Presence Of Estimation Errors Research Articles

Dental age assessment and dental scoring systems: combined different statistical methods.

Age Estimation has been considered as a human basic right, carried out through the use of tables for dental age assessment based on the chronology of tooth eruption. As such, the final aim of this investigation is to create tables with applicability to the Portuguese population, for the different scoring systems used and combined different statistical approaches. For this purpose, dental age assessment was achieved in all four third molars, using different scoring systems, in a total sample of 626 orthopantomograms (324 females, 302 males), aged between 12 and 25 years old, from the database population of Lisbon North University Hospital Center, approved by the Ethic Committee. The values of validation showed excellent results both on precision and on reproducibility. Mostly all methods showed statistically significant differences between the estimated age and the chronological age and, therefore, the presence of estimation errors. Kullman's and Mincer's methods are the ones with best applicability in the Portuguese population, in the lower third molars. The reliability measures (sensitivity, specificity and accuracy) values decrease as age increases. A combination of the scoring systems as a protocol for dental age assessment in Portuguese nationality was established. Tables, for all the scoring systems used, were made with applicability in the Portuguese population.

Performance Analysis of Random Access NOMA for Critical mIoT With Timer-Power Back-Off Strategy

Massive machine type communication (mMTC) and Internet-of-Things (IoT) networks provide global connectivity for massive number of end devices anytime-anywhere. The most challenging part in implementing such networks is the development of spectrum access strategies to provide ultra-reliable low-latency (URLL) transmissions for a large number of nodes with sporadic traffic behavior. Such networks have to deploy spectrum-efficient transmission schemes, and thus, non-orthogonal multiple-access (NOMA) is considered as a viable solution, that can be used to provide high number of URLL transmissions. We propose a random access NOMA transmission protocol (RA-NOMA) for IoT networks with large number of clustered IoT devices is proposed. The nodes in the proposed scheme adopt timer and power back-off strategies to transmit their short packets in a collision-free NOMA-based manner to achieve the URLL requirements. Closed-form expressions for network metrics, namely, delay violation probability, average packet latency, reliability, and effective sum rate (ESR) are analytically derived. Furthermore, the effect of blocklength, back-off timer (countdown value) and the number of active nodes on network metrics is explored. Additionally, the effect of the estimation error on the number of active nodes is analyzed and the impact of preamble transmit power on reliability in the presence of estimation error is investigated. Moreover, mathematical expressions for network metrics are also derived for NOMA-ALOHA with transmission diversity (NOMA-ALOHA-TD) in the underlying scenario, and the obtained results from NOMA-ALOHA-TD and the proposed RA-NOMA are compared.

Improving portfolio investment performance with distance‐based portfolio‐combining algorithms

AbstractWe propose distance‐based portfolio‐combining algorithms to improve out‐of‐sample performance in the presence of estimation errors. Our algorithms use approaches similar to the shrinkage method but with a different weighting scheme: the Euclidean distance. The Euclidean distance of a portfolio is its 2‐norm distance to the in‐sample tangency portfolio. These algorithms aim to construct a portfolio with a small Euclidean distance by making a convex combination of any number of portfolios. We propose three distance‐based portfolio‐combining algorithms: a distance‐based portfolio combination, a distance‐based asset combination, and a distance‐based asset combination with systematic errors (DAc‐S). Each algorithm consists of two steps. First, we predict the Euclidean distance of each portfolio using time‐series forecasting methods. Second, we increase (decrease) the combination level of a portfolio whose predicted Euclidean distance is small (large). We use 11 empirical data sets, and the numerical results show that our proposed algorithms significantly improve the Sharpe ratio with reasonably low portfolio turnovers. This outperformance stems from successfully decreasing the Euclidean distance. Most important, the DAc‐S achieves a significantly high Sharpe ratio and the smallest Euclidean distance.

Observer design for a nonlinear heat equation: Application to semiconductor wafer processing

In this paper, the problem of observer design for a class of 1D nonlinear heat equations with pointwise in-domain temperature measurements is addressed. A pointwise measurement injection observer is designed and the robust convergence of its estimation error in presence of bounded distributed perturbations is established by verifying input-to-state stability. The obtained convergence conditions express the underlying interplay between heat conduction and radiation and include specific dependencies on the sensor locations which are the main degrees of freedom in the design approach. The theoretical results are experimentally validated on a semiconductor wafer processing unit.

Stable robot manipulator parameter identification: A closed-loop input error approach

This paper presents an on-line parametric estimation method for robot manipulators. The identification algorithm estimates the parameters by using the input error between the robot and a parallel estimated model. Both, the robot and the estimated model are controlled by two Proportional–Derivative (PD) controller tuned with the same gain values, and a persistent excitation (PE) signal for ensuring parameters convergence is included. The exact model matching and the estimation error cases are analysed. Noisy state measurements and filters are avoided in the model parameterization by using only the states of the estimated model. A second parameter identification algorithm, which is based on a composite update law, is also proposed. It improves parameters convergence and robustness of the update rule in presence of estimation errors. The stability of the closed-loop dynamics related to the estimated model is assessed via Lyapunov stability theory. Simulations are carried out to validate the proposed approaches.

A variable sampling interval EWMA t chart with auxiliary information – A robustness study in the presence of estimation error

This article proposes the variable sampling interval (VSI) exponentially weighted moving average (EWMA) t chart for the process mean using auxiliary information (AI) (denoted as the VSI EWMA t-AI chart). The proposed chart allows different sampling intervals to be adopted based on prior process quality. The average time to signal (ATS) and expected average time to signal (EATS) criteria are used to evaluate the performance of the proposed chart. Numerical analyses are conducted and the results show that the proposed VSI EWMA t-AI chart surpasses the EWMA t-AI chart in the detection of all sizes of shifts in the process mean when there are no changes (or estimation error) in the process standard deviation. Additionally, the proposed VSI EWMA t-AI chart is found to be more robust than the VSI EWMA X¯ -AI chart when there are changes in the process standard deviation.

Transient-Suppressing Initialization for Low-Bandwidth Attitude Controllers

The use of low-bandwidth attitude controllers is a standard solution for spacecraft facing tight frequency-domain requirements for attitude-stable payloads and platforms. However, such controllers have difficulty responding to transients both planned and unexpected. This paper introduces a novel method of controller re-initialization to counteract a transient in progress. This method, the eigenmode initialization, pursues time-optimal performance for a given controller and plant by attempting to suppress the slow eigenmodes of the closed-loop system; the dynamics that remain are a function of the remaining eigenmodes. The derivation of this method from first principles is presented alongside analytical solutions for the ideal response and specific examples for which postinitialization transients decay 5, 7, and 30 times faster than their uninitialized counterparts. The method is extended to account for actuator bias and bound the actual response in the presence of estimation error. Finally, the method is validated through the high-fidelity simulation of a critical mode transition within the attitude control system of a legacy Airbus satellite, demonstrating the eigenmode initialization’s simple and effective implementation despite considerable nonlinearities in the sensor and actuator models employed.

Feedback-linearization based robust relatively optimal trajectory tracking controller for 3-DOF helicopter

This paper proposes a feedback linearization-based robust trajectory tracking controller for the elevation and pitch axes of three degrees of freedom (3-DOF) helicopter. The 3-DOF helicopter is a benchmark system that operates on the same principle of operation as that of a tandem-rotor helicopter. Accurate control of this laboratory set up in the presence of external disturbances is a sophisticated problem as it is easily affected by external disturbances due to its low weight. Hence, to ensure efficient trajectory tracking performance in the presence of uncertainties and disturbances a nonlinear disturbance observer is integrated with a feedback linearization (FL) based relatively optimal trajectory tracking controller (ROTTC). Feedback linearization of the nonlinear model results in a decoupled linear error dynamics for each axis, which is used for the design of the ROTTC. The stability of the 3-DOF helicopter in the presence of estimation error and parameter uncertainties is analyzed using the Lyapunov method. A comparison study with an FL-based robust linear quadratic regulator (RLQR) method illustrates the superiority of the proposed method in terms of tracking error and disturbance estimation. The efficacy of the proposed controller to accommodate external disturbances is demonstrated with real-time implementation on the 3-DOF helicopter with a strong wind disturbance as well as an impulse disturbance.

Backtesting Value-at-Risk and Expected Shortfall in the Presence of Estimation Error

AbstractWe investigate the effect of estimation error on backtests of expected shortfall (ES) forecasts. These backtests are based on first-order conditions of a recently introduced family of jointly consistent loss functions for value-at-risk (VaR) and ES. For both single and multiperiod horizons, we provide explicit expressions for the additional terms in the asymptotic covariance matrix that result from estimation error, and propose robust tests that account for it. Monte Carlo experiments show that the tests that ignore these terms suffer from size distortions, which are more pronounced for higher ratios of out-of-sample to in-sample observations. Robust versions of the backtests perform well with power against common alternatives. We also introduce a novel standardization of the conditional joint test statistic that removes the need to estimate higher-order moments and significantly improves its performance. In an application to VaR and ES forecasts for daily FTSE 100 index returns as generated by (GJR-)GARCH and HEAVY models, we find that estimation error substantially impacts the outcome of the backtests, and is not bound to particular subperiods such as the credit crisis.

Reduction of estimation error impact in the risk parity strategies

We consider the risk parity strategy in the presence of estimation errors. We show that risk contributions from constituents of this portfolio can be considerably sensitive to estimation errors in the sense that risk contributions are highly uneven on an ex post basis. In particular, we demonstrate that the sensitivity becomes exaggerated if Fama-French factors constitute the portfolio because of their characteristic of having low pairwise correlations. Our work demonstrates that the instability of the out-of-sample risk contributions is associated with a local property with statistical significance near to the constructed portfolio. Based on this observation, we propose a new algorithm for the risk parity strategy to mitigate the sensitivity of the optimized portfolio's out-of-sample risk contributions from estimation errors. Through empirical study, we find that the portfolio constructed by the proposed algorithm consistently outperforms its competitors in terms of the out-of-sample risk contributions.

Real-Time Wave Excitation Forces Estimation: An Application on the ISWEC Device

Optimal control strategies represent a widespread solution to increase the extracted energy of a Wave Energy Converter (WEC). The aim is to bring the WEC into resonance enhancing the produced power without compromising its reliability and durability. Most of the control algorithms proposed in literature require for the knowledge of the Wave Excitation Force (WEF) generated from the incoming wave field. In practice, WEFs are unknown, and an estimate must be used. This paper investigates the WEF estimation of a non-linear WEC. A model-based and a model-free approach are proposed. First, a Kalman Filter (KF) is implemented considering the WEC linear model and the WEF modelled as an unknown state to be estimated. Second, a feedforward Neural Network (NN) is applied to map the WEC dynamics to the WEF by training the network through a supervised learning algorithm. Both methods are tested for a wide range of irregular sea-states showing promising results in terms of estimation accuracy. Sensitivity and robustness analyses are performed to investigate the estimation error in presence of un-modelled phenomena, model errors and measurement noise.

The Jury is Still Out On the Performance of Naive Diversification (1/N rule)

DeMiguel et. al. (2009b) made a compelling case that estimation error dwarfs diversification benefits resulting in naive diversification (1/N) dominating mean-variance portfolios. We illustrate the necessary and sufficient conditions for risk-based allocation rules to be optimal in a mean-variance framework. We show empirically that many common datasets satisfy such conditions, making these rules preferred to mean-variance in the presence of estimation error. Our out-of-sample tests show that these rules outperform both mean-variance and 1/N. Further, we show that clustering the data using machine learning enhances the diversification benefits of these rules by making the data closer to the required conditions for optimality.

Modified OFDM configurations with equalization and CFO compensation for performance enhancement of OFDM communication systems using symmetry of the Fourier transform

The Orthogonal Frequency Division Multiplexing (OFDM) systems allow efficient spectrum usage and simple Frequency Domain Equalization (FDE). However, a large number of sub-carriers increases the computational complexity of the equalization process. In this paper, the conventional OFDM system is modified to enhance the Bit-Error-Rate (BER) performance or reduce the computational complexity. Also, the banded-matrix approximation is taken into account to reduce the equalization complexity. Simulation results show that the 1st proposed OFDM system based on Binary Phase Shift Keying (BPSK) can reduce the computational complexity to O(N/2) instead of O(N) compared to the conventional OFDM configuration based on the banded-matrix approximation concept. The 2nd proposed OFDM system based on BPSK requires approximately the same computational complexity of the conventional OFDM configuration and gives a Signal-to-Noise Ratio (SNR) gain of about 7.05 dB at BER = 10−3 compared to the corresponding conventional OFDM configuration. The 3rd proposed OFDM system based on Quadrature Phase Shift Keying (QPSK) gives an SNR gain of about 4.51 dB at a BER = 10−3 compared to the corresponding conventional OFDM configuration. The 2nd proposed OFDM system based on BPSK outperforms the different schemes in the presence of estimation errors.

Joint low‐complexity nonlinear equalization and carrier frequency offset compensation for multiple‐input multiple‐output orthogonal frequency division multiplexing communication systems

AbstractThe conventional zero forcing (ZF) equalizer suffers from the noise enhancement problem and the increasing complexity with the increase of the number of subcarriers. On the other hand, the minimum mean square error (MMSE) equalizer mitigates the noise enhancement, but it needs estimation of the signal‐to‐noise ratio (SNR) to work properly. In addition, the Joint Low‐complexity Regularized ZF (JLRZF) equalization and carrier frequency offset compensation scheme mitigates the noise enhancement using a constant parameter called the regularization parameter without SNR estimation. In this paper, we present a JLRZF with successive iInterference cancelation (JLRZF‐SIC) scheme for multiple‐input multiple‐output (MIMO) discrete Fourier transform orthogonal frequency division multiplexing (DFT‐OFDM) system to cope with the above‐mentioned problems. The proposed JLRZF‐SIC scheme jointly performs the equalization and the carrier frequency offset (CFO) compensation processes in two steps. The coupling nature of the MIMO channel is canceled in the first step. A regularization term is added in the second step to avoid the inter‐symbol‐interference (ISI). Simulation results show that the proposed JLRZF‐SIC scheme improves the system performance with low complexity, especially in the presence of estimation errors.

Predicting the VIX and the volatility risk premium: The role of short-run funding spreads Volatility Factors

This paper presents an innovative approach to extract Volatility Factors which predict the VIX, the S&P500 Realized Volatility (RV) and the Variance Risk Premium (VRP). The approach is innovative along two different dimensions, namely: (1) we extract Volatility Factors from panels of filtered volatilities — in particular large panels of univariate ARCH-type models and propose methods to estimate common Volatility Factors in the presence of estimation error and (2) we price equity volatility risk using factors which go beyond the equity class namely Volatility Factors extracted from panels of volatilities of short-run funding spreads. The role of these Volatility Factors is compared with the corresponding factors extracted from the panels of the above spreads as well as related factors proposed in the literature. Our monthly short-run funding spreads Volatility Factors provide both in- and out-of-sample predictive gains for forecasting the monthly VIX, RV as well as the equity premium, while the corresponding daily volatility factors via Mixed Data Sampling (MIDAS) models provide further improvements.

Estimation Error and the Fundamental Law of Active Management: Is Quant Fundamentally Flawed?

According to widely referenced applications of the Grinold (1989) Fundamental Law theory, simply adding securities to an optimization universe, adding factors to a forecast return model, trading more frequently, or reducing constraints can add investment value to an optimized investment strategy. The authors show with intuitive discussion followed by Monte Carlo simulation that many applications of Grinold theory for optimized portfolio design are often unreliable and self-defeating. Critical limitations of the theory are due to ignoring estimation error (Michaud 1989) and constraints required in practical applications. A substantial fraction of professional actively managed funds may be negatively impacted. This article was originally published as “Estimation Error and the Fundamental Law of Active Management” Is Quant Fundamentally Flawed: by Richard Michaud, PhD, David Esch, PhD, and Robert Michaud, and is available at https://www.newfrontieradvisors.com/media/1798/fundamental-law-march-2020.pdf. <b>TOPICS:</b>Portfolio theory, portfolio construction <b>Key Findings</b> • Estimation error cannot be ignored as a dangerous source of underperformance for quantitative managers, especially when mean-variance optimizers are used to construct portfolios. A substantial proportion of actively managed funds may be impacted by neglecting estimation error. • The four implied principles of management often taught as corollary to Grinold’s Fundamental Law of Active Management—(1) more assets in the investment universe, (2) more factors used in forecasting, (3) more frequent trading, and (4) removing constraints from optimizations—are not necessarily additive in the presence of estimation error and can harm out-of-sample performance when applied aggressively, contrary to the guidance of the Fundamental Law formulas. • Grinold’s formulation of the Fundamental Law is often taught as fact by many institutional education programs. The real-world failure of many of the necessary conditions for the mathematical proof are seldom included in finance curricula but should be noted.

Joint equalization and CFO compensation for performance enhancement of MIMO-OFDM communication systems using different transforms with banded-matrix approximation

The conventional Zero Forcing (ZF), and Minimum Mean Square Error (MMSE) equalizers suffer from noise enhancement, and high complexity, respectively. Moreover, the MMSE equalizer needs the estimation of the Signal-to-Noise Ratio (SNR) to work properly. In this paper, we propose Joint Low-Complexity Regularized ZF (JLCRZF) equalizers based on Successive Interference Cancellation (SIC) for Orthogonal Frequency Division Multiplexing (OFDM). The Bit-Error-Rate (BER) performance of the OFDM system model is tested using different transforms such as Discrete Fourier Transform (DFT), Discrete Sine Transform (DST), Discrete Cosine Transform (DCT), and Discrete Wavelet Transform (DWT). The proposed JLCRZF-SIC equalizers jointly perform the equalization and Carrier Frequency Offset (CFO) compensation processes with lower complexity using banded-matrix approximation. Simulation results prove that the proposed JLCRZF-SIC equalizers outperform different linear, and non-linear equalizers, especially in the presence of estimation errors.

Equalization and blind CFO estimation for performance enhancement of OFDM communication systems using discrete cosine transform

SummaryIn wireless communication systems, equalization is one of the most important schemes to improve the system performance. This paper consists of two main parts. The first part presents a blind carrier frequency offset (CFO) estimation scheme based on discrete cosine transform (DCT). The second part presents a joint low‐complexity equalization, and CFO compensation in orthogonal frequency division multiplexing (OFDM) systems. Moreover, in the second part, we present a joint low‐complexity regularized zero‐forcing (JLRZF) equalizer based on the proposed CFO estimation scheme. Simulation results show that the proposed configuration has the ability to perform blind CFO estimation and enhance the system performance in the presence of estimation errors.

An Explicit Reference Governor for the Intersection of Concave Constraints

The explicit reference governor (ERG) is a simple and systematic approach that provides constraint handling capabilities to prestabilized systems. The basic idea behind this approach is to translate state and input constraints into an upper-bound on the value of the Lyapunov function, which is then enforced by suitably manipulating the derivative of the applied reference. When designing the ERG, one of the main challenges is the determination of an upper-bound on the value of the Lyapunov function that ensures constraints satisfaction. This paper proposes a systematic approach for estimating online the optimal upper-bound for systems subject to the intersection of concave constraints. To do this, the Barrier function method is used. The effect of the estimation error caused by the time-varying nature of the auxiliary reference on the constraint satisfaction capability of the ERG is studied analytically. A procedure is proposed to modify the estimated upper-bound to avoid constraints violation in the presence of estimation errors. The effectiveness of the proposed scheme is demonstrated through a simulation study on an overhead gantry crane system.

Two-Layered Superposition of Broadcast/Multicast and Unicast Signals in Multiuser OFDMA Systems

We study optimal delivery strategies of one common and ${K}$ independent messages from a source to multiple users in wireless environments. In particular, two-layered superposition of broadcast/multicast and unicast signals is considered in a downlink multiuser OFDMA system. In the literature and industry, the two-layer superposition is often considered as a pragmatic approach to make a compromise between the simple but suboptimal orthogonal multiplexing (OM) and the optimal but complex fully-layered non-orthogonal multiplexing. In this work, we show that only two-layers are necessary to achieve the maximum sum-rate when the common message has higher priority than the ${K}$ individual unicast messages, and OM cannot be sum-rate optimal in general. We develop an algorithm that finds the optimal power allocation over the two-layers and across the OFDMA radio resources in static channels and a class of fading channels. Two main use-cases are considered: i) Multicast and unicast multiplexing when ${K}$ users with uplink capabilities request both common and independent messages, and ii) broadcast and unicast multiplexing when the common message targets receive-only devices and ${K}$ users with uplink capabilities additionally request independent messages. Finally, we develop a transceiver design for broadcast/multicast and unicast superposition transmission based on LTE-A-Pro physical layer and show with numerical evaluations in mobile environments with multipath propagation that the capacity improvements can be translated into significant practical performance gains compared to the orthogonal schemes in the 3GPP specifications. The impact of real channel estimation is also analyzed and it is shown that significant gains in terms of spectral efficiency or increased coverage area are still available even in the presence of estimation errors and imperfect interference cancellation for the two-layered superposition system.