Problem Of Simultaneous Estimation Research Articles

SCAD-penalized regression in additive partially linear proportional hazards models with an ultra-high-dimensional linear part

We consider the problem of simultaneous variable selection and estimation in additive partially linear Cox’s proportional hazards models with high-dimensional or ultra-high-dimensional covariates in the linear part. Under the sparse model assumption, we apply the smoothly clipped absolute deviation (SCAD) penalty to select the significant covariates in the linear part and use polynomial splines to estimate the nonparametric additive component functions. The oracle property of the estimator is demonstrated, in the sense that consistency in terms of variable selection can be achieved and that the nonzero coefficients are asymptotically normal with the same asymptotic variance as they would have if the zero coefficients were known a priori. Monte Carlo studies are presented to illustrate the behavior of the estimator using various tuning parameter selectors.

Variable selection in the high-dimensional continuous generalized linear model with current status data

In survival studies, current status data are frequently encountered when some individuals in a study are not successively observed. This paper considers the problem of simultaneous variable selection and parameter estimation in the high-dimensional continuous generalized linear model with current status data. We apply the penalized likelihood procedure with the smoothly clipped absolute deviation penalty to select significant variables and estimate the corresponding regression coefficients. With a proper choice of tuning parameters, the resulting estimator is shown to be a root n/pn-consistent estimator under some mild conditions. In addition, we show that the resulting estimator has the same asymptotic distribution as the estimator obtained when the true model is known. The finite sample behavior of the proposed estimator is evaluated through simulation studies and a real example.

Assessment of Frequency and Harmonic Distortions During Wind Farm Rejection Test

<?Pub Dtl=""?> This paper proposes a new application of the self-tuning least squares (STLS) estimation algorithm for understanding transient processes during a rejection experiment at a wind farm site in Denmark. The problems of simultaneous estimation of frequency and harmonic distortion in a wind farm are investigated. An adaptive and robust application of the STLS algorithm is proposed to estimate the unknown parameters during the dynamic changes due to forced islanding conditions. Equipped with a self-tuning procedure, the algorithm is resistant to noise which significantly improves its accuracy. The system frequency is considered as an unknown model parameter and estimated simultaneously with fundamental and harmonic components. The outcome is an estimation method which is not sensitive to variations of system frequency. To demonstrate the efficiency of the proposed algorithm, a number of computer simulated tests are also presented. Several interesting results can be observed during the rejection experiment: the large deviations of three phase voltages and currents, the changes of total harmonic distortion, and variations of power system frequency.

Simultaneous input and state estimation for nonlinear systems with applications to flow field estimation

This paper studies the problem of simultaneous input and state estimation (SISE) for nonlinear dynamical systems with and without direct input–output feedthrough. We take a Bayesian perspective to develop a sequential joint input and state estimation approach. Our scheme gives rise to a nonlinear Maximum a Posteriori optimization problem, which we solve using the classical Gauss–Newton method. The proposed approach generalizes a number of SISE methods presented in the literature. We illustrate the effectiveness of the proposed scheme for nonlinear systems with direct feedthrough in an oceanographic flow field estimation problem involving submersible drogues that measure position intermittently and acceleration continuously.

Multiple testing and interval estimates of correlated correlations

The method of Cohen, Ma and Sackrowitz (2012) [3] is applied to the problems of multiple testing and simultaneous interval estimation of correlated correlations. A large sample method is assumed and thus the basic statistics considered are Fisher’s z statistics. The asymptotic joint distribution of the z statistics is derived and utilized in the procedure. An example using data from Westfall and Young (1993) [10] is provided.

On simultaneous on-line state and parameter estimation in non-linear state-space models

On-line estimation plays an important role in process control and monitoring. Obtaining a theoretical solution to the simultaneous state-parameter estimation problem for non-linear stochastic systems involves solving complex multi-dimensional integrals that are not amenable to analytical solution. While basic sequential Monte-Carlo (SMC) or particle filtering (PF) algorithms for simultaneous estimation exist, it is well recognized that there is a need for making these on-line algorithms non-degenerate, fast and applicable to processes with missing measurements. To overcome the deficiencies in traditional algorithms, this work proposes a Bayesian approach to on-line state and parameter estimation. Its extension to handle missing data in real-time is also provided. The simultaneous estimation is performed by filtering an extended vector of states and parameters using an adaptive sequential-importance-resampling (SIR) filter with a kernel density estimation method. The approach uses an on-line optimization algorithm based on Kullback–Leibler (KL) divergence to allow adaptation of the SIR filter for combined state-parameter estimation. An optimal tuning rule to control the width of the kernel and the variance of the artificial noise added to the parameters is also proposed. The approach is illustrated through numerical examples.

Local search for the generalized tree alignment problem.

BackgroundA phylogeny postulates shared ancestry relationships among organisms in the form of a binary tree. Phylogenies attempt to answer an important question posed in biology: what are the ancestor-descendent relationships between organisms? At the core of every biological problem lies a phylogenetic component. The patterns that can be observed in nature are the product of complex interactions, constrained by the template that our ancestors provide. The problem of simultaneous tree and alignment estimation under Maximum Parsimony is known in combinatorial optimization as the Generalized Tree Alignment Problem (GTAP). The GTAP is the Steiner Tree Problem for the sequence edit distance. Like many biologically interesting problems, the GTAP is NP-Hard. Typically the Steiner Tree is presented under the Manhattan or the Hamming distances.ResultsExperimentally, the accuracy of the GTAP has been subjected to evaluation. Results show that phylogenies selected using the GTAP from unaligned sequences are competitive with the best methods and algorithms available. Here, we implement and explore experimentally existing and new local search heuristics for the GTAP using simulated and real data.ConclusionsThe methods presented here improve by more than three orders of magnitude in execution time the best local search heuristics existing to date when applied to real data.

Simultaneous variable selection and estimation in semiparametric modeling of longitudinal/clustered data

We consider the problem of simultaneous variable selection and estimation in additive, partially linear models for longitudinal/clustered data. We propose an estimation procedure via polynomial splines to estimate the nonparametric components and apply proper penalty functions to achieve sparsity in the linear part. Under reasonable conditions, we obtain the asymptotic normality of the estimators for the linear components and the consistency of the estimators for the nonparametric components. We further demonstrate that, with proper choice of the regularization parameter, the penalized estimators of the non-zero coefficients achieve the asymptotic oracle property. The finite sample behavior of the penalized estimators is evaluated with simulation studies and illustrated by a longitudinal CD4 cell count data set.

Variable selection for high-dimensional varying coefficient partially linear models via nonconcave penalty

In this paper, we consider the problem of simultaneous variable selection and estimation for varying-coefficient partially linear models in a “small \(n\), large \(p\)” setting, when the number of coefficients in the linear part diverges with sample size while the number of varying coefficients is fixed. Similar problem has been considered in Lam and Fan (Ann Stat 36(5):2232–2260, 2008) based on kernel estimates for the nonparametric part, in which no variable selection was investigated besides that \(p\) was assume to be smaller than \(n\). Here we use polynomial spline to approximate the nonparametric coefficients which is more computationally expedient, demonstrate the convergence rates as well as asymptotic normality of the linear coefficients, and further present the oracle property of the SCAD-penalized estimator which works for \(p\) almost as large as \(\exp \{n^{1/2}\}\) under mild assumptions. Monte Carlo studies and real data analysis are presented to demonstrate the finite sample behavior of the proposed estimator. Our theoretical and empirical investigations are actually carried out for the generalized varying-coefficient partially linear models, including both Gaussian data and binary data as special cases.

Real-Time Implementation of Bi Input-Extended Kalman Filter-Based Estimator for Speed-Sensorless Control of Induction Motors

This paper presents the real-time implementation of a bi input-extended Kalman filter (EKF) (BI-EKF)-based estimator in order to overcome the simultaneous estimation problem of the variations in stator resistance <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rs</i> and rotor resistance <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rr</i> ' aside from the load torque <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tL</i> and all states required for the speed-sensorless control of induction motors (IMs) in the wide speed range. BI-EKF algorithm consists of a single EKF algorithm using consecutively two inputs based on two extended IM models developed for the simultaneous estimation of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rr</i> ' and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rs</i> . Therefore, from the point of real-time implementation, it requires less memory than previous EKF-based studies exploiting two separate EKF algorithms for the same aim. By using the measured stator phase voltages and currents, the developed estimation algorithm is tested with real-time experiments under challenging variations of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rs</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rr</i> ', and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tL</i> in a wide speed range; the results obtained from BI-EKF reveal significant improvement in the all estimated states and parameters when compared with those of the single EKFs estimating only <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rr</i> ' or <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rs</i> .

Variable selection in a partially linear proportional hazards model with a diverging dimensionality

We consider the problem of simultaneous variable selection and estimation in partially linear proportional hazards models when the number of covariates in the linear part diverges with the sample size. We apply the smoothly clipped absolute deviation (SCAD) penalty to select the significant covariates in the linear part. Some simulations and a real data set are presented.

Group selection in high-dimensional partially linear additive models

We consider the problem of simultaneous variable selection and estimation in partially linear additive models with a large number of grouped variables in the linear part and a large number of nonparametric components. In our problem, the number of grouped variables may be larger than the sample size, but the number of important groups is “small” relative to the sample size. We apply the adaptive group Lasso to select the important groups, using spline bases to approximate the nonparametric components and the group Lasso to obtain an initial consistent estimator. Under appropriate conditions, it is shown that, the group Lasso selects the number of groups which is comparable with the underlying important groups and is estimation consistent, the adaptive group Lasso selects the correct important groups with probability converging to one as the sample size increases and is selection consistent. The results of simulation studies show that the adaptive group Lasso procedure works well with samples of moderate size. A real example is used to illustrate the application of the proposed penalized method.

Game theory approach to state and input simultaneous estimation for discrete-time LTV systems

This article aims to provide a simple approach realising state observation and input estimation simultaneously for discrete-time LTV systems in H∞ setting. Through solving a two-player zero sum differential game, appealing results are obtained in two folds. First, necessary and sufficient solvability conditions for state and input simultaneous estimation problem are given in terms of solution to a set of difference Riccati recursion. Second, one estimator is presented with special innovation structure, where innovation information is used to update state observation tuned by gain matrix and to provide input estimation through a projector matrix, where gain matrix and projector matrix are constructed from solution to difference Riccati recursion. At last, simulation results are provided to justify proposed approach.

Improved estimators for the common mean and ordered means of two normal distributions with ordered variances

We first consider the problem of estimating the common mean of two normal distributions with unknown ordered variances. We give a broad class of estimators which includes the estimators proposed by Nair (1982) and Elfessi et al. (1992) and show that the estimators stochastically dominate the estimators which do not take into account the order restriction on variances, including the one given by Graybill and Deal (1959). Then we propose a broad class of individual estimators of two ordered means when unknown variances are ordered. We show that in estimating the mean with larger variance, estimators which do not take into account the order restriction on variances are stochastically dominated by the proposed class of estimators which take into account both order restrictions. However, in estimating the mean with smaller variance, similar improvement is not possible even in terms of mean squared error. We also show a domination result in the simultaneous estimation problem of two ordered means. Further, improving upon the unbiased estimators of the two means is discussed.

Nonparametric empirical Bayes estimator in simultaneous estimation of Poisson means with application to mass spectrometry data

We consider the problem of simultaneous Poisson mean vector estimation and discuss the performance of nonparametric empirical Bayes (NPEB) estimator from the view point of risk consistency. We define the structural uniform risk consistency with respect to some classes of priors and show that the NPEB estimator achieves a structural uniform risk consistency with respect to some class of priors. It is shown that the NPEB estimator performs better than the maximum-likelihood estimator (MLE) and James–Stein estimators from the view point of structural uniform risk consistency. We also present numerical studies which support the asymptotic results and compare with the MLE and James–Stein-type estimators. We provide a real example of mass spectrometry data from a breast cancer study in Sauter et al. [Sauter, E.R., Davis, W., Qin, W., Scanlon, S., Mooney, B., Bromert, K., and Folk, W.R. (2009), ‘Identification of a β-Casein-Like Peptide in Breast Nipple Aspirate Fluid that is Associated with Breast Cancer’, Biomarkers in Medicine, 3, 577–588] with comparison of various estimators.

State Estimation and Fault Detection for Linear Switched Systems with Unstable Internal Dynamics

The problem of simultaneous estimation of the continuous and discrete state with additive faults in linear switched systems is addressed. Under mild structural conditions a robust estimator is designed to solve the problem. The proposed strategy includes a technique for fault detection. Simulation results support the proposed estimation scheme.

On stable simultaneous input and state estimation for discrete‐time linear systems

AbstractThis work is devoted to solving simultaneous input and state estimation (SISE) problem for discrete‐time linear systems. Our aim is to develop stable SISE algorithms. By applying the minimum variance unbiased estimation technique, we derive two SISE algorithms in the presence or absence of direct feedthrough, respectively. Riccati‐like equations are formulated and presented to analyze the stability conditions of the proposed algorithms. Simulation examples are provided to further illustrate the effectiveness of the proposed algorithms and support the theoretical findings. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Robust Output Feedback Disturbance Rejection Control by Simultaneously Estimating State and Disturbance

This paper tackles the problem of simultaneous estimation of the state and the unknown disturbance of an MIMO disturbed system and designs the disturbance rejection controller according to the estimation information. Through a series of transformations, we can transform the original system into two subsystems and then propose a sliding mode observer and a descriptor system form observer, respectively. Our algorithm can simultaneously estimate the state and the unknown disturbance. The estimation error is shown to be bounded within a small region. Moreover, the controller algorithm developed in this paper can effectively avoid the peaking phenomenon. Finally, the feasibility and the performance using the proposed method are analyzed and demonstrated with two simulated examples.

Data Compression for Multi-Parameter Estimation for Emitter Location

Because a primary task of multi-sensor systems is to make estimates based on the data collected and shared throughout the sensor system, it is important to design data compression methods that reduce the volume of data to be shared, while causing only a minimal degradation of the quality of these estimates. An important aspect, not specifically considered previously in compression research for sensor systems, is that sensor systems generally have to make multiple estimates from the data. Furthermore, it is unrecognized in the literature that these multiple estimates generally have conflicting compression requirements and that finding the right way to balance these conflicts is crucial. The key tools we bring to bear on this area are: 1) the use of a Fisher-information-based distortion measure that is designed specifically for multiple estimates, and 2) the use of numerical optimization methods to achieve desired compression trade-offs among the multiple estimates. We first develop results that support using the trace of the Fisher information matrix (FIM) as a distortion measure for the simultaneous multiple-parameter estimation problem. We then apply these results to the problem of time-difference-of-arrival (TDOA) and-frequency-difference-of-arrival- (FDOA) based location estimation of an RF emitter. We show that within this problem there is a fundamental trade-off between the impact of compression on TDOA estimation and the impact of compression on FDOA estimation; furthermore, we show that this trade-off can be addressed by adapting the compression scheme to the sensor-emitter geometry using a geometry-adaptive compression scheme.

Robust Filtering for State and Fault Estimation of Linear Stochastic Systems with Unknown Disturbance

This paper presents a new robust filter structure to solve the simultaneous state and fault estimation problem of linear stochastic discrete-time systems with unknown disturbance. The method is based on the assumption that the fault and the unknown disturbance affect both the system state and the output, and no prior knowledge about their dynamical evolution is available. By making use of an optimal three-stage Kalman filtering method, an augmented fault and unknown disturbance models, an augmented robust three-stage Kalman filter (ARThSKF) is developed. The unbiasedness conditions and minimum-variance property of the proposed filter are provided. An illustrative example is given to apply this filter and to compare it with the existing literature results.