Minimum Mean Square Error Prediction Research Articles

Colorimetric Concurrent Determination of Ultra-Trace Amounts of Pilocarpine and Timolol as anti-Glaucoma Drugs in Binary Mixtures Using a Multivariate Calibration Approach Based on the Aggregation of Gold Nanoparticles.

To study the ultra-trace simultaneous determination of drugs, the colorimetric method in combination with chemometrics can be used. In this study, a simple, rapid, and sensitive UV-Vis spectrophotometric method using gold nanoparticles (AuNPs) was introduced for the simultaneous determination of ultra-trace amounts of Pilocarpine (PIL) and Timolol (TIM) in binary mixtures and biological sample. AuNPs interacted with components and the aggregation mode of NPs occurred and finally, the color change of the solution (red to gray) was observed with the naked eye without the most modern and expensive instruments. The characterization of AuNPs was evaluated by transmission electron microscopy (TEM) and dynamic light scattering (DLS). The validation of the colorimetric way was studied in the concentration range of 100-800 and 100-600 μg/L with good linearity equal to 0.9772 and 0.9891 for PIL and TIM, respectively. The limit of detection (LOD) was found to be 165.00 and 92.40 μg/L, where the limit of quantitation (LOQ) was 500.00 and 280.00 μg/L for PIL and TIM, respectively. The effect of some factors such as interaction time, the concentration of components, and the volume of buffer on absorbance was investigated. Partial least squares (PLS) as an efficient multivariate calibration method was combined with colorimetry for the simultaneous determination of PIL and TIM in binary mixtures. The optimum number of latent variables was selected by k-fold cross-validation based on minimum mean square error prediction (MSEP) and the number of components equal to 1 with MSEP of 1.085 and 0.763 was considered for PIL and TIM, respectively. The mean recovery was obtained at 100.20% and 101.55% for PIL and TIM, respectively. The colorimetric method can be introduced as a proper option for the simultaneous determination of components in pharmaceutical formulations and other samples. A colorimetric method using AuNPs was proposed.PLS method was coupled with a colorimetric method for the ultra-trace simultaneous estimation of PIL and TIM in binary mixtures.Ultra-trace amounts of PIL and TIM were also determined in biological sample.The proposed method is simple, fast and less expensive than chromatography methods.

Evaluating bias control strategies in observational studies using frequentist model averaging

ABSTRACT Estimating a treatment effect from observational data requires modeling treatment and outcome subject to uncertainty/misspecification. A previous research has shown that it is not possible to find a uniformly best strategy. In this article we propose a novel Frequentist Model Averaging (FMA) framework encompassing any estimation strategy and accounting for model uncertainty by computing a cross-validated estimate of Mean Squared Prediction Error (MSPE). We present a simulation study with data mimicking an observational database. Model averaging over 15+ strategies was compared with individual strategies as well as the best strategy selected by minimum MSPE. FMA showed robust performance (Bias, Mean Squared Error (MSE), and Confidence Interval (CI) coverage). Other strategies, such as linear regression, did well in simple scenarios but were inferior to the FMA in a scenario with complex confounding.

A recursive linear MMSE filter for dynamic systems with unknown state vector means

In this contribution we extend Kalman-filter theory by introducing a new recursive linear minimum mean squared error (MMSE) filter for dynamic systems with unknown state-vector means. The recursive filter enables the joint MMSE prediction and estimation of the random state vectors and their unknown means, respectively. We show how the new filter reduces to the Kalman-filter in case the state-vector means are known and we discuss the fundamentally different roles played by the intitialization of the two filters.

OFDM Joint Data Detection and Phase Noise Cancellation for Constant Modulus Modulations

This correspondence proposes a new algorithm for the OFDM joint data detection and phase noise (PHN) cancellation for constant modulus modulations. We highlight that it is important to address the overfitting problem since this is a major detrimental factor impairing the joint detection process. In order to attack the overfitting problem we propose an iterative approach based on minimum mean square prediction error (MMSPE) subject to the constraint that the estimated data symbols have constant power. The proposed constrained MMSPE algorithm (C-MMSPE) significantly improves the performance of existing approaches with little extra complexity being imposed. Simulation results are also given to verify the proposed algorithm.

On spatial skew‐Gaussian processes and applications

AbstractIn many applications, observed spatial variables have skewed distributions. It is often of interest to model the shape of the skewed marginal distributions as well as the spatial correlations. We propose a class of stationary processes that have skewed marginal distributions. The covariance function of the process can be given explicitly. We study maximum likelihood inference through a Monte Carlo EM algorithm, and develop a method for the minimum mean‐square error prediction. We also present two applications of the process. Copyright © 2009 John Wiley & Sons, Ltd.

Linear Predictive Detection for Power Line Communications Impaired by Colored Noise

Robust detection algorithms capable of mitigating the effects of colored noise are of primary interest in communication systems operating on power line channels. In this paper, we present a sequence detection scheme based on linear prediction to be applied in single-carrier power line communications impaired by colored noise. The presence of colored noise and the need for statistical sufficiency requires the design of an optimal front-end stage, whereas the need for a low-complexity solution suggests a more practical suboptimal front-end. The performance of receivers employing both optimal and suboptimal front-ends has been assessed by means of minimum mean square prediction error (MMSPE) analysis and bit-error rate (BER) simulations. We show that the proposed optimal solution improves the BER performance with respect to conventional systems and makes the receiver more robust against colored noise. As case studies, we investigate the performance of the proposed receivers in a low-voltage (LV) power line channel limited by colored background noise and in a high-voltage (HV) power line channel limited by corona noise.

Power Control and Diversity in Feedback Communications Over a Fading Channel

Pilot-symbol-assisted modulation system using feedback minimum mean-square error (MMSE) power control in subject to an unavoidable feedback delay, and in conjunction with diversity, is considered over a slow Rayleigh fading channel. Feedback MMSE power control is defined as a power-control function, with feedback MMSE predictions of the current channel fading gains as input that minimizes the system-error probability. The use of feedback requires causality, and an MMSE predictor has to be employed for the purpose of power control. Previously, in the literature, the predictor was used also in detection. The pilot-symbol system with MMSE power control is shown to achieve a clear performance improvement by employing a smoother, instead of the predictor, in detection. Furthermore, the performance loss caused by a feedback delay of 10%-20% from the channel coherence time appeared to be minor with reasonable bit-error rate levels. Finally, additional performance improvement using low-order diversity was shown to be considerable.

Reliable Adaptive Modulation Aided by Observations of Another Fading Channel

Adaptive transmission techniques, such as adaptive modulation and coding, adaptive power control, adaptive transmitter antenna diversity, etc., generally require precise channel estimation and feedback of channel state information (CSI). For fast vehicle speeds, reliable adaptive transmission also requires long-range prediction of future CSI, since the channel conditions are rapidly time variant. In this paper, we propose using past channel observations of one carrier to predict future CSI and perform adaptive modulation without feedback for another correlated carrier. We derive the minimum mean-square error (MMSE) long-range channel prediction that uses the time- and frequency-domain correlation function of the Rayleigh fading channel. An adaptive MMSE prediction method is also proposed. A statistical model of the prediction error that depends on the frequency and time correlation is developed and is used in the design of reliable adaptive modulation methods. We use a standard stationary fading channel model (Jakes model) and a novel physical channel model to test our algorithm. Significant gains relative to nonadaptive techniques are demonstrated for sufficiently correlated channels and realistic prediction range.

Optimal Interpolation and the Appropriateness of Cross-Validating Variogram in Spatial Generalized Linear Mixed Models

This article considers some computational issues related to the minimum mean squared error (MMSE) prediction of non-Gaussian variables under a spatial generalized linear mixed model (GLMM). Earlier literature decribes how this model has been used to model spatial non-Gaussian variables, under which MMSE prediction of non-Gaussian variables can be computed. Because the MMSE prediction is nonlinear and cannot be computed in closed form, Markov chain Monte Carlo techniques are employed to approximate the predictor. We first establish some analytical results and show through three examples how these results can be used to make the MMSE predictions computationally more efficient. We then examine the effectiveness of cross-validating variogram in a spatial GLMM through a simulation study. Cross-validation is closely related to prediction since it uses partial data to predict the remaining. Our results show that cross-validation may fail to indicate the obvious lack of fit of a variogram in a spatial non-Gaussian GLMM.

Optimal nonlinear adaptive prediction and modeling of MPEG video in ATM networks using pipelined recurrent neural networks

This paper investigates the application of a pipelined recurrent neural network (PRNN) to the adaptive traffic prediction of MPEG video signal via dynamic ATM networks. The traffic signal of each picture type (I, P, and B) of MPEG video is characterized by a general nonlinear autoregressive moving average (NARMA) process. Moreover, a minimum mean-squared error predictor based on the NARMA model is developed to provide the best prediction for the video traffic signal. However, the explicit functional expression of the best mean-squared error predictor is actually unknown. To tackle this difficulty, a PRNN that consists of a number of simpler small-scale recurrent neural network (RNN) modules with less computational complexity is conducted to introduce the best nonlinear approximation capability into the minimum mean-squared error predictor model in order to accurately predict the future behavior of MPEG video traffic in a relatively short time period based on adaptive learning for each module from previous measurement data, in order to provide faster and more accurate control action to avoid the effects of excessive load situation. Since those modules of PRNN can be performed simultaneously in a pipelined parallelism fashion, this would lead to a significant improvement in the total computational efficiency of PRNN. In order to further improve the convergence performance of the adaptive algorithm for PRNN, a learning-rate annealing schedule is proposed to accelerate the adaptive learning process. Another advantage of the PRNN-based predictor is its generalization from learning that is useful for learning a dynamic environment for MPEG video traffic prediction in ATM networks where observations may be incomplete, delayed, or partially available. The PRNN-based predictor presented in this paper is shown to be promising and practically feasible in obtaining the best adaptive prediction of real-time MPEG video traffic.

Predicting the value of an integer-valued random variable

Predicting the value of a random variable Y, based on the observed value of another random variable X is a common objective of data analysis. It is well-known that the minimum mean-squared error predictor of Y is the mean of the conditional distribution of Y, given X. In cases where Y is necessarily integer-valued, the conditional mean is not always a feasible value for Y and, therefore, is an unsatisfactory predicted value. In this paper, it is shown how minimum mean-squared error integer-valued predictors can be obtained.

A simple and versatile decentralized control for slotted ALOHA, reservation ALOHA, and local area networks

A simple, decentralized control for reducing the delays and stabilizing random-access channels is presented. The control, which is based on a computationally efficient recursive implementation of the minimum mean-squared error (MMSE) predictor of the channel backlog, applies to slotted ALOHA, to reservation ALOHA, and to local area networks (LANs) with carrier-sense multiple access (CSMA) or CSMA with collision detection (CSMA/CD) protocols. The MMSE predictor controller (MMSE-PC) can stabilize the slotted ALOHA for all traffic rates not exceeding e/sup -1/, and it can achieve stable throughput arbitrarily close to one with finite delays in the reservation ALOHA and in LANs. Extensive simulation has shown that the MMSE-PC performs extremely well in all three random-access environments. For the implementation of the MMSE-PC in LANs, synchronization of transmissions is not required but it is required in slotted ALOHA and reservation ALOHA. The MMSE-PC has been implemented in hardware and tested in asynchronous LANs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the design of nonlinear discrete-time predictors (Corresp.)

The problem of minimum mean-squared error prediction of a discrete-time random process using a nonlinear filter consisting of a zero-memory nonlinearity followed by a linear filter is studied. Classes of random processes for which the best predictor is realizable using a nonlinear filter of the above form are discussed. For those random processes for which the best predictor is not realizable using the above nonlinear filter, an iterative procedure is presented for finding a suboptimal nonlinear filter; special attention is directed to the case where the nonlinearity is a polynomial. Also, a noniterative approach based on nonlinear regression is presented.

Adaptive prediction for DPCM coding of TV signals

An adaptive minimum mean-squared error prediction algorithm has been derived for DPCM coding of video signals. Its parallel structure guarantees the possibility of high-speed implementation. Simulations show that there is only little gain in terms of signal-to-noise ratio as compared to optimum fixed prediction. However, if the autocorrelation function of the input is not known a priori and there is a mismatch in the prediction coefficients, the gain due to a fixed predictor experiences a severe dropoff, and adaptive prediction proves superior.

Two-dimensional linear prediction: Autocorrelation arrays, minimum-phase prediction error filters, and reflection coefficient arrays

In this paper, a number of results in one-dimensional (1-D) linear prediction theory are extended to the two-dimensional (2-D) case. It is shown that the class of 2-D minimum mean-square linear prediction error filters with continuous support have the minimum-phase property and the correlation-matching property, and that they can be solved by means of a 2-D Levinson algorithm. A significant practical result to emerge from this theory is a reflection coefficient representation for 2-D minimum-phase filters. This representation provides a domain in which to construct 2-D filters, such that the minimum-phase condition is automatically satisfied.