A class of ratio, product and difference (R.P.D.) estimators in systematic sampling

A class of estimators is proposed for estimating the population parameter (mean) of the study character y, using information on an auxiliary character x, in systematic sampling of which the estimator is proposed by Swain [J. Indian Statist. Ass. 2 (213), 160–164 (1964)], Sukla [Proceedings of the All-India Seminar on Demography and Statistics, pp. 243–248. Varanasi, India (1971)] and difference estimator in systematic sampling are particular cases. The conditions in which this class of estimators performs better than other estimators are derived.     

The statistical performance of some instantaneous frequencyestimators

The authors examine the class of smoothed central finite difference (SCFD) instantaneous frequency (IF) estimators which are based on finite differencing of the phase of the analytic signal. These estimators are closely related to IF estimation via the (periodic) first moment, with respect to frequency of discrete time-frequency representations (TFRs) in L. Cohen's (1966) class. The authors determine the distribution of this class of estimators and establish a framework which allows the comparison of several other estimators such as the zero-crossing estimator and one based on linear regression on the signal phase. It is found that the regression IF estimator is biased and exhibits a large threshold for much of the frequency range. By replacing the linear convolution operation in the regression estimator with the appropriate convolution operation for circular data the authors obtain the parabolic SCFD (PSCFD) estimator, which is unbiased and has a frequency-independent variance, yet retains the optimal performance and simplicity of the original estimator     

Local Linear Estimators for the Bioelectromagnetic Inverse Problem

Linear estimators have been used widely in the bioelectromagnetic inverse problem, but their properties and relationships have not been fully characterized. Here, we show that the most widely used linear estimators may be characterized by a choice of norms on signal space and on source space. These norms depend, in part, on assumptions about the signal space and source space covariances. We demonstrate that two estimator classes (standardized and weight vector normalized) yield unbiased estimators of source location for simple source models (including only the noise-free case) but biased estimators of source magnitude. In the presence of instrumental (white) noise, we show that the nonadaptive standardized estimator is a biased estimator of source location, while the adaptive weight vector normalized estimator remains unbiased. A third class (distortionless) is an unbiased estimator of source magnitude but a biased estimator of source location.     

Unified analysis of a class of blind feedforward symbol timing estimators employing second-order statistics

In this letter, all the previously proposed digital blind feedforward symbol timing estimators employing second-order statistics are casted into a unified framework. The finite sample mean-square error (MSE) expression for this class of estimators is established. Simulation results are also presented to corroborate the analytical results. It is found that the feedforward conditional maximum likelihood (CML) estimator and the square law nonlinearity (SLN) estimator with a properly designed prefilter perform the best and their performances coincide with the asymptotic conditional Cramer-Rao bound (CCRB), which is the performance lower bound for the class of estimators under consideration.     

Optimal blind nonlinear least-squares carrier phase and frequency offset estimation for general QAM modulations

This paper introduces a family of blind feedforward nonlinear least-squares (NLS) estimators for joint estimation of the carrier phase and frequency offset of general quadrature amplitude modulated (QAM) transmissions. As an extension of the Viterbi and Viterbi (1983) estimator, a constellation-dependent optimal matched nonlinear estimator is derived such that its asymptotic (large sample) variance is minimized. A class of conventional monomial estimators is also proposed. The asymptotic performance of these estimators is established in closed-form expression and compared with the Cramer-Rao lower bound. A practical implementation of the optimal matched estimator, which is a computationally efficient approximation of the latter and exhibits negligible performance loss, is also derived. Finally, computer simulations are presented to corroborate the theoretical performance analysis and indicate that the proposed optimal matched nonlinear estimator improves significantly the performance of the classic fourth-power estimator.     

Stability in linear estimation

The stability with respect to model uncertainty of linear estimators of the coefficients of a linear combination of deterministic signals in noise is investigated. A class of estimators having nominal performances constrained to be close to that of the nominal linear, unbiased, minimum-variance (LUMV) estimator is specified. Two estimator stability indexes are defined, one based on a worst-case estimate mean-square error and the other on a type of signal-to-noise ratio. The estimator minimizing each index, subject to the optimality constraints, is found by reference to related LUMV estimation results. In most cases, the minimizing (or most stable) estimator is the same under the two indexes     

On estimation of population mean using known coefficient of variation

For the estimation of population mean, a generalized class of estimators using known coefficient of variation C_y of the study variable y is proposed, its bias and mean square error (MSE) are found and its comparative study with the usual mean per unit estimator has been done. As an illustration, an empirical study is also included.     

Blind feedforward cyclostationarity-based timing estimation for linear modulations

By exploiting a general cyclostationary (CS) statistics-based framework, this letter develops a rigorous and unified asymptotic (large sample) performance analysis setup for a class of blind feedforward timing epoch estimators for linear modulations transmitted through time nonselective flat-fading channels. Within the proposed CS framework, it is shown that several estimators proposed in the literature can be asymptotically interpreted as maximum likelihood (ML) estimators applied on a (sub)set of the second- (and/or higher) order statistics of the received signal. The asymptotic variance of these ML estimators is established in closed-form expression and compared with the modified Crame/spl acute/r-Rao bound. It is shown that the timing estimator proposed by Oerder and Meyr achieves asymptotically the best performance in the class of estimators which exploit all the second-order statistics of the received signal, and its performance is insensitive to oversampling rates P as long as P/spl ges/3. Further, an asymptotically best consistent estimator, which achieves the lowest asymptotic variance among all the possible estimators that can be derived by exploiting jointly the second- and fourth-order statistics of the received signal, is also proposed.     

Comparison of some ratio-type estimators

Some ratio-type estimators are compared, and it is found that the estimator proposed by Sisodia and Dwivedi (Biomet. J.23, (2) 133–139) performs well compared with other estimators, for all situations.     

Statistical analysis of the geometric de-eutrophicationsoftware-reliability model

A detailed statistical analysis of the Moranda geometric de-eutrophication software-reliability model, which appears to be a particular case of a class of general models with proportional failure rates, is given. Statistical inference on the unknown parameters is discussed. The distribution of the maximum-likelihood estimator of the main parameter provides exact confidence intervals and a novel reliability-growth test. Explicit estimators based on a least-squares method are proposed. The model is satisfactorily applied to real software error data. The geometric de-eutrophication model presents interesting theoretical and practical aspects. It is conceptually well founded and the parameters, which have useful practical interpretation, can be estimated by methods which provide prediction with good statistical properties     

On the efficiency of on-line density estimators

An on-line density estimator may be defined to be one where each update, following the arrival of a new data value, may be accomplished after no more than a fixed number of calculations. This definition should also apply to any empirical bandwidth selection rule for such an estimator. Recursive estimators comprise only a special case of on-line estimators, but even there, on-line bandwidth formulas have not been developed. The authors introduce a class of on-line estimators, and discuss efficiency in this context. It is shown that some nonrecursive members of the class achieve greater efficiency than any recursive estimators, and that efficiency increases to 100% as the order of the estimated derivative increases. On-line bandwidth selection rules, enabling these high orders of efficiency to be achieved asymptotically, are introduced     

An iterative algorithm for the computation of the MVDR filter

Statistical conditional optimization criteria lead to the development of an iterative algorithm that starts from the matched filter (or constraint vector) and generates a sequence of filters that converges to the minimum-variance-distortionless-response (MVDR) solution for any positive definite input autocorrelation matrix. Computationally, the algorithm is a simple, noninvasive, recursive procedure that avoids any form of explicit autocorrelation matrix inversion, decomposition, or diagonalization. Theoretical analysis reveals basic properties of the algorithm and establishes formal convergence. When the input autocorrelation matrix is replaced by a conventional sample-average (positive definite) estimate, the algorithm effectively generates a sequence of MVDR filter estimators; the bias converges rapidly to zero and the covariance trace rises slowly and asymptotically to the covariance trace of the familiar sample-matrix-inversion (SMI) estimator. In fact, formal convergence of the estimator sequence to the SMI estimate is established. However, for short data records, it is the early, nonasymptotic elements of the generated sequence of estimators that offer favorable bias covariance balance and are seen to outperform in mean-square estimation error, constraint-LMS, RLS-type, orthogonal multistage decomposition, as well as plain and diagonally loaded SMI estimates. An illustrative interference suppression example is followed throughout this presentation     

Wavelet-based estimators of scaling behavior

Various wavelet-based estimators of self-similarity or long-range dependence scaling exponent are studied extensively. These estimators mainly include the (bi)orthogonal wavelet estimators and the wavelet transform modulus maxima (WTMM) estimator. This study focuses both on short and long time-series. In the framework of fractional autoregressive integrated moving average (FARIMA) processes, we advocate the use of approximately adapted wavelet estimators. For these "ideal" processes, the scaling behavior actually extends down to the smallest scale, i.e., the sampling period of the time series, if an adapted decomposition is used. But in practical situations, there generally exists a cutoff scale below which the scaling behavior no longer holds. We test the robustness of the set of wavelet-based estimators with respect to that cutoff scale as well as to the specific density of the underlying law of the process. In all situations, the WTMM estimator is shown to be the best or among the best estimators in terms of the mean-squared error (MSE). We also compare the wavelet estimators with the detrended fluctuation analysis (DFA) estimator which was previously proved to be among the best estimators which are not wavelet-based estimators. The WTMM estimator turns out to be a very competitive estimator which can be further generalized to characterize multiscaling behavior     

Reduced-rank technique for joint channel estimation in TD-SCDMA systems

In time division-synchronous code division multiple access systems, increasing the system capacity by exploiting the inserting of the largest number of users in one time slot (TS) requires adding more estimation processes to estimate the joint channel matrix for the whole system. The increase in the number of channel parameters due the increase in the number of users in one TS directly affects the precision of the estimator's performance. This article presents a novel channel estimation with low complexity, which relies on reducing the rank order of the total channel matrix H. The proposed method exploits the rank deficiency of H to reduce the number of parameters that characterise this matrix. The adopted reduced-rank technique is based on truncated singular value decomposition algorithm. The algorithms for reduced-rank joint channel estimation (JCE) are derived and compared against traditional full-rank JCEs: least squares (LS) or Steiner and enhanced (LS or MMSE) algorithms. Simulation results of the normalised mean square error showed the superiority of reduced-rank estimators. In addition, the channel impulse responses founded by reduced-rank estimator for all active users offers considerable performance improvement over the conventional estimator along the channel window length.     

Covariance shaping least-squares estimation

A new linear estimator is proposed, which we refer to as the covariance shaping least-squares (CSLS) estimator, for estimating a set of unknown deterministic parameters, x, observed through a known linear transformation H and corrupted by additive noise. The CSLS estimator is a biased estimator directed at improving the performance of the traditional least-squares (LS) estimator by choosing the estimate of x to minimize the (weighted) total error variance in the observations subject to a constraint on the covariance of the estimation error so that we control the dynamic range and spectral shape of the covariance of the estimation error. The presented CSLS estimator is shown to achieve the Cramer-Rao lower bound for biased estimators. Furthermore, analysis of the mean-squared error (MSE) of both the CSLS estimator and the LS estimator demonstrates that the covariance of the estimation error can be chosen such that there is a threshold SNR below which the CSLS estimator yields a lower MSE than the LS estimator for all values of x. As we show, some of the well-known modifications of the LS estimator can be formulated as CSLS estimators. This allows us to interpret these estimators as the estimators that minimize the total error variance in the observations, among all linear estimators with the same covariance.     

Monte Carlo Comparisons of Parameter Estimators of the 2-parameter Weibull Distribution

A Monte Carlo Simulation was carried out in order to compare three different estimators of the 2-parameter Weibull distribution. The estimators were the ML (maximum likelihood) estimators and two other estimator pairs suggested by Bain & Antle. The Bain-Antle estimators are better than the ML estimator for small samples (in that their bias, standard deviation, and rms error are smaller), whereas the ML estimator is superior in large samples.     

Étude de la précision de l’estimation de la densité spectrale de puissance croisée,obtenue par transformation de fourier de la fonction de corrélation

The authors compare two different estimators of the crosscorrelation function and show that they give equivalent estimators in the frequency domain. They calculate the first and second order moments of the estimator of the cross-spectral-density (DSPC)due to the statistical errors and the quantification of inputs. From these general formulas, they perform numerical calculations for a particular case and they compare them to practical measurements. They show the interesting fact, that the variance of the statistical errors on the dspc is inferior by estimating its phase than by estimating its module. Furthermore, the quantification of the inputs may influence the variance of the phase of the DSPC estimated.     

Empirical Bayes Estimators of Reliability for Lognormal Failure Model

Empirical Bayes (EB) procedures are considered for estimating the reliability R(t;?,?) = gaufc[(ln t -?)/?] for the lognormal failure model. EB estimators are obtained for the 2 cases: i)? is unknown and ? is known, and both ? and ? are unknown. The empirical Cdf of the maximum likelihood estimators of the parameters is used to obtain the EB estimators. ii) A smooth EB estimator of R(t;?,?) is developed when ? is unknown and ? is known. A modification of this estimator is proposed for both ? and ? unknown. In both cases, EB estimators are obtained for complete samples at each testing stage. Monte Carlo simulations are presented to compare the EB estimators and the maximum likelihood (ML) estimators of R(t;?,?). The simulations indicate that the smooth EB estimators have smaller mean squared errors than the other EB estimators or the ML estimators.     

A class of shrinkage estimators for the scale parameter of theexponential distribution

A class of shrinkage estimators for the scale parameter of the exponential distribution is suggested. It includes some previously published estimators as special cases. An analogous estimator based on censored samples is considered. An example is given     

Estimating the number of errors in a system using a martingaleapproach

A new, efficient procedure estimates the number of errors in a system. A known number of seeded errors are inserted into a system. The failure intensities of the seeded and real errors are allowed to be different and time dependent. When an error is detected during the test, it is removed from the system. The testing process is observed for a fixed amount of time τ. Martingale theory is used to derive a class of estimators for the number of seeded errors in a continuous time setting. Some of the estimators and their associated standard deviations have explicit expressions. An optimal estimator among the class of estimators is obtained. A simulation study assesses the performance of the proposed estimators