Properties of linear estimation and filtering

AbstractThis paper considers the estimation and filtering of fractional random fields, of which fractional Brownian motion and fractional Riesz-Bessel motion are important special cases. A least-squares solution to the problem is derived by using the duality theory and covariance factorisation of fractional generalised random fields. The minimum fractional duality order of the information random field leads to the most general class of solutions corresponding to the largest function space where the output random field can be approximated. The second-order properties that define the class of random fields for which the least-squares linear estimation problem is solved in a weak-sense are also investigated in terms of the covariance spectrum of the information random field.

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Recursibility and optimal linear estimation and filtering

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) ◽

10.1109/cdc.2004.1430300 ◽

2004 ◽

Author(s):

X. Rong Li

Keyword(s):

Linear Estimation ◽

Optimal Linear ◽

Estimation And Filtering

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Local linear estimation of the regression function for twice censored data

Statistical Papers ◽

10.1007/s00362-021-01240-5 ◽

2021 ◽

Author(s):

Ouafae Benrabah ◽

Feriel Bouhadjera ◽

Elias Ould Saïd

Keyword(s):

Censored Data ◽

Regression Function ◽

Linear Estimation ◽

Local Linear ◽

Local Linear Estimation

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Local linear estimation for covariate-adjusted varying-coefficient models

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2018.1481976 ◽

2019 ◽

Vol 48 (15) ◽

pp. 3816-3835 ◽

Cited By ~ 1

Author(s):

Yiqiang Lu ◽

Feng Li ◽

Sanying Feng

Keyword(s):

Varying Coefficient Models ◽

Linear Estimation ◽

Varying Coefficient ◽

Local Linear ◽

Local Linear Estimation

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On Updating Algorithms and Inference for Stochastic Point Processes

Journal of Applied Probability ◽

10.1017/s0021900200047690 ◽

1975 ◽

Vol 12 (S1) ◽

pp. 239-259 ◽

Cited By ~ 1

Author(s):

D. Vere-Jones

Keyword(s):

Stochastic Process ◽

Maximum Likelihood ◽

Stochastic Approximation ◽

Approximation Theory ◽

Point Processes ◽

Maximum Likelihood Estimates ◽

Doubly Stochastic ◽

Stochastic Point Processes ◽

Asymptotically Efficient ◽

Estimation And Filtering

This paper is an attempt to interpret and extend, in a more statistical setting, techniques developed by D. L. Snyder and others for estimation and filtering for doubly stochastic point processes. The approach is similar to the Kalman-Bucy approach in that the updating algorithms can be derived from a Bayesian argument, and lead ultimately to equations which are similar to those occurring in stochastic approximation theory. In this paper the estimates are derived from a general updating formula valid for any point process. It is shown that almost identical formulae arise from updating the maximum likelihood estimates, and on this basis it is suggested that in practical situations the sequence of estimates will be consistent and asymptotically efficient. Specific algorithms are derived for estimating the parameters in a doubly stochastic process in which the rate alternates between two levels.

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The Concentration Ellipsoid of a Random Vector Revisited

Econometric Theory ◽

10.1017/s0266466600004539 ◽

1991 ◽

Vol 7 (3) ◽

pp. 397-403 ◽

Cited By ~ 2

Author(s):

Kenneth Nordström

Keyword(s):

Quadratic Form ◽

Random Vector ◽

Crucial Role ◽

Type Inequality ◽

Estimation Theory ◽

Linear Estimation ◽

Nonnegative Definite

Alternative definitions of the concentration ellipsoid of a random vector are surveyed, and an extension of the concentration ellipsoid of Darmois is suggested as being the most convenient and natural definition. The advantage of the proposed definition in providing substantially simplified proofs of results in (linear) estimation theory is discussed, and is illustrated by new and short proofs of two key results. A not-so-well-known, but elementary, extremal representation of a nonnegative definite quadratic form, together with the corresponding Cauchy-Schwarẓ-type inequality, is seen to play a crucial role in these proofs.

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