Displaying similar documents to “Filtering and fixed-point smoothing from an innovation approach in systems with uncertainty.”

Exponential smoothing for time series with outliers

Tomáš Hanzák, Tomáš Cipra (2011)

Kybernetika

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Recursive time series methods are very popular due to their numerical simplicity. Their theoretical background is usually based on Kalman filtering in state space models (mostly in dynamic linear systems). However, in time series practice one must face frequently to outlying values (outliers), which require applying special methods of robust statistics. In the paper a simple robustification of Kalman filter is suggested using a simple truncation of the recursive residuals. Then this...

Estimation of nuisance parameters for inference based on least absolute deviations

Wojciech Niemiro (1995)

Applicationes Mathematicae

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Statistical inference procedures based on least absolute deviations involve estimates of a matrix which plays the role of a multivariate nuisance parameter. To estimate this matrix, we use kernel smoothing. We show consistency and obtain bounds on the rate of convergence.

One Bootstrap suffices to generate sharp uniform bounds in functional estimation

Paul Deheuvels (2011)

Kybernetika

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We consider, in the framework of multidimensional observations, nonparametric functional estimators, which include, as special cases, the Akaike–Parzen–Rosenblatt kernel density estimators ([1, 18, 20]), and the Nadaraya–Watson kernel regression estimators ([16, 22]). We evaluate the sup-norm, over a given set 𝐈 , of the difference between the estimator and a non-random functional centering factor (which reduces to the estimator mean for kernel density estimation). We show that, under...

Estimation and prediction in regression models with random explanatory variables

Nguyen Bac-Van

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The regression model X(t),Y(t);t=1,...,n with random explanatory variable X is transformed by prescribing a partition S 1 , . . . , S k of the given domain S of X-values and specifying X ( 1 ) , . . . , X ( n ) ∩ S i = X i 1 , . . . , X i α ( i ) , i = 1 , . . . , k . Through the conditioning α ( i ) = a ( i ) , i = 1 , . . . , k , X i 1 , . . . , X i α ( i ) ; i = 1 , . . . , k = x 11 , . . . , x k a ( k ) the initial model with i.i.d. pairs (X(t),Y(t)),t=1,...,n, becomes a conditional fixed-design ( x 11 , . . . , x k a ( k ) ) model Y i j , i = 1 , . . . , k ; j = 1 , . . . , a ( i ) where the response variables Y i j are independent and distributed according to the mixed conditional distribution Q ( · , x i j ) of Y given X at the observed value x i j .Afterwards, we investigate the case ( Q ) E ( Y ' | x ) = ∑ i = 1 k b i ( x ) θ i I S i ( x ) , ( Q ) D ( Y | x ) = ∑ i = 1 k d i ( x ) Σ i I S i ( x ) which...

Moment estimation methods for stationary spatial Cox processes - A comparison

Jiří Dvořák, Michaela Prokešová (2012)

Kybernetika

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In the present paper we consider the problem of fitting parametric spatial Cox point process models. We concentrate on the moment estimation methods based on the second order characteristics of the point process in question. These methods represent a simulation-free faster-to-compute alternative to the computationally intense maximum likelihood estimation. We give an overview of the available methods, discuss their properties and applicability. Further we present results of a simulation...