Search results for "unbiased"
showing 10 items of 28 documents
Effective state estimation of stochastic systems
2003
In the present paper, for constructing the minimum risk estimators of state of stochastic systems, a new technique of invariant embedding of sample statistics in a loss function is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant estimator, which has smaller risk than any of the well‐known estimators. There exists a class of control systems where observations are not …
Constrained minimum variance control of nonsquare LTI MIMO systems
2010
Constrained minimum variance control is offered for nonsquare LTI MIMO systems. A constrained control design takes advantage of the so-called control zeros. The new control strategy is compared with familiar generalized minimum variance control and possible application areas of the two are discussed.
Construction and optimality of a special class of balanced designs
2006
The use of balanced designs is generally advisable in experimental practice. In technological experiments, balanced designs optimize the exploitation of experimental resources, whereas in marketing research experiments they avoid erroneous conclusions caused by the misinterpretation of interviewed customers. In general, the balancing property assures the minimum variance of first-order effect estimates. In this work the authors consider situations in which all factors are categorical and minimum run size is required. In a symmetrical case, it is often possible to find an economical balanced design by means of algebraic methods. Conversely, in an asymmetrical case algebraic methods lead to e…
Signal Restoration via a Splitting Approach
2012
International audience; In the present study, a novel signal restoration method from noisy data samples is presented and is termed as "signal split (SSplit)" approach. The new method utilizes Stein unbiased risk estimate estimator to split the signal, the Lipschitz exponents to identify noise elements and a heuristic approach for the signal reconstruction. However, unlike many noise removal techniques, the present method works only in the non-orthogonal domain. Signal restoration was performed on each individual part by finding the best compromise between the data samples and the smoothing criteria. Statistical results are quite promising and suggest better performance than the conventional…
Comparing Correlation Matrix Estimators Via Kullback-Leibler Divergence
2011
We use a self-averaging measure called Kullback-Leibler divergence to evaluate the performance of four different correlation estimators: Fourier, Pearson, Maximum Likelihood and Hayashi-Yoshida estimator. The study uses simulated transaction prices for a large number of stocks and different data generating mechanisms, including synchronous and non-synchronous transactions, homogeneous and heterogeneous inter-transaction time. Different distributions of stock returns, i.e. multivariate Normal and multivariate Student's t-distribution, are also considered. We show that Fourier and Pearson estimators are equivalent proxies of the `true' correlation matrix within all the settings under analysis…
A kriging interpolation strategy for the optimization of Acidithiobacillus ferrooxidans biomass production using fed-batch bioreactors
2008
In this work, a procedure for the optimization of Acidithiobacillus ferrooxidans biomass production in fed-batch reactors using a model based on optimal spatial interpolation of experimental data is proposed. The approach is useful in those cases where specific growth and substrate consumption rates are unknown. Based on interpolation, the optimal values of biomass and substrate concentrations set points are obtained at the minimum of 2-dimensional cost function. In the fed-batch reactor biomass and substrate concentrations are controlled at their set points by changing the input flow and its concentration. We propose a minimum variance control strategy which improves the classical proporti…
Limits on entropic uncertainty relations
2010
We consider entropic uncertainty relations for outcomes of the measurements of a quantum state in 3 or more mutually unbiased bases (MUBs), chosen from the standard construction of MUBs in prime dimension. We show that, for any choice of 3 MUBs and at least one choice of a larger number of MUBs, the best possible entropic uncertainty relation can be only marginally better than the one that trivially follows from the relation by Maassen and Uffink for 2 bases.
Wavelet-like orthonormal bases for the lowest Landau level
1994
As a first step in the description of a two-dimensional electron gas in a magnetic field, such as encountered in the fractional quantum Hall effect, we discuss a general procedure for constructing an orthonormal basis for the lowest Landau level, starting from an arbitrary orthonormal basis in L2(R). We discuss in detail two relevant examples coming from wavelet analysis, the Haar and the Littlewood-Paley bases.
Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
2011
We present a comprehensive analysis of the performance of different classes of Gaussian states in the estimation of Gaussian phase-insensitive dissipative channels. In particular, we investigate the optimal estimation of the damping constant and reservoir temperature. We show that, for two-mode squeezed vacuum probe states, the quantum-limited accuracy of both parameters can be achieved simultaneously. Moreover, we show that for both parameters two-mode squeezed vacuum states are more efficient than either coherent, thermal or single-mode squeezed states. This suggests that at high energy regimes two-mode squeezed vacuum states are optimal within the Gaussian setup. This optimality result i…
Statistical Analysis of a Method to Predict Drug–Polymer Miscibility
2015
In this study, a method proposed to predict drug-polymer miscibility from differential scanning calorimetry measurements was subjected to statistical analysis. The method is relatively fast and inexpensive and has gained popularity as a result of the increasing interest in the formulation of drugs as amorphous solid dispersions. However, it does not include a standard statistical assessment of the experimental uncertainty by means of a confidence interval. In addition, it applies a routine mathematical operation known as "transformation to linearity," which previously has been shown to be subject to a substantial bias. The statistical analysis performed in this present study revealed that t…