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A sufficient condition for admissibility in linear estimation

Czesław Stępniak (1988)

Aplikace matematiky

It was recently shown that all estimators which are locally best in the relative interior of the parameter set, together with their limits constitute a complete class in linear estimation, both unbiased and biased. However, not all these limits are admissible. A sufficient condition for admissibility of a limit was given by the author (1986) for the case of unbiased estimation in a linear model with the natural parameter space. This paper extends this result to the general linear model and to biased...

A theory for non-linear prediction approach in the presence of vague variables: with application to BMI monitoring

R. Pourmousa, M. Rezapour, M. Mashinchi (2015)

Dependence Modeling

In the statistical literature, truncated distributions can be used for modeling real data. Due to error of measurement in truncated continuous data, choosing a crisp trimmed point caucuses a fault inference, so using fuzzy sets to define a threshold pointmay leads us more efficient results with respect to crisp thresholds. Arellano-Valle et al. [2] defined a selection distribution for analysis of truncated data with crisp threshold. In this paper, we define fuzzy multivariate selection distribution...

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2005)

ESAIM: Probability and Statistics

We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate ∫ ℝ f 2 ( x ) d x is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U -statistics of order 2 due to Houdré and Reynaud.

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2010)

ESAIM: Probability and Statistics

We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate ∫ ℝ f 2 ( x ) d x is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U-statistics of order 2 due to Houdré and Reynaud.

Adaptive hard-thresholding for linear inverse problems

Paul Rochet (2013)

ESAIM: Probability and Statistics

A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. These filter methods are generally restricted to monotonic transformations, e.g. the Tikhonov regularization or the spectral cut-off. However, in several cases, non-monotonic sequences of filters may appear more appropriate. In this paper, we study a hard-thresholding regularization method that extends the spectral cut-off procedure to non-monotonic sequences....

Adaptive trimmed likelihood estimation in regression

Tadeusz Bednarski, Brenton R. Clarke, Daniel Schubert (2010)

Discussiones Mathematicae Probability and Statistics

In this paper we derive an asymptotic normality result for an adaptive trimmed likelihood estimator of regression starting from initial high breakdownpoint robust regression estimates. The approach leads to quickly and easily computed robust and efficient estimates for regression. A highlight of the method is that it tends automatically in one algorithm to expose the outliers and give least squares estimates with the outliers removed. The idea is to begin with a rapidly computed consistent robust...

Additional Experiment and Linear Statistical Models

Lubomír Kubáček (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

An accuracy of parameter estimates need not be sufficient for their unforeseen utilization. Therefore some additional measurement is necessary in order to attain the required precision. The problem is to express the correction to the original estimates in an explicit form.

Admissible invariant estimators in a linear model

Czesław Stępniak (2014)

Kybernetika

Let 𝐲 be observation vector in the usual linear model with expectation 𝐀 β and covariance matrix known up to a multiplicative scalar, possibly singular. A linear statistic 𝐚 T 𝐲 is called invariant estimator for a parametric function φ = 𝐜 T β if its MSE depends on β only through φ . It is shown that 𝐚 T 𝐲 is admissible invariant for φ , if and only if, it is a BLUE of φ , in the case when φ is estimable with zero variance, and it is of the form k φ ^ , where k ∈ 0 , 1 and φ ^ is an arbitrary BLUE, otherwise. This result is used in...

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