An outline of the paper is as follows: Section II describes the adaptive filtering problem, now in the FrFT domain. Section III presents the full rank MMSE-FrFT solution proposed in [13]. Sections IV - VI describe the three new algorithms, termed DD-FrFT, WD-FrFT, and MWF-FrFT, respectively; MMSE-FrFT has been previously shown to outperform FFT methods, so we do not discuss the FFT, which fails here [14]. Section VII shows simulation results to compare all four algorithms. We compare the values of „a‟ as well as the **mean**-**square** **error** (MSE) estimates. Finally, conclusions and remarks on future work are given in Section VIII.

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Abstract The Nummellin’s split chain construction allows to decompose a Markov chain Monte Carlo (MCMC) trajectory into i.i.d. “excursions”. Regenerative MCMC algorithms based on this technique use a random number of samples. They have been proposed as a promising alternative to usual fixed length simulation [25, 33, 14]. In this note we derive nonasymptotic bounds on the **mean** **square** **error** (MSE) of regenerative MCMC estimates via techniques of renewal theory and sequential statistics. These results are applied to costruct confidence intervals. We then focus on two cases of particular interest: chains satisfying the Doeblin condition and a ge- ometric drift condition. Available explicit nonasymptotic results are compared for different schemes of MCMC simulation.

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Abstract – Channel Estimation (CE) in multicarrier system especially in Orthogonal Frequency Division Multiplexing (OFDM) systems has become an important technique in wireless communication to reduce the overall effect of high data rate and increase links performance. In wireless channel, which has frequency selective distribution, the transmitted signals are corrupted and resulted in high **error** at the receiver. However, the existing techniques in use such as Least **Square** Estimation (LSE), Minimum **Mean** **Square** **Error** (MMSE) are based on single carrier system with pilot symbols for channel estimation to reduce the **error**. Therefore, in this paper, investigation of the performance of blind channel estimation in sixteen (16) subcarriers OFDM system using a Constant Modulus Algorithm (CMA) is carried out. The system model for sixteen subcarriers OFDM incorporating CMA is developed over the frequency selective fading channel. OFDM system consists of the following signal processing techniques; sixteen channel demultiplexer, Inverse Fast Fourier transform (IFFT), Cyclic Prefix (CP), sixteen channels multiplexer and the Radio Frequency (RF) transmit antenna all at the transmitter. Also, at the receiver are RF receive antenna, sixteen channel demultiplexer, Fast Fourier transform (FFT), sixteen channel multiplexer, Cyclic Prefix (CP) removal and decoder. The input data are generated randomly, converted to bits and divided among the subcarriers to reduce overlapping of bits. The signal processing techniques at both the transmitter and receiver process the signal. The system model is simulated by MATLAB application package and evaluated using **Mean** **Square** **Error** (MSE). This is now compared with the LSE and MMSE estimation. The results obtained using 16- subcarrier OFDM with CMA give lower MSE than with LSE over frequency selective environment.

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BOUNDS FOR THE MEAN SQUARE ERROR OF RELIABILITY ESTIMATION FROM GAMMA DISTRIBUTION IN PRESENCE OF AN OUTLIER OBSERVATION M.E.. GHITANY and W.H.[r]

The quality of transmit pre-coding to control multiuser interference is degraded due to the coarse knowledge of CSI at the transmitter. Hence channel estimation technique employing reliable soft symbols to improve the channel estimation and subsequent detection quality of MU-MIMO [10] systems was proposed. In order to jointly estimate the channel and data symbols, the expectation maximization (EM) algorithm is employed where the channel estimation and data decoding are performed iteratively. Distributed Channel Estimation and Pilot Contamination (DCEPC) [11] analysis was proposed for finding reliable data carriers and to reduce carrier interference in the data. Data aided estimation technique is used to determine the reliable data carriers and distributed minimum **mean** **square** **error** algorithm is proposed to achieve optimal channel estimates using spatial correlation among antenna array elements. However this technique has large computational cost and channel overheads are high because of multi-cell massive MIMO-OFDM wireless system.

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A cepstrum estimator is proposed based on a weighted multitaper spectrum. An evaluation of different approx- imations for bias and variance of the multitaper log- spectrum is made, and a **mean** **square** **error** criterion is proposed that includes novel approximations of the bias and variance. The weights of the multitaper spectrum are optimized, and the new estimator, the optimal weights combined with the sinusoidal tapers, is evaluated for cep- strum estimation of speech-like processes. The results show that a 10% to 20% reduction of the **mean** **square** **error** of the cepstrum can be achieved, to the cost of two or three additional periodogram computations.

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Daily 615.33 771.54 Weekly -11.19 6.94 Monthly 1.64 -11.91 Quarterly 11.37 -0.98 From Table 1, we can see that the ARIMA model can represent monthly and quarterly series, whereas the ARMA model can represent daily and weekly series. Then, the time horizon of forecasting were calculated and short terms forecasting were chosen by considering the smallest value of Root **Mean** **Square** **Error** (RMSE). Forecasting results are summarized in Table 2.

Light-field imaging can capture both spatial and angular information of a 3D scene and is considered as a prospective acquisition and display solution to supply a more natural and fatigue-free 3D visualization. However, one problem that occupies an important position to deal with the light-field data is the sheer size of data volume. In this context, efficient coding schemes for such particular type of image are needed. In this paper, we propose a scalable kernel-based minimum **mean** **square** **error** estimation (MMSE) method to further improve the coding efficiency of light-field image and accelerate the prediction process. The whole prediction procedure is decomposed into three layers. By using different prediction method in different layers, the coding efficiency of light-field image is further improved and the computation complexity is reduced both in encoder and decoder side. In addition, we design a layer management mechanism to determine which layers are to be employed to perform the prediction of the coding block by using the high correlation between the coding block and its adjacent known blocks. Experimental results demonstrate the advantage of the proposed compression method in terms of different quality metrics as well as the visual quality of views rendered from decompressed light-field content, compared to the HEVC intra-prediction method and several other prediction methods in this field.

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Abstract :- Smart CCTV (Closed-Circuit Television) technology has increasingly been developed in the last few years to judge the situation and notify the administer or take immediate action for security and surveillance motives. Earlier, the Difference Method (FDM),Background Subtraction Method (BSM), and Adaptive Background Subtraction Method (ABSM) is used for motion object detection but these methods could not recognize rapid scene changes or an object does not move relatively for a long time. To solve such problem , we proposed a novel moving object detection method which showed high performance with regard to the MSE(**Mean** Squared **Error** ) and the accuracy of detecting the moving object contours compared to other existing methods. It also reduces the time complexity and provides the accuracy .It is also good for observation of many places at the same time with only a single CCTV system.

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Furthermore, the forecasting **error** method that is used in this research is **Mean** Absolute **Error** (MAE), **Mean** **Square** **Error** (MSE), and Standard Deviation **error** (SDE). Analysis results indicate that the SES method resulted in the lowest forecasting **error** compares with other quantitative forecasting methods. It also happens when forecasting results produced by deploying the SES method compares with judgmental forecasting and the combination of SES method and judgmental forecasting using 50%-50% weight for each method. In addition, the findings of the research show that the quantitative forecasting method (in this study, SES method has the best performance of forecasting) has a clear procedure to do the forecasting tasks and suitable for the products that have time-series data. Furthermore, qualitative forecasting method such as human judgment is needed for a particular situation (for example for the new products, promotion event, etc.) and when managers have some contextual information regarding the products under concern.

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It can be concluded from the mathematical background and subsequent results that the proposed system yields high accuracy for text mining data. The data used here are in the form of tweets. The training algorithm used is Levenberg-Marquardt (LM) which yields stability in **error** prediction. The proposed system uses 997 tweets out of which 70% has been used for training and the rest of the 30% have been used for testing. The data division in to training and testing data sets has been kept random. The number of neurons in the hidden layer has been kept as 10. The accuracy achieved by the propose system in terms of **Mean** **Square** **Error** (MSE) is 95.15%

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ABSTRACT: The Long term evolution (LTE) is the current extension of the third generation (3G) mobile communication system that provides high improvement in data rate, coverage and spectral efficiency. Since downlink is always an important factor in coverage and capacity aspects, special attention has been given in selecting technologies for LTE downlink. In proposed work, least **square** **error** (LSE) and minimum **mean** **square** **error** (MMSE) channel estimation techniques are presented for long term evolution (LTE). The performance of two channel estimators for LTE Downlink systems, the Least **Square** **Error** (LSE) and the Minimum **Mean** **Square** **Error** (MMSE) are studied and finally compared their simulation results under different multipath fading. The proposed work will demonstrate the efficiency of LSE and MMSE over different Fading channel like AWGN, Rayleigh fading and Nakagami fading with mobility and without mobility. Then, a polynomial interpolation algorithm using the method of Lagrange is represented which greatly reduces the complexity of the transceiver. MATLAB simulations are used to evaluate the performance of the studied estimators. These simulation results show that Lagrange interpolation technique performs better than MMSE and LSE for both the case without mobility and with mobility under all three multipath fading channels. Further, mobility increases the **Mean** **Square** **Error** (MSE) of the system.

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Simulation is carried out for various parameters and they were tested using many combination of parameters in independent experiments. The optimal prediction data for various ANN models were obtained by comparing with the parameter of **error** estimates such as **Mean** Absolute **Error** (MAE), **Mean** **Square** **Error** (MSE), **Mean** Absolute Percentage **Error** (MAPE) and Root **Mean** **Square** **Error**(RMSE).Among the predictors ,the most important factor influencing Colon Cancer is obesity,followed by eating red meat,smoking,taking medicines like aspirin and last of all lack of physical activity.

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Webster et al. ([W+76]), Latent root regression follows the same principle as the Principal Component Regression. In fact, it can be rightly referred to as an extension of Principal Component for examining alternative prediction equation and for the elimination of predictor variables. It was first proposed by Webster, Gunst and Mason ([W+76]) – Latent Root regression attempts to identify and eliminate multicollinearity. It will be noted that it is reduced to the Least Squares when no terms are actually deleted from the original data. Gunst et al. ([W+76]) and Gunst and Mason ([GM77]), indicate that Latent Root Regression may provide considerable improvement in the **Mean** **Square** **Error** (MSE) over Least Squares. Gunst and Mason ([GM80]), points out that it can produce regression coefficients that are very similar to those found by Principal Component Regression, particularly when there are only one or two strong multicollinearity in X data.

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Best fitted model were analyze using statistical criteria of Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE) The best model used for forecasting the r[r]

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Image processing (IP) is an approach to convert an image into digital shape and carry out a few operations on it to attain some beneficial statistics from it. The main intention of image processing is to visualization, Image polishing and healing, and picture retrieval, dimension of sample, picture popularity. In Digital Image Processing (DIP), the images are more prone to noise due to image capture and transmission. Digital images (DI) are contaminated via numerous varieties of noises which include Gaussian, Speckle and Impulse noise. There are numerous technique of denoise image. The most necessary property of ID model is that it should completely reduce noise as much as possible and edge preservation. This paper gives an insight view of some major work in the field of ID. This study affords a robust-discrete wavelet transform (DWT)-Discrete cosine Transform (DCT) based approach that denoises the image by adding weighted high pass filtering coefficients in wavelet domain. Thereafter denoised algorithm further enhanced by Exposure based Sub-Image Histogram Equalization (ESIHE) that is the novelty of the proposed work. Experimental results show that proposed algorithm enhances the denoising performance measured in terms of performance parameter and gives better visual quality. **Mean** **Square** **Error** (MSE), Root **Mean** **Square** **Error** (RMSE) and Peak Signal to Noise Ratio (PSNR) used as a performance parameters which degree the feature of an picture.

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The performance of the proposed algorithm is given in terms of **Mean** **Square** **Error** (MSE), **Mean** Absolute **Error** (MAE) and Peak Signal to Noise Ratio (PSNR) and it is compared with standard median filters, weighted median filters, center weighted median filters, Recursive weighted median filters and Lin’s Adaptive length recursive weighted median filters using median controlled algorithm.

The block diagram of a dual input adaptive noise canceller is shown in Figure 3. The adaptive noise canceller mainly consists of two sensors: primary sensor, which intends to supply a desired signal along with noise and a reference sensor which is responsible for supplying noise alone. The signal and noise at the output of the primary sensor are uncorrelated and the noise at the output of the reference sensor is correlated with the noise component of the primary- sensor output. The adaptive filter operates on the reference sensor output and thus produces an estimate of the noise and this is subtracted from the primary sensor output [2]. The adjustments applied to the tap weights in the adaptive filter are controlled with the aid of the overall output of the adaptive noise canceller. The adaptive canceller tends to minimize the **mean**-**square** **error** (MSE) value of the overall output, thereby causing the output to be the best estimate of the desired signal in the minimum-**mean**-**square** **error** sense [3].

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In the recent years, the crude oil is one of the most important commodities worldwide. This paper discusses the prediction of crude oil using artificial neural networks techniques. The research data used in this study is from 1 st Jan 2000- 31 st April 2014. Normally, Crude oil is related with other commodities. Hence, in this study, the commodities like historical data’s of gold prices, Standard & Poor’s 500 stock index (S & P 500) index and foreign exchange rate are considered as inputs for the network. A radial basis function is better than the back propagation network in terms of classification and learning speed. When creating a radial basis functions, the factors like number of radial basis neurons, radial layer’s spread constant are taken into an account. The spread constant is determined using a bio inspired particle swarm optimization algorithm. A hybrid Radial Basis Function is proposed for forecasting the crude oil prices. The accuracy measures like **Mean** **Square** **Error**, **Mean** Absolute **Error**, Sum **Square** **Error** and Root **Mean** **Square** **Error** are used to access the performance. From the results, it is clear that hybrid radial basis function outperforms the other models.

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In the track irregularity detection, the acceleration signals of the inertial measurement unit (IMU) output which with low frequency components and noise, this paper studied a de-noising algorithm. Based on the criterion of consecutive **mean** **square** **error**, a de-noising method for IMU accelera- tion signals based on empirical mode decomposition (EMD) was proposed. This method can divide the intrinsic mode functions (IMFs) derived from EMD into signal dominant modes and noise do- minant modes, then the modes reflecting the important structures of a signal were combined to- gether to form partially reconstructed de-noised signal. Simulations were conducted for simulated signals and a real IMU acceleration signals using this method. Experimental results indicate that this method can efficiently and adaptively remove noise, and this method can better meet the pre- cision requirement.

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