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Dimensionality reduction is a method used in machine learning and data science to reduce the dimensions in a dataset. While linear methods are generally less effective at dimensionality reduction than nonlinear methods, they can provide a linear relationship between the original data and the dimensionality-reduced representation, leading to better interpretability. In this research, we present a tied-weight autoencoder as a dimensionality reduction model with the merit of both linear and nonlinear methods. Although the tied-weight autoencoder is a nonlinear dimensionality reduction model, we approximate it to function as a linear model. This is achieved by removing the hidden layer units that are largely inactivated by the input data, while preserving the model's effectiveness. We evaluate the proposed model by comparing its performance with other linear and nonlinear models using benchmark datasets. Our results show that the proposed model performs comparably to the nonlinear model of a similar autoencoder structure to the proposed model. More importantly, we show that the proposed model outperforms the linear models in various metrics, including the mean square error, data reconstruction, and the classification of low-dimensional projections of the input data. Thus, our study provides general recommendations for best practices in dimensionality reduction., (© 2024. The Author(s).)

This paper addresses the issue of estimating the population mean for non-response using simple random sampling. A new family of estimators is proposed for estimating the population mean with auxiliary information on the sample mean and the rank of the auxiliary variable. Bias and mean square errors of existing and proposed estimators are obtained using the first order of measurement. Theoretical comparisons are made of the performance of the proposed and existing estimators. We show that the proposed family of estimators is more efficient than existing estimators in the literature under the given constraints using these theoretical comparisons.

The recent advancement and enhancement that optimized uncoded space-time labelling diversity (USTLD) have provided significant diversity gains. By adopting the use of evolutionary algorithms, labelling diversity (LD) mapper designs produced are near-optimal in quality. The only disadvantage to the use of evolutionary algorithms is that the produced solution is not always optimal. To ease the calculation of how much a mapper design had achieved LD, this paper proposes a machine learning-based analysis to predict the amount of LD achieved by a mapper. In this paper, only the 16QAM constellation is studied as a simple case. Six machine learning-based algorithms were proposed in this paper, namely multi-linear regression (MLR), support vector regression (SVR), decision trees (DT), random forest (RF), K-nearest neighbours (KNN) and a simple artificial neural network (ANN). From the results obtained from the experiments, it can be seen that the MLR algorithm is the least time complex while the ANN is the most time complex. It is also important to note that the DT and KNN algorithms take a comparatively short amount of time to execute. When compared in terms of machine learning metrics, it was shown that the ANN algorithm performed the best with the least amount of error while the MLR algorithm performed the worst with the highest amount of error. Thus, it could be seen that the results from this paper provide a positive outlook on applying machine learning algorithms to the LD problem.

We introduce two-exponential shrinkage estimator using two stage two phase sampling for estimating population mean of study variable. Some properties of the proposed two-exponential shrinkage estimator are presented. The mathematical comparison in terms of the mean square error is done in order to demonstrate some conditions for which the proposed shrinkage estimators is more efficient than the already existing estimators in literature. A real life application is provided to show the performance of the proposed shrinkage estimator.

Fuzzy time series models have been proposed by many researchers around the world for rainfall forecasting, but the forecasting has not been as accurate as existing methods. Frequency density or ratio-based segmentation methods have been used to represent discourse segmentation. In this paper, to make such predictions, we used interval-based segmentation as the discourse segmentation and the urban mean rainfall in the Trichy district as the discourse universe. Fuzzy models are used for forecasting in many fields such as admissions prediction, stock price analysis, agricultural production, horticultural production, marine production, weather forecasting, and more.

One of the first important steps in elucidating the function of microRNAs (miRNAs) is expression profiling. Many methods including low-density qPCR arrays are increasingly used to profile the expression of miRNAs. Normalization techniques are necessary due to certain biases in profiling approaches, and the techniques can significantly affect the accuracy of miRNA quantification. Most normalization methods for continous expression data have been developed for mRNA microarrays and new and modified methods should be used for miRNA studies in general and RT-qPCR miRNA arrays in particular. Previously, cyclic normalization using support vector regression has been successfully applied to mRNA arrays. Here, a new method based on support vector regression is introduced for miRNA normalization and the cyclic nature of algorithm in cyclic spline normalization has also been modified. It was shown that by creating a baseline array, it is possible to remove the cyclic nature of the normalization to achieve faster normalization, with no loss of accuracy. To assess how much the mentioned normalization method reduces technical error, mean square error (MSE) in two real miRNA qPCR array datasets and a simulated dataset before and after normalizations was robustly modelled and compared. Our method was also systematically compared with the most commonly used methods for normalization of qPCR miRNA arrays. The new method showed lower MSE values corresponding to other common methods of miRNA normalization.

Survey sampling commonly faces the challenge of missing information, prompting the development of various imputation-based mean estimation methods to address this concern. Among these, ratio-type regression estimators have been devised to compute population parameters using only current sample data. However, recent pioneering research has revolutionized this approach by integrating both past and current sample information through the application of exponentially weighted moving averages (EWMA). This groundbreaking methodology has given rise to the creation of memory-type estimators tailored for surveys conducted over time. In this paper, we present novel imputation-based memory-type mean estimators that leverage EWMA and quantile regression to handle missing observations. For the performance assessment between traditional, adapted and proposed estimators, real-life time-scaled datasets related to the stock market and humidity are considered. Furthermore, we conduct a simulation study using an asymmetric dataset to further validate the effectiveness of the introduced estimators. The humidity data results show that the proposed estimators (Tpq(0.25), Tpq(0.45), Tpq(0.25)′, Tpq(0.45)′, Tpq(0.25)″, Tpq(0.45)″) have the minimum MSE. The stock market data results show that the proposed estimators (Tpq(0.85), Tpq(0.85)′, Tpq(0.85)″) also have the minimum MSE. Additionally, the simulation results demonstrate that the proposed estimators (Tpq(0.45), Tpq(0.45)′, Tpq(0.45)″) have the minimum MSE when compared to traditional and adapted estimators. Therefore, in conclusion, the use of the proposed estimators is recommended over traditional and adapted ones.

It has been known for at least 150 years that fatigue life data exhibits a considerable amount of variability. Furthermore, statistically modeling fatigue life adequately is challenging. Different empirical approaches have been used, each of which has merit; however, none is appropriate universally. Even when a sufficiently robust database exists, the scatter in the fatigue lives may be extremely large and difficult to characterize. The purpose of this work is to review traditional and more modern empirically based methodologies for estimating the statistical behavior of fatigue data. The analyses are performed on two historic sets of data for annealed aluminum wire and annealed electrolytic copper wire tested in reverse torsion fatigue. These data are readily available In publications. Specifically, the review considers a traditional method for stress-cycle (S-N) analysis which includes linear regression through load dependent medians and mean square error (MSE) confidence bounds. Another approach that is used is Weibull distribution estimation for each loading condition, from which estimations for the median behavior and confidence bounds are determined. The preferred technique is the development of a cumulative distribution functions for fatigue life, which contains aspects of traditional reliability, classical S-N, and applied loading modeling. Again, confidence bounds are estimated for this technique. Even though it is an empirical technique, there are mechanistic aspects that underlie the empiricism. This approach is suggested because the method is very robust, and the estimation is more accurate than the other methods.

Photon counting detector arrays are commonly used for deep space optical communication receivers operating on the principle of intensity modulation/direct detection (IM/DD). In scenarios where beam parameters can vary at the receiver due to scattering, it is important to estimate beam parameters in order to minimize the probability of error. The use of array of detectors increases the sensitivity of the receiver as compared to single photo-detector of the same size. In this paper, we present the derivation of a maximum likelihood estimator (ML) for peak optical intensity, providing both numerical and closed form expressions for the estimator. Performance of both forms of ML estimator are compared using the mean squared error (MSE) criterion and Cramer–Rao Lower Bound (CRLB) is also derived to assess the proposed estimator’s efficiency. This research contributed to the advancement of estimation techniques and has practical implications for optimizing deep space optical communication systems.

The ratio, product, difference estimators, and unbiased estimator under systematic sampling scheme has been studied in the presence of measurement error. The methods of estimation have been proposed for the estimation of the finite population mean. To exhibit the effect of measurement error, the study variable and auxiliary variable are supposed to be observed with measurement error. The properties of estimators' viz. bias and MSE have been obtained. The simulation study has been conducted to compute the effect of measurement error on the MSE for the different levels of correlation coefficient and different levels of error variance. [ABSTRACT FROM AUTHOR]

Poisson regression is used to deal with count data. The Poisson regression ratio estimator of the population mean is extended from single to double sampling. This is made possible by the provision of the population mean of an auxiliary variable. The mean square errors of the proposed estimators are expressed up to the first order. Theoretical and numerical results demonstrate that the proposed double-sampling Poisson-regression ratio estimator has a lower mean square error than the double-ratio and the single-sampling estimator. For Covid-19, the minimum mean square errors yielded by the proposed estimator of the total number of cases are 0.095 cases per day and 67.8 cases, compared with 0.112 cases per day and 84.8 cases with the double-ratio estimator. [ABSTRACT FROM AUTHOR]

Air pollution in Bangkok, Thailand, is mainly due to fine particles emitted in exhaust gases. However, many data on fine particle concentrations are missing, a fact which may bias the statistics. Exponential-type imputation minimizing the mean square error allows for estimating the missing values of these concentrations and provides an estimate with smaller mean square error of the mean concentration levels. The bias and mean square error of the proposed estimator are calculated. Simulation shows that the relative efficiency is 5% higher up to 50 observations, 12% higher for 100 observations, and 25% higher for 200 observations. Application to the measurement of fine particle concentration in Bangkok yields a mean square error of 0.73 micrograms per cubic meter squared, for a mean level of 47.40 micrograms per cubic meter, while the mean square error by the best alternative estimator selected is 0.90 micrograms per cubic meter squared, for a mean level of 48.20 micrograms per cubic meter. [ABSTRACT FROM AUTHOR]

In numerous application areas, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, the inverse Gaussian regression model (IGRM) is an effective approach in such scenarios. The problem of multicollinearity is very common in several application areas like chemometrics, biology, finance, and so forth. The effects of multicollinearity can be reduced using the ridge estimator. This research proposes new ridge estimators to address the issue of multicollinearity in the IGRM. The performance of the new estimators is compared with the maximum likelihood estimator and some other existing estimators. The mean square error is used as a performance evaluation criterion. A Monte Carlo simulation study is conducted to assess the performance of the new ridge estimators based on the minimum mean square error criterion. The Monte Carlo simulation results show that the performance of the proposed estimators is better than the available methods. The comparison of proposed ridge estimators is also evaluated using two real chemometrics applications. The results of Monte Carlo simulation and real applications confirmed the superiority of the proposed ridge estimators to other competitor methods. [ABSTRACT FROM AUTHOR]

Sousa et al. and Gupta et al. presented ratio and regression estimators of population mean of a sensitive variable using auxiliary information in simple random sampling without replacement. In this article, we propose a generalized randomized response technique (RRT) model and use it to develop some exponential estimators in two-phase sampling. We also discuss the privacy protection level of the proposed RRT model. Theoretical and empirical results are presented to examine the performance of the proposed mean estimators in relation to other mean estimators. [ABSTRACT FROM AUTHOR]

Channel estimation is essential in a Multiple Input Multiple Output (MIMO) wireless communication in 5G. In the MIMO system, numerous antennas are utilized on the sender and receiver sides for enhancing spectral efficiency and reliability. The channel estimation can improve the exactness of the received signal. Increasing the number of channel coefficients can make channel estimation fairly complex. Transmitting multiple paths have some delay and signal echoes. Therefore, channel assessment is very necessary for efficiently receiving the transmitted signals. A novel Enhanced Convolution Neural African Buffalo approach was developed for channel estimation purposes to overcome such issues. Moreover, the additive white Gaussian noise channel is created for MIMO communication. The simulation of this research is done using the network simulator platform. Sequentially, the proposed system outcomes are compared with other techniques in terms of throughput, accuracy, signal to noise ratio, mean square error, and bit error rate. The comparison results also proved the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this article, a class of Poisson-regression based estimators has been proposed for estimating the finite population mean in simple random sampling without replacement (SRSWOR). The Poisson-regression model is the most common method used to model count responses in many studies. The expression for bias and mean square error (MSE) of proposed class of estimators are obtained up to first order of approximation. The proposed estimators have been compared theoretically with the existing estimators, and the condition under which the proposed class of estimators perform better than existing estimators have been obtained. Two real data sets are considered to assess the performance of the proposed estimators. Numerical findings confirms that the proposed estimators dominate over the existing estimators such as Koc (2021) and Usman et al. (2021) in terms of mean squared error. [ABSTRACT FROM AUTHOR]

Infinite Impulse Response (IIR) systems identification is complicated by traditional learning approaches. When reduced-order adaptive models are utilised for such identification, the performance suffers dramatically. The IIR system is identified as an optimization issue in this study. For system identification challenges, a novel population-based technique known as Elitist teacher learner-based optimization (ETLBO) is used to calculate the best coefficients of unknown infinite impulse response (IIR) systems. The MSE function is minimised and the optimal coefficients of an unknown IIR system are found in the system identification problem. The MSE is the difference between an adaptive IIR system's outputs and an unknown IIR system's outputs. For the unknown system coefficients of the same order and decreased order cases, exhaustive simulations have been performed. In terms of mean square error, convergence speed, and coefficient estimation, the results of actual and reduced-order identification for the standard system using the novel method outperform state-of-the-art techniques. For approximating the same-order and reduced-order IIR systems, four benchmark functions are examined utilizing GA, PSO, CSO, and BA. To demonstrate the improvements, the approach is evaluated on three conventional IIR systems of 2nd, 3rd, and 4th order models. On the basis of computing the mean square error (MSE) and fitness function, the suggested ETLBO approach for system identification is proven to be the best among others. Furthermore, it is confirmed that the suggested ETLBO method outperforms some of the other known system identification strategies. Finally, the efficiency of the dynamic nature of the control parameters of DE, TLBO, and BA in finding near parameter values of unknown systems is demonstrated through comparison data. The simulation results show that the suggested system identification approach outperforms the current methods for system identification. [ABSTRACT FROM AUTHOR]

The modern digital world comprises of transmitting media files like image, audio, and video which leads to usage of large memory storage, high data transmission rate, and a lot of sensory devices. Compressive sensing (CS) is a sampling theory that compresses the signal at the time of acquiring it. Compressive sensing samples the signal efficiently below the Nyquist rate to minimize storage and recoveries back the signal significantly minimizing the data rate and few sensors. The proposed paper proceeds with three phases. The first phase describes various measurement matrices like Gaussian matrix, circulant matrix, and special random matrices which are the basic foundation of compressive sensing technique that finds its application in various fields like wireless sensors networks (WSN), internet of things (IoT), video processing, biomedical applications, and many. Finally, the paper analyses the performance of the various reconstruction algorithms of compressive sensing like basis pursuit (BP), compressive sampling matching pursuit (CoSaMP), iteratively reweighted least square (IRLS), iterative hard thresholding (IHT), block processing-based basis pursuit (BP-BP) based on mean square error (MSE), and peak signal to noise ratio (PSNR) and then concludes with future works. [ABSTRACT FROM AUTHOR]

Digital images play a very important role in developing computer-aided systems. The motion blur and blur in such types of images affect the accuracy of the system. Therefore, it is a challenging task to estimate and remove the blur in the images. In the present paper, an attempt is made to use a Convolutional Neural Network (CNN) model to estimate and remove the blur in the images. The CNN model with different functions helps to improve the accuracy of removing blur from the images. Different network functions, such as ReLU and Sigmoid, and their combinations are analyzed for the modeling of CNN. The performance of CNN is analyzed with different parameters, such as blur estimation, PSNR, RMSE, SSIM, and MSE. The performance is measured by considering different image categories, such as more blur images, less blur images, dark blur images, and biomedical images. Considering the parameters, it is observed that CNN with ReLU and Sigmoid functions is giving better performance than other network functions. It is observed that CNN models are giving successful performance to remove blur and correct the blur than any other traditional models. [ABSTRACT FROM AUTHOR]

Mini light‐emitting diodes (Mini‐LEDs) have been considered as promising light sources for direct‐lit backlight modules (BLU). To achieve uniform illumination, double freeform lenses are usually employed to redistribute rays from Mini‐LEDs. The traditional design method of a single lens under the point light source can achieve high uniformity on the observation plane. However, in the array configuration, especially when the horizontal distance between Mini‐LEDs is not equal to the vertical distance, the uniformity decreases when it is applied under the extended light source. To solve this problem, a lens design method is proposed in this paper to satisfy the requirement on uniformity. Firstly, the illuminance value is numerically calculated based on array configuration and illuminance superposition method. Then we optimize the illuminance distribution curve with the feedback method. A double freeform lens is designed based on the optimized illuminance curve. On the target plane, the simulation results show that compared with the traditional method of lens design, the uniformity improves from 77.69% to 88.03%. The design method is simple, effective, and easy to implement. [ABSTRACT FROM AUTHOR]

In this manuscript, we propose the combined and separate difference and ratio type estimators of population mean using stratified ranked set sampling. Additionally, several well-known estimators are identified as the sub-class of the suggested estimators. The characteristics of the suggested estimators have been analyzed and their effective performances are compared with the prominent estimators existing till date. Moreover, to prove the credibility of the theoretical findings, an extensive empirical study is administered over some real and hypothetically yielded symmetric and asymmetric populations. [ABSTRACT FROM AUTHOR]

Many varieties of technologies have been introduced for mobile communication and data traffic plays a major role in each generation of communication systems. 5G is termed as Next Generation Wireless Mobile Networks that has higher bandwidth, maximum spectral efficiency, super-speed connection, minimum energy consumption, when compared to 4G wireless networks. Next Generation of Mobile communication will use mmWave frequency bands for 5G systems. Millimeter wave transmission is one of the greatest technology in 5G mobile communication systems having higher bandwidth. It is also considered to be having high user demands and have a mobile growth in coming years. It is a promising technology having a non-shortage bandwidth and traffic demands. The major drawback in this system is Phase noise, In-phase and Quadrature timing mismatch, PAPR, local oscillator noise and blockage effects. The phase noise occurs due to the imperfections in local oscillators. In this paper, we discuss the Phase noise issues in millimeter wave systems. This review will act as guide for researchers to compare the various emerging phase noise problems and mitigation techniques for future 5G wireless networks. [ABSTRACT FROM AUTHOR]

In this paper, we suggest an exponential type estimator for estimation of population mean for missing data under suggested imputation techniques. Family of proposed estimator is obtained for missing data. Expression for Bias and MSE's are acquired in the form of population parameters up to the terms of first order of approximation. Theoretical results depict the superiority of proposed estimator and its family over other estimators. The empirical study in support of theoretical results is also included to verify the results numerically. [ABSTRACT FROM AUTHOR]

In this article, we proposed a novel dual to ratio cum product type exponential estimator in stratified random sampling. The bias and mean square error up to the first degree of approximation of the proposed estimator have been obtained. The proposed estimator has been compared with the unbiased estimator in stratified random sampling, combined ratio and product estimators, dual to combined ratio, and product estimators. Our results showed a great improvement in terms of relative efficiency. Also, the results are supported by empirical studies. [ABSTRACT FROM AUTHOR]

The present research article emphasizes on proposing an improved generalized regression-cum-exponential (GRE) estimator to achieve better efficiency for estimating the mean. The proposed GRE estimator is based on optimal use of the available known conventional and non-conventional parameters of the auxiliary variable such as coefficient of skewness, coefficient of kurtosis, median, quartile deviation, Downton's scale method and probability weighted moments. The expressions of bias and mean square error of the proposed estimator are obtained under large sample approximation to study their properties. The optimal condition for obtaining the minimum mean square error of the proposed estimators is determined up to the first order of approximation. Theoretical as well as empirical comparisons have elaborately been presented to exhibit the efficiency of suggested estimators over the conventional and other promising relevant estimators. The performances of suggested GRE estimators over the well-known discussed contemporary estimators in the text have also been confirmed through a simulation study. [ABSTRACT FROM AUTHOR]

In this article we have proposed some new improved ratio estimators based on robust regression that are robust against outliers and provide reliable results even when outliers are present; the properties are also investigated. The proposed class of estimators has been shown to be more effective than the current classes of estimators. An empirical analysis was conducted to see how well the proposed class of estimators compared to others. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the interpretable models from real gasification datasets of the project "Centre for Energy and Environmental Technologies" (CEET) discovered by symbolic regression. To evaluate CEET models based on input data, two different statistical metrics to quantify their accuracy are usually used: Mean Square Error (MSE) and the Pearson Correlation Coefficient (PCC). However, if the testing points and the points used to construct the models are not chosen randomly from the continuum of the input variable, but instead from the limited number of discrete input points, the behavior of the model between such points very possibly will not fit well the physical essence of the modelled phenomenon. For example, the developed model can have unexpected oscillatory tendencies between the used points, while the usually used statistical metrics cannot detect these anomalies. However, using dynamic system criteria in addition to statistical metrics, such suspicious models that do fit well-expected behavior can be automatically detected and abandoned. This communication will show the universal method based on dynamic system criteria which can detect suitable models among all those which have good properties following statistical metrics. The dynamic system criteria measure the complexity of the candidate models using approximate and sample entropy. The examples are given for waste gasification where the output data (percentage of each particular gas in the produced mixture) is given only for six values of the input data (temperature in the chamber in which the process takes place). In such cases instead, to produce expected simple spline-like curves, artificial intelligence tools can produce inappropriate oscillatory curves with sharp picks due to the known tendency of symbolic regression to produce overfitted and relatively more complex models if the nature of the physical model is simple. [ABSTRACT FROM AUTHOR]

The transformation method can be used to increase the efficiency of the variable of interest for estimating population mean. Two classes of combined population mean estimators utilizing transformation on an auxiliary variable and on both an auxiliary variable and a study variable have been proposed under double sampling. The formulas of the biases and mean square errors of the proposed estimators are obtained. Simulation studies and an application to fine particulate matter 2.5 and nitrogen dioxide pollution data in Chiang Rai, Thailand have been investigated to assess performance of the proposed estimators compared to other existing estimators. Under certain conditions, the results indicate that the proposed combined estimators perform much better than other existing estimators. [ABSTRACT FROM AUTHOR]

Unbiased estimators of the population parameters are often used to make an inference about the population. In cases where unbiased estimators have large variance, biased estimators such as shrinkage estimators may be preferred. In this study, shrinkage estimators of the location parameter of the normal distribution were obtained under ranked set sampling and median ranked set sampling. In addition, mean square errors of shrinkage estimators were obtained theoretically under ranked set sampling and median ranked set sampling. In order to examine the efficiency of the estimators, the mean square errors were calculated under different conditions using Monte Carlo simulation study. According to the results, it was observed that the shrinkage estimators obtained under median ranked set sampling were more efficient than the shrinkage estimators obtained under ranked set sampling and simple random sampling. [ABSTRACT FROM AUTHOR]

This work is an extension to the work of [1] on ratio estimators of variance, by modification using dual to ratio method. The consistency conditions, bias, mean square error, optimum mean square error and efficiency have been derived and its performance is illustrated using natural populations. It is observed that the proposed class of estimators is most efficient at its optimum value, due to highest percent relative efficiency generated by it, when compared to the usual unbiased estimator for variance. [ABSTRACT FROM AUTHOR]

In this study, the influence of the process parameter setting of the hot-air leaf moisturizer on the quality index of the exit leaf during the secondary leaf conditioning of threshing and redrying is studied, and the corresponding prediction model is established. A BP neural network prediction model is established based on the characteristics of the secondary leaf conditioning process data. The current popular neural network writing framework TensorFlow’s high-level API interface is called to construct the neural network structure. The activation function, optimizer, number of hidden layer neurons and other key parameters are gradually adjusted in the neural network structure to make the prediction result of the test set reach the best state. By inputting the parameters of the front steam nozzle pressure, front-end water flow rate, hot air temperature, return air temperature, feed blade temperature, and feed blade moisture combination, the two key tobacco leaf evaluation indicators, namely, outlet leaf moisture and temperature, are predicted. According to the mean square error, root mean square error, and average absolute error of the prediction results, it is concluded that when the number of neurons in the hidden layer is 7, the activation function selects ReLU, and the optimizer selects RMSprop, the effect is the best. [ABSTRACT FROM AUTHOR]

Real-time monitoring has received considerable attention recently due to its potential in automatic driving, tele-surgery, and factory automation in the 6G era. In remote estimation or reconstruction of stochastic processes, the statistical properties of stochastic processes to be monitored play a central role. Among the stochastic processes interested by real-time applications, the Brownian motion, also known as the Wiener processes is a typical one. In this paper, we are interested in how to monitor Brownian motions efficiently, timely, and reliably. To achieve this goal, we reveal that the real-time estimation error is jointly determined by the quantization error and freshness of data samples. Based on this observation, we present an optimal joint sampling and quantization scheme that efficiently balances the quantization distortion and the age-of-information (AoI). Furthermore, we find that the error accumulation will lead to infinite distortion as monitoring time increases. To overcome this, a multi-layer error correction method is presented for infinite-time monitoring, in which bounded distortion can be achieved with limited data rate. Finally, to conquer the accumulation of transmission errors in unreliable channels, we present an error correction mechanism based on periodic feedback. Diffusion approximation is then adopted to determine the optimal feedback rate and interval. [ABSTRACT FROM AUTHOR]