Search results for "Efficient estimator"
showing 10 items of 11 documents
Inclusion ratio based estimator for the mean length of the boolean line segment model with an application to nanocrystalline cellulose
2014
A novel estimator for estimating the mean length of fibres is proposed for censored data observed in square shaped windows. Instead of observing the fibre lengths, we observe the ratio between the intensity estimates of minus-sampling and plus-sampling. It is well-known that both intensity estimators are biased. In the current work, we derive the ratio of these biases as a function of the mean length assuming a Boolean line segment model with exponentially distributed lengths and uniformly distributed directions. Having the observed ratio of the intensity estimators, the inverse of the derived function is suggested as a new estimator for the mean length. For this estimator, an approximation…
Stochastic discretized learning-based weak estimation: a novel estimation method for non-stationary environments
2016
The task of designing estimators that are able to track time-varying distributions has found promising applications in many real-life problems.Existing approaches resort to sliding windows that track changes by discarding old observations. In this paper, we report a novel estimator referred to as the Stochastic Discretized Weak Estimator (SDWE), that is based on the principles of discretized Learning Automata (LA). In brief, the estimator is able to estimate the parameters of a time varying binomial distribution using finite memory. The estimator tracks changes in the distribution by operating a controlled random walk in a discretized probability space. The steps of the estimator are discre…
A novel Stochastic Discretized Weak Estimator operating in non-stationary environments
2012
The task of designing estimators that are able to track time-varying distributions has found promising applications in many real-life problems. A particularly interesting family of distributions are the binomial/multiomial distributions. Existing approaches resort to sliding windows that track changes by discarding old observations. In this paper, we report a novel estimator referred to as the Stochastic Discretized Weak Estimator (SDWE), that is based on the principles of Learning Automata (LA). In brief, the estimator is able to estimate the parameters of a time varying binomial distribution using finite memory. The estimator tracks changes in the distribution by operating on a controlled…
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 …
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…
Variance Estimation and Asymptotic Confidence Bands for the Mean Estimator of Sampled Functional Data with High Entropy Unequal Probability Sampling …
2013
For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson estimator can be approximated by the Hajek formula. The interest of this asymptotic variance approximation is that it only involves the first order inclusion probabilities of the statistical units. We extend this variance formula when the variable under study is functional and we prove, under general conditions on the regularity of the individual trajectories and the sampling design, that it asymptotically provides a uniformly consistent estimator of the variance function of the Horvitz-Thompson estimator of the mean function. Rates of convergence to the true variance function are gi…
Symmetrised M-estimators of multivariate scatter
2007
AbstractIn this paper we introduce a family of symmetrised M-estimators of multivariate scatter. These are defined to be M-estimators only computed on pairwise differences of the observed multivariate data. Symmetrised Huber's M-estimator and Dümbgen's estimator serve as our examples. The influence functions of the symmetrised M-functionals are derived and the limiting distributions of the estimators are discussed in the multivariate elliptical case to consider the robustness and efficiency properties of estimators. The symmetrised M-estimators have the important independence property; they can therefore be used to find the independent components in the independent component analysis (ICA).
Extended differential geometric LARS for high-dimensional GLMs with general dispersion parameter
2018
A large class of modeling and prediction problems involves outcomes that belong to an exponential family distribution. Generalized linear models (GLMs) are a standard way of dealing with such situations. Even in high-dimensional feature spaces GLMs can be extended to deal with such situations. Penalized inference approaches, such as the $$\ell _1$$ or SCAD, or extensions of least angle regression, such as dgLARS, have been proposed to deal with GLMs with high-dimensional feature spaces. Although the theory underlying these methods is in principle generic, the implementation has remained restricted to dispersion-free models, such as the Poisson and logistic regression models. The aim of this…
Robust estimation and inference for bivariate line-fitting in allometry.
2011
In allometry, bivariate techniques related to principal component analysis are often used in place of linear regression, and primary interest is in making inferences about the slope. We demonstrate that the current inferential methods are not robust to bivariate contamination, and consider four robust alternatives to the current methods -- a novel sandwich estimator approach, using robust covariance matrices derived via an influence function approach, Huber's M-estimator and the fast-and-robust bootstrap. Simulations demonstrate that Huber's M-estimators are highly efficient and robust against bivariate contamination, and when combined with the fast-and-robust bootstrap, we can make accurat…
k-Step shape estimators based on spatial signs and ranks
2010
In this paper, the shape matrix estimators based on spatial sign and rank vectors are considered. The estimators considered here are slight modifications of the estimators introduced in Dümbgen (1998) and Oja and Randles (2004) and further studied for example in Sirkiä et al. (2009). The shape estimators are computed using pairwise differences of the observed data, therefore there is no need to estimate the location center of the data. When the estimator is based on signs, the use of differences also implies that the estimators have the so called independence property if the estimator, that is used as an initial estimator, has it. The influence functions and limiting distributions of the es…