Modified Least-squares Estimator Research Articles

Statistical Inference for Geometric Process with the Power Lindley Distribution.

The geometric process (GP) is a simple and direct approach to modeling of the successive inter-arrival time data set with a monotonic trend. In addition, it is a quite important alternative to the non-homogeneous Poisson process. In the present paper, the parameter estimation problem for GP is considered, when the distribution of the first occurrence time is Power Lindley with parameters and . To overcome the parameter estimation problem for GP, the maximum likelihood, modified moments, modified L-moments and modified least-squares estimators are obtained for parameters a, and . The mean, bias and mean squared error (MSE) values associated with these estimators are evaluated for small, moderate and large sample sizes by using Monte Carlo simulations. Furthermore, two illustrative examples using real data sets are presented in the paper.

Prediction Error Based Adaptive Jacobian Tracking for Free-Floating Space Manipulators

The work presented here investigates task-space trajectory tracking control for free-floating space robots with uncertain kinematics and dynamics. To deal with these two kinds of uncertainties, we propose a prediction error based adaptive Jacobian controller, which includes a modified task-space computed torque controller and two modified least-squares estimators. By defining a new variable that is termed as the estimate of the spacecraft angular acceleration, the proposed controller can work without requiring measurement of the spacecraft angular acceleration. The kinematic and dynamic parameter adaptations are driven by prediction errors. Using input-output stability analysis, we obtain explicit stability results of the closed-loop system and show the asymptotic convergence of the end-effector motion tracking errors of the free-floating manipulator. Furthermore, it is shown that the performance of the proposed controller has a tight relationship with the estimated generalized Jacobians of free-floating manipulators. Simulation results are presented to show the performance of the proposed controller, and in addition some implementation issues of the proposed control algorithm are discussed.

A Modified Least-Squares Regression Approach to the Estimation of Risk Difference

Risk ratio and risk difference are parameters of interest in many medical studies. The risk ratio has a property that the value for the outcome Y = 0 is not the inverse of the risk ratio for the outcome Y = 1. This property makes risk ratios inappropriate in some situations. Estimation of risk difference often encounters the problem that the binomial regression model fails to converge. Recently discussed alternatives may have the same problem of nonconvergence or are difficult to implement. Here the author proposes a modified least-squares regression approach--unweighted least-squares regression with a Huber-White robust standard error--for estimation of risk differences. Four versions of the robust standard error are considered. The binomial, ordinary least-squares, and modified least-squares estimators are compared analytically in a simple situation of one exposure variable. Multivariable regression analyses are simulated to demonstrate the usefulness of the approach. For sample sizes of approximately 200 or less, a small-sample version of the robust standard error is recommended. The method is illustrated with data from a patient survey in which the binomial regression fails to converge in the analyses of four out of five outcome variables.

Inference About the First-Order Autoregressive Coefficient

ABSTRACT Several estimators of the coefficient of an AR(1) process can be expressed as the ratio of two quadratic forms. In this article, we are considering the ordinary least-squares, a modified least-squares, the Yule–Walker, and Burg's estimators. It will be shown that the modified least-squares estimator is the least biased and that the ordinary least-squares and Burg's estimators share very similar distributional properties. An integral representation of the moments of these estimators is provided and a methodology is proposed for correcting their bias. Bounds for the supports of the Yule–Walker and Burg's estimators are determined and the density functions of those estimators are then approximated in terms of Jacobi polynomials. Finally, confidence intervals for the autoregressive coefficient are determined from replicated series.

On sequential estimation of parameters in semimartingale regression models with continuous time parameter

We consider the problem of parameter estimation for multidimensional continuous-time linear stochastic regression models with an arbitrary finite number of unknown parameters and with martingale noise. The main result of the paper claims that the unknown parameters can be estimated with prescribed mean-square precision in this general model providing a unified description of both discrete and continuous time process. Among the conditions on the regressors there is one bounding the growth of the maximal eigenvalue of the design matrix with respect to its minimal eigenvalue. This condition is slightly stronger as compared with the corresponding conditions usually imposed on the regressors in asymptotic investigations but still it enables one to consider models with different behavior of the eigenvalues. The construction makes use of a two-step procedure based on the modified least-squares estimators and special stopping rules.

Density function approximation using reduced sufficient statistics for joint estimation of linear and nonlinear parameters

A new algorithm is presented for the joint estimation of linear and nonlinear parameters of a deterministic signal embedded in additive Gaussian noise. The algorithm is an approximation to the reduced sufficient statistics (RSS) method introduced by Kulhavy (1990) which estimates the posterior parameter density via minimization of the cross-entropy (Kullback-Leibler distance). In the modified RSS algorithm presented, the components of the posterior density representing the nonlinear parameter are modeled using Haar basis scale functions, and the components corresponding to the linear parameters are represented by Gaussian densities. In the additive Gaussian noise measurement model, the RSS algorithm employs a parallel bank of modified least-squares estimators for the linear parameters, coupled with a nonlinear estimator for the nonlinear parameters. Simulation results are presented for the problem of estimating parameters of a chirp signal embedded in multipath, and the averaged squared error (ASE) of the parameter estimates is compared with the Cramer-Rao bound. Finally, an application of the algorithm is presented in which the delay, multipath coefficients, and Doppler shift of a digitally modulated waveform received over a fading channel are jointly estimated.

Consistency of modified LS estimation method for identifying 2-D noncausal SAR model parameters

Least squares (LS) and maximum likelihood (ML) are the two main methods for parameter estimation of two-dimensional (2D) noncausal simultaneous autoregressive (SAR) models. ML is asymptotically consistent and unbiased but computationally unattractive. On the other hand, conventional LS is computationally efficient but does not produce accurate parameter estimates for noncausal models. Recently, Zhao-Yu (1993) proposed a modified LS estimation method and was shown to be unbiased. In this paper we prove that, under certain assumptions, the method introduced by Zhao-Yu is also consistent. >

Robust adaptive control of time-varying linear plants using polynomial approximation

The robust adaptive control of time-varying linear systems in the presence of bounded external disturbances is discussed. A new polynomial approximation scheme is proposed to approximate unknown time-varying parameters of the plant. A modified least-squares estimator with a relative dead zone is applied to identify the resulting unknown parameters. The control law is derived by minimising a quadratic cost function which penalises both model tracking errors and excessive control actions. It is shown theoretically that robust stability can be established in the presence of unmodelled dynamics due to approximate errors and external disturbances. Simulation results demonstrate the effectiveness of the proposed new controller.

Identification of stochastic time lag systems in the presence of colored noise

This paper is concerned with identification of stochastic time lag systems corrupted by colored noise. Correlation analysis is used for time delay estimation. Some important extensions are made via time series analysis so that the time delay can be estimated accurately even when the input to the identified plant is a common stationary signal and is correlated with the process noise. By applying a new modified least-squares estimation method to eliminating the bias in the system parameters estimates arising from colored noise, an unbiased identification algorithm for jointly estimating the time delay and system parameters can be obtained based on correlation analysis. The proposed identification schemes may be used both in batches and recursively. Numerical examples are given as well.

Recursive parameter estimation of an autoregressive process disturbed by white noise

Abstract The problem of estimating parameters of an autoregressive process based on the data corrupted by unknown white noise is considered. We shall mainly discuss two methods, the one based on the Yule–Walker equations and the other based on the modified least-squares estimation previously proposed by Sagara and Wada. The latter is based on the fact that a consistent estimator may be obtained by compensating an asymptotic bias on the least-squares estimator. An asymptotic expression of the error covariance matrix of the latter estimator is derived by using the periodogram technique. In order to compare the accuracies of above two estimators, simulation results and theoretical error covariances are presented together with the corresponding Cramer-Rao bound. Simulation results indicate the correctness of the theoretical error covariance matrix. For comparison, simulation results by the bootstrap method due to Mayne and Rowe are also presented. It may be concluded that on the whole, the modified least-squa...