHOR]

Measurement error, which occurs when some variables of interest cannot be observed exactly. It often leads to invalid conclusions and lamentable implications if ignored. Therefore, the aim of the present work is to investigate ways to handle them when the observations on both the study and auxiliary variables are spoiled with measurement errors. A general class of estimators for the estimation of population mean in presence of correlated measurement errors on study and auxiliary variables has been considered. The variations in the properties of the estimators under the influence of measurement errors has been discussed in detail. The considered class of estimators is compared with the recently proposed family of exponential-type estimators. Simulation studies are carried out to show the impact on the behavior of estimators due to variation in parameters of the measurement error model. [ABSTRACT FROM AUTHOR]

A common problem faced in clinical studies is that of estimating the effect of the most effective (e.g. the one having the largest mean) treatment among $$k (\ge2)$$ k (≥ 2) available treatments. The most effective treatment is adjudged based on numerical values of some statistic corresponding to the $$k$$ k treatments. A proper design for such problems is the so-called "Drop-the-Losers Design (DLD)". We consider two treatments whose effects are described by independent Gaussian distributions having different unknown means and a common known variance. To select the more effective treatment, the two treatments are independently administered to $${n_1}$$ n 1 subjects each and the treatment corresponding to the larger sample mean is selected. To study the effect of the adjudged more effective treatment (i.e. estimating its mean), we consider the two-stage DLD in which $${n_2}$$ n 2 subjects are further administered the adjudged more effective treatment in the second stage of the design. We obtain some admissibility and minimaxity results for estimating the mean effect of the adjudged more effective treatment. The maximum likelihood estimator is shown to be minimax and admissible. We show that the uniformly minimum variance conditionally unbiased estimator (UMVCUE) of the selected treatment mean is inadmissible and obtain an improved estimator. In this process, we also derive a sufficient condition for inadmissibility of an arbitrary location and permutation equivariant estimator and provide dominating estimators in cases, where this sufficient condition is satisfied. The mean squared error and the bias performances of various competing estimators are compared via a simulation study. A real data example is also provided for illustration purpose. [ABSTRACT FROM AUTHOR]

The unique properties of carbon monoxide and its high combustibility have led to the creation of various sensors, such as electrochemical sensors and different circuits, to read its output. In this article, a deflection-type Wheatstone bridge is used to measure changes in the sensor resistance, and the output voltage is connected to a 12-bit analogto-digital converter through an adjustable precision amplifier. Next, a new method is proposed for self-calibrating the CO sensor. The Levenberg-Marquardt backpropagation algorithm (LMBP) is utilized in the Artificial Neural Network model to minimize the Mean Squared Error (MSE) and identify the most suitable parameters in the proposed method. The model under consideration has been developed and trained using real-time data. Based on the experimental and evaluation outcomes, it can be concluded that the suggested model has an MSE value of 0.28249 and an R2 coefficient of determination of 0.99992, indicating high accuracy and precision. The proposed sensor and calibration method have potential applications in various applications, including industrial and domestic environments where CO monitoring is necessary. [ABSTRACT FROM AUTHOR]

Knowledge distillation (KD) has been widely used in different tasks as a practical model compression technique. Due to the poor performance of directly using Mean Square Error (MSE) between the intermediate features of the teacher and student, most feature-based detector distillation methods are primarily concerned with proposing diverse attention mechanisms and employing MSE to guide the student in learning critical information. However, the significance of MSE in detector distillation is often overlooked. To enhance the distillation performance of MSE and provide a novel perspective, we propose channel-level M atching K nowledge D istillation via MSE (MKD). The idea of MKD is simple but effective: based on the match or mismatch of student and teacher channel features in Feature Pyramid Networks (FPN), we divide channels at the same location in the FPN layers of the student and teacher into match channels and mismatch channels and then assign different weights to them to calculate the MSE-based distillation loss, which forces the student to distinguish the teacher's channels and imitate the features of the corresponding channels to achieve better performance. We conduct extensive experiments on MS COCO and PASCAL VOC benchmarks to prove that MKD is superior to state-of-the-art distillation methods. For example, with a powerful RetinaNet-ResNeXt101 detector as the teacher, ResNet-50 based RetinaNet and RepPoints with our distillation method achieve 40.9% and 42.2% mAP on COCO2017, which are 3.5% and 3.6% higher than the baseline, respectively. • We propose MKD to improve detector distillation performance by enhancing the often-overlooked MSE loss. • MKD effectively addresses the issue of poor detector distillation results caused by channel mismatch when using direct MSE. • MKD outperforms state-of-the-art distillation methods on MS COCO and PASCAL VOC benchmarks. [ABSTRACT FROM AUTHOR]

In unveiling the non-parametric estimation of the conditional hazard function through the local linear method, our study yields key insights into the method's behavior. We present rigorous analyses demonstrating the mean square convergence of the estimator, subject to specific conditions, within the realm of independent observations with missing data. Furthermore, our contributions extend to the derivation of expressions detailing both bias and variance of the estimator. Emphasizing the practical implications, we underscore the applicability of two distinct models discussed in this paper for single index estimation scenarios. These findings not only enhance our understanding of survival analysis methodologies but also provide practitioners with valuable tools for navigating the complexities of missing data in the estimation of conditional hazard functions. Ultimately, our results affirm the robustness of the local linear method in non-parametrically estimating the conditional hazard function, offering a nuanced perspective on its performance in the challenging context of independent observations with missing data. [ABSTRACT FROM AUTHOR]

We propose and study three confidence intervals (CIs) centered at an estimator that is intentionally biased to reduce mean squared error. The first CI simply uses an unbiased estimator's standard error; compared to centering at the unbiased estimator, this CI has higher coverage probability for confidence levels above 91. 7%, even if the biased and unbiased estimators have equal mean squared error. The second CI trades some of this "excess" coverage for shorter length. The third CI is centered at a convex combination of the two estimators to further reduce length. Practically, these CIs apply broadly and are simple to compute. [ABSTRACT FROM AUTHOR]

AbstractStatistical inference with the ordinary least squares (OLS) estimator is frequently influenced when there is a multicollinearity in the linear regression model. In this article, to reduce these effects of multicollinearity, we generalize the modified Kibria–Lukman principal component (MKLPC) estimator in the linear regression model by combining the principal component regression (PCR) estimator and the modified Kibria–Lukman (MKL) estimator. Meanwhile, the necessary and sufficient conditions for the superiority of the MKLPC estimator over OLS, PCR, Ridge, r-k, Liu, r-d, k-d, KL, and MKL estimators in the mean squared error (MSE) criterion are derived. Furthermore, we conduct Monte Carlo simulation and empirical analysis to compare these estimators under the MSE criterion. [ABSTRACT FROM AUTHOR]

In this article, we propose a framework for small area estimation with multiply imputed survey data. Many statistical surveys suffer from (a) high nonresponse rates due to sensitive questions and response burden and (b) too small sample sizes to allow for reliable estimates on (unplanned) disaggregated levels due to budget constraints. One way to deal with missing values is to replace them by several plausible/imputed values based on a model. Small area estimation, such as the model by Fay and Herriot, is applied to estimate regionally disaggregated indicators when direct estimates are imprecise. The framework presented tackles simultaneously multiply imputed values and imprecise direct estimates. In particular, we extend the general class of transformed Fay-Herriot models to account for the additional uncertainty from multiple imputation. We derive three special cases of the Fay-Herriot model with particular transformations and provide point and mean squared error estimators. Depending on the case, the mean squared error is estimated by analytic solutions or resampling methods. Comprehensive simulations in a controlled environment show that the proposed methodology leads to reliable and precise results in terms of bias and mean squared error. The methodology is illustrated by a real data example using European wealth data. [ABSTRACT FROM AUTHOR]

Multicollinearity is the problem when there is linear dependency among the independent variables. The Ordinary least squares estimator (OLSE) that is commonly adopted is not suitable for the linear regression model when the independent variables are correlated. This is due to the high variance in OLSE and hence the accuracy of OLSE reduces in the presence of multicollinearity. Hence, the estimator named k-almost unbiased regression estimator (KAURE) was proposed as an alternative to OLSE in this paper. KAURE was developed by using the definition of an almost unbiased estimator to further reduce the bias of Liu-type estimator-special case (LTESC). The properties of KAURE including bias, variance-covariance and mean squared error (MSE) were derived. Theoretical comparison and real-life data comparison were carried out to evaluate the performance of the KAURE based on the MSE criterion. The application of the real-life data supported the theoretical comparison that showed the superiority of KAURE over OLSE and LTESC. The results revealed that KAURE could be considered as an alternative estimator for the linear regression model to combat the problem of multicollinearity. [ABSTRACT FROM AUTHOR]

In this paper, a new scrambled randomized response (SRR) model has been proposed for estimating the population mean of a sensitive variable in presence of scrambled response under simple random sampling with replacement (SRSWR). The utility of proposed SRR model under two occasions successive sampling is also explored. It is found that the proposed SRR model is superior to the additive model of Gjestvang and Singh (2009) under SRSWR and successive sampling. We also proposed a composite class of estimators for estimating the population mean of sensitive variable under two occasions successive sampling. The proposed composite class of estimators under optimum conditions is shown to be more efficient than the classical ratio and exponential ratio type estimators respectively. [ABSTRACT FROM AUTHOR]

Measurement errors affect the properties of obtained optimal estimators. Further, they affect the accuracy of estimation, although the size of the measurement error required to invalidate an estimation method remains unknown. In this study, we described the effects of measurement errors on estimation and the derived asymptotic covariance matrix by using the properties of unbiased estimating equations. We evaluated different estimation methodologies using various combinations of sample sizes and average reliability ratios. Simulation studies have compared estimators in terms of simulated bias, mean squared error, and coverage probability for the slope parameter. By comparing estimation approaches in terms of bias, mean squared error, and coverage probability, we found that the average reliability ratio of 0.65 and a sample size of 20 yielded estimator stability, with only slight differences in these three attributes. If the sample size was increased, the cutoff point for the average reliability ratio could be relaxed. This process has been in this study illustrated using real datasets. [ABSTRACT FROM AUTHOR]

The ridge regression estimator (RRE) is a widely used estimation method for the multiple linear regression model when the explanatory variables are correlated. The situation becomes problematic for the RRE when the data set contains outliers in the y-direction. The use of the RRE in the presence of outliers may have some adverse effects on parameter estimates. To address this issue, the robust ridge estimators based on M-estimator are available in the literature which are less sensitive to the presence of outliers. It is a well-known fact that the selection of ridge parameter k is very crucial while using the RRE and the same phenomenon may happen in the case of robust ridge estimators. This study proposes some robust ridge estimators for the ridge parameter k. The performance of proposed estimators is evaluated with the help of the Monte Carlo simulations and a real application where the mean squared error (MSE) is considered as a performance evaluation criterion. Results show a better performance of the proposed robust ridge estimators as compared to the RRE, least square and M-estimation methods. While for modified ridge M-estimator, different ridge parameters found to be better for different conditions. [ABSTRACT FROM AUTHOR]

In this article, maximum likelihood estimation and Bayes estimators are derived for linear exponential distribution based on one- and m-cycle extreme ranked set sampling and simple random sample. These estimators are compared via their biases and mean squared error. This is done with respect to both symmetric and asymmetric loss functions. A reallife data set and simulation study are used to illustrate our procedures. This unequivocally shows that, in all circumstances taken into consideration for this study, ranked set sampling is more effective than both extreme ranked set sampling and simple random sample. Over a high number of cycles, a significant improvement is shown. [ABSTRACT FROM AUTHOR]

Recently, Di Crescenzo and Paolillo [Di Crescenzo A, Paolillo L. Analysis and applications of the residual varentropy of random lifetimes. Probab Eng Informational Sci. 2021;35(3):680–698] and Maadani et al. [Maadani S, Mohtashami Borzadaran GR, Rezaei Roknabadi AH. Varentropy of order statistics and some stochastic comparisons. Commun Stat - Theory Methods. 2021;51(18):6447–6460.] presented the applications of varentropy in reliability theory. The present article introduces some estimators of the varentropy of a continuous random variable. Properties of the proposed estimators are stated, and comparisons are made in terms of the mean squared error. Then, the proposed estimators are applied and some tests for uniformity are constructed. Percentage points and power values of the tests against seven alternatives are reported. The results of a simulation study show that the tests have good performance in terms of power. [ABSTRACT FROM AUTHOR]

This paper uses classical and shrinkage estimators to estimate the system reliability (R) in the stress-strength model when the stress and strength follow the Inverse Chen distribution (ICD). The comparisons of the proposed estimators have been presented using a simulation that depends on the mean squared error (MSE) criteria. [ABSTRACT FROM AUTHOR]

In multiple linear regression models, the explanatory variables should be uncorrelated within each other but this assumption is violated in most of the cases. Generally, ordinary least square (OLS) estimator produces larger variances when explanatory variables are highly multicollinear. So, in this paper, we propose some new ridge parameters under Bayesian perspective relative to different loss functions, using Tierney and Kadane (T-K) approximation technique to overcome the effect of multicollinearity. We conduct the simulation study to compare the performance of the proposed estimators with OLS estimator and ordinary ridge estimator with some available best ridge parameters using mean squared error as the performance evaluation criterion. A real application is also consider to show the superiority of proposed estimators against competitive estimators. Based on the results of simulation and real application, we conclude that Bayesian ridge parameter estimated under general entropy loss function is better as compared to the OLS estimator and ordinary ridge estimator, when explanatory variables are small. This statement is also true for larger explanatory variables with small sample size. While for larger sample sizes and explanatory variables, the ordinary ridge estimator with best ridge parameter gives the better performance as others. [ABSTRACT FROM AUTHOR]

The beta regression model is commonly used when analyzing data that come in the form of rates or percentages. However, a problem that may encounter when analyzing these kinds of data that has not been investigated for this model is the multicollinearity problem. It is well known that the maximum likelihood (ML) method is very sensitive to high inter-correlation among the explanatory variables. Therefore, this paper proposes some ridge estimators for the beta regression model to remedy the problem of instability of the traditional ML method and increase the efficiency of estimation. The performance of ridge estimators is compared to the ML estimator through the mean squared error (MSE) and the mean absolute error (MAE) criteria by conducting a Monte-Carlo simulation study and through an empirical application. According to the simulation and application results, the proposed estimators outperform the ML estimator in terms of MSE and MAE. [ABSTRACT FROM AUTHOR]

The reliability of hybrid systems is important in modern technology, specifically in engineering and industrial fields; it is an indicator of the machine's efficiency and ability to operate without interruption for an extended period of time. It also allows for the evaluation of machines and equipment for planning and future development. This study looked at reliability of hybrid (parallel series) systems with asymmetric components using exponential and Pareto distributions. Several simulation experiments were performed to estimate the reliability function of these systems using the Maximum Likelihood method (ML) and the Standard Bayes method (SB) with a quadratic loss (QL) function and two priors: non-informative (Jeffery) and informative (Conjugate). Different sample sizes and parameter values are used in these simulation experiments, and the Mean Squared Error (MSE) was used to compare those experiments. The simulation results showed that the standard Bayes method with Conjugate loss function is better than the results from the maximum likelihood method. [ABSTRACT FROM AUTHOR]

In this paper a generalized difference-based mixed two-parameter estimator in partially linear model is presented, when stochastic linear restrictions are assumed to hold. We also discussed the properties of the new estimator and a method to select the biasing parameters is discussed. Finally a simulation study is given to show the performances of the estimators. [ABSTRACT FROM AUTHOR]

Video compression is necessary to recreate a video without sacrificing quality. Nowadays, researchers are focusing on global optimization approaches to determine the optical flow of the neighboring pixels in video processing. In this work, a novel improved diamond search-hybrid teaching-learning based optimization (IDS-HTLBO) methodology has been proposed to compress the videos and increase the video quality. This method uses a diamond search pattern with a secure number of search points for per frame of the video. The hybridization of DS algorithm and TLBO algorithm are applied in this methodology to reduce computational complexity. Moreover, this method reduces the computational unpredictability of block matching. The quality of the image was validated with 3D reconstruction by the structured light approaches. The experimental result shows that the proposed IDS-HTLBO algorithm achieves a maximum average value of 53.17 dB, 0.44 and 11.57 in terms of peak-to-signal-noise ratio, mean squared error, and compression ratio respectively. [ABSTRACT FROM AUTHOR]

This paper discusses the difficulty of approximating the population average of a variable y by knowledge about a supplementary variable x in the context of two successive (rotation) sampling occasions. The paper proposes a group of exponential-class estimators that includes the regular balanced estimator, produce-class estimator, and proportion-class estimator and suggests that these estimators are superior to existing estimators. The paragraph also mentions that the paper discusses optimal substitute statements and then the implementation of the recommended estimators, which may be important considerations for practical applications of the proposed methods. Finally, an empirical study is mentioned as supporting evidence for the research. [ABSTRACT FROM AUTHOR]

Abstract Being an important probability distribution with moderate skewness, the two-parameter gamma distribution is widely used in statistics. However, the maximum likelihood estimators (MLEs) of its parameters do not have closed forms, making them difficult to be implemented in applications. Moreover, the MLE of its shape parameter has low estimation efficiency due to its considerable bias. Thus, many other estimators have been investigated in the literature. We propose an easy computation of the MLEs in this article, where the MLE of the shape parameter is modified to be highly efficient and significantly better than most of existing estimators. [ABSTRACT FROM AUTHOR]

An improved class of imputation procedures are proposed for estimating the finite population mean by using the known population mean and higher order moments of the auxiliary variable. Mathematical expressions for bias and mean square error of proposed and existing imputation procedures are derived up to first order approximation. The theoretical results are supported by numerical study of five empirical populations and three hypothetical populations by taking different values of ρyx at varying response. [ABSTRACT FROM AUTHOR]

To evaluate the time-domain positioning performance of arctic marine structures, it is necessary to generate an ice load appropriate for the current position and heading of the structure. The position and orientation angle of a floating body continuously change with time. Therefore, an ice load is required for any attitude in the time-domain simulation. In this study, we present a fundamental technique for analyzing ice loads in the frequency domain based on data measured at various angles in the ice-water tank experiment. We perform spectral analysis instead of general FFT to analyze the ice load, which has the characteristics of a random signal. To generate the necessary ice load in the time domain, we must first interpolate the measured data in the frequency domain. Using the Blackman-Tukey method, we estimate the spectrum for the measured data, then process the data to generate the training set required for machine learning. Based on the results, we perform regression analysis by applying four representative techniques, including linear regression, random forest, or neural network, and compare the results with MSE. The deep neural network method performed best, but we provide further discussion for each model. [ABSTRACT FROM AUTHOR]

A digital twin is a simulator of a physical system, which is built upon a series of models and computer programs with real-time data (from sensors or devices). Digital twins are used in various industries, such as manufacturing, healthcare, and transportation, to understand complex physical systems and make informed decisions. However, predictions and optimizations with digital twins can be time-consuming due to the high computational requirements and complexity of the underlying computer programs. This poses significant challenges in making well-informed and timely decisions using digital twins. This paper proposes a novel methodology, called the "digital triplet", to facilitate real-time prediction and decision-making. A digital triplet is an efficient representation of a digital twin, constructed using statistical models and effective experimental designs. It offers two noteworthy advantages. Firstly, by leveraging modern statistical models, a digital triplet can effectively capture and represent the complexities of a digital twin, resulting in accurate predictions and reliable decision-making. Secondly, a digital triplet adopts a sequential design and modeling approach, allowing real-time updates in conjunction with its corresponding digital twin. We conduct comprehensive simulation studies to explore the application of various statistical models and designs in constructing a digital triplet. It is shown that Gaussian process regression coupled with sequential MaxPro designs exhibits superior performance compared to other modeling and design techniques in accurately constructing the digital triplet. [ABSTRACT FROM AUTHOR]

The empirical best linear unbiased predictor (EBLUP) is a linear shrinkage of the direct estimate toward the regression estimate and useful for the small area estimation in the sense of increasing precision of estimation of small area means. However, one potential difficulty of EBLUP is that the overall estimate for a larger geographical area based on a sum of EBLUP is not necessarily identical to the corresponding direct estimate like the overall sample mean. To fix this problem, the paper suggests a new method for benchmarking EBLUP in the Fay–Herriot model without assuming normality of random effects and sampling errors. The resulting benchmarked empirical linear shrinkage (BELS) predictor has novelty in the sense that coefficients for benchmarking are adjusted based on the data from each area. To measure the uncertainty of BELS, the second‐order unbiased estimator of the mean squared error is derived. [ABSTRACT FROM AUTHOR]

In signal estimation, an optimal estimator is frequently unachievable because its closed form may not be analytically tractable or is too complex to implement. Alternatively, one can turn to suboptimal yet easily implementable estimators for practical signal estimation tasks. In this paper, an optimal noise-boosted estimator is designed and the adaptive stochastic resonance method is implemented to simultaneously exploit the beneficial role of the injected noise as well as the learning ability of the estimator parameter. Aiming to effectively improve the estimation performance, we use the kernel function method to find an approximate solution for the probability density function (PDF) of the optimal injected noise. During this process, the noise PDF and the estimator parameter establish a finite-dimensional non-convex optimization space for maximizing the estimation performance, which is adaptively searched by the sequential quadratic programming (SQP) algorithm at each iteration. Two representative estimation problems are explored. The obtained results demonstrate that this adaptive stochastic resonance method can improve the performance of the suboptimal estimators and bring it very close to that of the optimal estimator. [ABSTRACT FROM AUTHOR]

This article addresses the issue of multicollinearity for the distributed lag model via Bayesian approach. We introduce the Bayes Almon ridge estimator under this approach by employing prior information. Specifically, the resulting estimator is a new Bayesian estimator that is the mean of posterior density function for the coefficient of the Almon model. Also, a restricted version of this estimator is proposed by using Lagrange multipliers to optimize the coefficients under the additional exact linear constraints. In mathematical sense, theoretical comparisons are carried out by employing mean squared error utilizing matrix theory. Additionally, we investigate a selection method for the biasing parameter of the new estimators with the help of the mean squared error comparisons. To test the theoretical suggestions, we perform a real-life data analysis as a means of applied mathematics. Moreover, we benefit from Monte Carlo simulation techniques where we use several levels of different parameters. The outcomes of numerical example and simulation study favor the new estimators and, hence we succeed in eliminating the multicollinearity. [ABSTRACT FROM AUTHOR]

Ranked set sampling is an approach to data collection originally combines simple random sampling with the field investigator's professional knowledge and judgment to pick places to collect samples. Alternatively, field screening measurements can replace professional judgment when appropriate and analysis that continues to stimulate substantial methodological research. The use of ranked set sampling increases the chance that the collected samples will yield representative measurements. This results in better estimates of the mean as well as improved performance of many statistical procedures. Moreover, ranked set sampling can be more cost-efficient than simple random sampling because fewer samples need to be collected and measured. The use of professional judgment in the process of selecting sampling locations is a powerful incentive to use ranked set sampling. This paper is devoted to the study, we introduce an approach to the mean estimators in ranked set sampling. The amount of information carried by the auxiliary variable is measured with the on populations and samples and to use this information in the estimator, the basic ratio and the generalized exponential ratio estimators are as an improved form of a difference cum exponential ratio type estimator under the ranked set sampling in order to estimate the population mean Y of study variate Y using single auxiliary variable X. The expressions for the mean squared error of propose estimator under ranked set sampling is derived and theoretical comparisons are made with competing estimators. We show that the proposed estimator has a lower mean square error than the existing estimators. In addition, these theoretical results are supported with the aid of some real data sets using R studio. Therefore, Under RSS architecture, a better difference cum exponential ratio type estimator has been suggested. The estimator's mathematical form has been developed, and its efficiency requirements have been developed in relation to various already-existing estimators from the literature. By imputing various values for the constants used in the creation of our proposed estimator, we also provide several specific situations of our estimator. [ABSTRACT FROM AUTHOR]

Abstract In many real-world problems, there are situations where the dependent variable may have a Gamma distribution. The Gamma Regression Models (GRMs) are preferred when the response variable assumes a Gamma distribution with a given set of independent variables. The Maximum Likelihood Estimator (MLE) is used to estimate the unknown parameters. In the presence of multicollinearity, the variance of the MLE becomes inflated and the inference based on the MLE may not be reasonable. In this article, we propose a new biased estimator called the new Liu-type estimator in the GRMs to combat multicollinearity. The proposed estimator is a general estimator which includes other biased estimators, such as the Gamma ridge estimator, Gamma Liu estimator, and the estimators with two biasing parameters as special cases. Furthermore, several methods are proposed to determine the biasing parameters in the estimators. Also, a Monte Carlo simulation study has been conducted to assess the performance of the proposed biased estimator where the Estimated Mean Squared Error (EMSE) is considered as a performance criterion. Finally, two numerical examples are given to investigate the performance of the proposed estimator over existing estimators. [ABSTRACT FROM AUTHOR]

In this article, we propose three nonparametric estimators for quantile-based Shannon differential entropy function for complete samples. Asymptotic properties of the estimators are established under suitable regularity conditions. Simulation study are carried out to compare the performance of the proposed estimators and with other important entropy estimators. The usefulness of the new estimators are also illustrated using real data sets. [ABSTRACT FROM AUTHOR]

Over the course of technological development, data security while transmission and storing has always been a field of continuous advancements and key importance. In the recent times, its importance has increased even further and the main reason behind this is the increase in the amount of data that is being transferred over internet and various networks. Although there are cryptographic approaches to handle these situations, steganography provides a different aspect to the solution. While cryptography encrypts the data such that the cipher text is visible to human eye, but the meaning of that encrypted text is never known. Steganography is the process of hiding data in plain sight inside some images, audio, video and so on, such that it is very difficult for the viewer to directly differentiate if there is some data hidden in the host or not. This paper consists a study of various methodologies to implement Image steganography like spatial domain manipulation, encryption based and deep learning approaches. The paper focuses upon recent advances in all these approaches for image steganography and aims to help other researches in this domain to understand recent developments as well future advancements possible in the same field. Furthermore, this paper illustrates about how different image formats effect various image steganography methods and how the various image color models interact with image steganography. Later this article sheds some light on the domain of steganalysis and reports about the fundamental principles as well as various implementations of steganalysis systems in recent times. [ABSTRACT FROM AUTHOR]

In this paper, we propose a class of general pretest estimators for the univariate normal mean. The main mathematical idea of the proposed class is the adaptation of randomized tests, where the randomization probability is related to a shrinkage parameter. Consequently, the proposed class includes many existing estimators, such as the pretest, shrinkage, Bayes, and empirical Bayes estimators as special cases. Furthermore, the proposed class can be easily tuned for users by adjusting significance levels and probability function. We derive theoretical properties of the proposed class, such as the expressions for the distribution function, bias, and MSE. Our expressions for the bias and MSE turn out to be simpler than those previously derived for some existing formulas for special cases. We also conduct simulation studies to examine our theoretical results and demonstrate the application of the proposed class through a real dataset. [ABSTRACT FROM AUTHOR]

We propose a novel family of estimators for the population mean under non-response and obtain the MSE equation of the suggested estimator for each situation in theory. These theoretical conditions are applied to three popular data sets in literature and we see that the suggested estimators are more efficient than the traditional estimators, such as ratio, regression estimators, in Case 1; whereas, in Case 2, the suggested estimators are also more efficient than the Unal-Kadilar exponential estimators that are more efficient than the traditional estimators for the same data sets. [ABSTRACT FROM AUTHOR]

The ordinary least squares and ridge regression estimators in a multiple linear regression model with multicollinearity and y-direction outliers lead to unfavorable results. In order to mitigate such situation, the available literature provides few ridge M-estimators to get precise estimates. The ridge parameter, k, plays a vital role in a bias-variance tradeoff for these estimators. However, for high signal-to-noise ratio and multicollinearity with y-direction outliers, the available methods may not perform well in terms of their mean squared error. In this article, we propose a new quantile based ridge M-estimator. The new estimator gives an automated choice of quantile probability of ridge parameter according to the level of noise and multicollinearity. Based on a simulation study, the new estimator outperforms the ordinary least square estimator, ridge estimator, and other considered ridge M-estimators especially for high multicollinearity, significant error variance, and y-direction outliers. Besides normal distribution, new estimator also performs well for heavy-tailed error distribution. Finally, two real-life examples are used to illustrate the application of the proposed estimator. [ABSTRACT FROM AUTHOR]

Missing data often complicates survey practitioners to construct reliable estimates of the required population parameters. Remembering this fact and motivated with the recent work, this article deals with some imputation methods to handle the missing data problem at the beginning of the analysis and some estimation procedures of the current population mean have been proposed in two-occasion successive sampling. The expressions for the bias, mean squared error and optimum mean squared error are derived using the concept of large sample approximations. The empirical performances are shown over the similar type of estimators designated for the complete response situation and over recently developed estimator which are defined for the situation when missing observations are observed in the sample data. Suitable recommendations have been made for survey researchers. [ABSTRACT FROM AUTHOR]

The bell regression is used, when the response variable is in the form of counts with over dispersion. The bell regression coefficients are generally estimated using the maximum likelihood estimator (MLE). It is known that the performance of the traditional MLE is very sensitive to multicollinearity. Therefore, we propose a Bell ridge regression (BRR) as a solution to the multicollinearity problems. For the assessment of BRR, we conduct a Monte Carlo simulation study to monitor the performance of the proposed estimator where the mean squared error (MSE) is considered as an evaluation criterion. Also, two real examples are included to show the superiority of the BRR estimator. [ABSTRACT FROM AUTHOR]

This paper discusses new approaches to parameter estimation of gamma distribution based on representative points. In the first part, the existence and uniqueness of gamma mean squared error representative points (MSE-RPs) are discussed theoretically. In the second part, by comparing three types of representative points, we show that gamma MSE-RPs perform well in parameter estimation and simulation. The last part proposes a new Harrel–Davis sample standardization technique. Simulation studies reveal that the standardized samples can be used to improve estimation performance or generate MSE-RPs. In addition, a real data analysis illustrates that the proposed technique yields efficient estimates for gamma parameters. [ABSTRACT FROM AUTHOR]

In the present paper, a general class of estimators has been proposed for estimating the population mean of the study variable using auxiliary variable when the population mean of the auxiliary variable is known in stratified random sampling. The bias and mean squared error of the proposed class of estimators are derived under stratified sampling to the first degree of approximation. Members of the proposed class of estimators are also obtained by giving suitable values to the constants used. Comparisons of the proposed strategy with the usual unbiased estimator and other estimators have been made. Empirical and simulation study is carried out to demonstrate the performance of the proposed estimator. [ABSTRACT FROM AUTHOR]

Repeated testing in a group sequential trial can result in bias in the maximum likelihood estimate of the unknown parameter of interest. Many authors have therefore proposed adjusted point estimation procedures, which attempt to reduce such bias. Here, we describe nine possible point estimators within a common general framework for a two-stage group sequential trial. We then contrast their performance in five example trial settings, examining their conditional and marginal biases and residual mean square error. By focusing on the case of a trial with a single interim analysis, additional new results aiding the determination of the estimators are given. Our findings demonstrate that the uniform minimum variance unbiased estimator, whilst being marginally unbiased, often has large conditional bias and residual mean square error. If one is concerned solely about inference on progression to the second trial stage, the conditional uniform minimum variance unbiased estimator may be preferred. Two estimators, termed mean adjusted estimators, which attempt to reduce the marginal bias, arguably perform best in terms of the marginal residual mean square error. In all, one should choose an estimator accounting for its conditional and marginal biases and residual mean square error; the most suitable estimator will depend on relative desires to minimise each of these factors. If one cares solely about the conditional and marginal biases, the conditional maximum likelihood estimate may be preferred provided lower and upper stopping boundaries are included. If the conditional and marginal residual mean square error are also of concern, two mean adjusted estimators perform well. [ABSTRACT FROM AUTHOR]