Correction to the paper “On the two-sided quality control”

František Rublík

Displaying similar documents to “Correction to the paper “On the two-sided quality control””

On the two-sided quality control

František Rublík (1982)

Aplikace matematiky

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Let the random variable $X$ have the normal distribution $N (μ, σ^{2})$ . Explicit formulas for maximum likelihood estimator of $μ, σ$ are derived under the hypotheses $μ + c σ \leq m + δ, μ - c σ \geq m - δ$ , where $c, m, δ$ are arbitrary fixed numbers. Asymptotic distribution of the likelihood ratio statistic for testing this hypothesis is derived and some of its quantiles are presented.

Estimator selection in the gaussian setting

Yannick Baraud, Christophe Giraud, Sylvie Huet (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We consider the problem of estimating the mean $f$ of a Gaussian vector $Y$ with independent components of common unknown variance $σ^{2}$ . Our estimation procedure is based on estimator selection. More precisely, we start with an arbitrary and possibly infinite collection $𝔽$ of estimators of $f$ based on $Y$ and, with the same data $Y$ , aim at selecting an estimator among $𝔽$ with the smallest Euclidean risk. No assumptions on the estimators are made and their dependencies with respect to $Y$ may be unknown....

The Bayes choice of an experiment in estimating a success probability

Alicja Jokiel-Rokita, Ryszard Magiera (2002)

Applicationes Mathematicae

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A Bayesian method of estimation of a success probability p is considered in the case when two experiments are available: individual Bernoulli (p) trials-the p-experiment-or products of r individual Bernoulli (p) trials-the $p^{r}$ -experiment. This problem has its roots in reliability, where one can test either single components or a system of r identical components. One of the problems considered is to find the degree r̃ of the $p^{r ̃}$ -experiment and the size m̃ of the p-experiment such that the...

Compact hypothesis and extremal set estimators

João Tiago Mexia, Pedro Corte Real (2003)

Discussiones Mathematicae Probability and Statistics

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In extremal estimation theory the estimators are local or absolute extremes of functions defined on the cartesian product of the parameter by the sample space. Assuming that these functions converge uniformly, in a convenient stochastic way, to a limit function g, set estimators for the set ∇ of absolute maxima (minima) of g are obtained under the compactness assumption that ∇ is contained in a known compact U. A strongly consistent test is presented for this assumption. Moreover, when...

Instrumental weighted variables under heteroscedasticity Part I – Consistency

Jan Ámos Víšek (2017)

Kybernetika

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The proof of consistency instrumental weighted variables, the robust version of the classical instrumental variables is given. It is proved that all solutions of the corresponding normal equations are contained, with high probability, in a ball, the radius of which can be selected - asymptotically - arbitrarily small. Then also $\sqrt{n}$ -consistency is proved. An extended numerical study (the Part II of the paper) offers a picture of behavior of the estimator for finite samples under various...

An estimator for parameters of a nonlinear nonnegative multidimensional AR(1) process

Jiří Anděl (1998)

Applications of Mathematics

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Let $𝕖_{t} = {(e_{t 1}, \dots, e_{t p})}^{'}$ be a $p$ -dimensional nonnegative strict white noise with finite second moments. Let $h_{i j} (x)$ be nondecreasing functions from $[0, \infty)$ onto $[0, \infty)$ such that $h_{i j} (x) \leq x$ for $i, j = 1, \dots, p$ . Let $𝕌 = (u_{i j})$ be a $p \times p$ matrix with nonnegative elements having all its roots inside the unit circle. Define a process $𝕏_{t} = {(X_{t 1}, \dots, X_{t p})}^{'}$ by $X_{t j} = u_{j 1} h_{1 j} (X_{t - 1, 1}) + \dots + u_{j p} h_{p j} (X_{t - 1, p}) + e_{t j}$ for $j = 1, \dots, p$ . A method for estimating $𝕌$ from a realization $𝕏_{1}, \dots, 𝕏_{n}$ is proposed. It is proved that the estimators are strongly consistent.

Correction to “Walsh equiconvergence for best $l_{2}$ approximates” Studia Math.. 77 (1984), 523-528

A. Sharma, Z. Ziegler (1987)

Studia Mathematica

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$M$ -estimators of structural parameters in pseudolinear models

Friedrich Liese, Igor Vajda (1999)

Applications of Mathematics

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Real valued $M$ -estimators ${\hat{θ}}_{n} : = min \sum_{1}^{n} ρ (Y_{i} - τ (θ))$ in a statistical model with observations $Y_{i} \sim F_{θ_{0}}$ are replaced by $ℝ^{p}$ -valued $M$ -estimators ${\hat{β}}_{n} : = min \sum_{1}^{n} ρ (Y_{i} - τ (u (z_{i}^{T} β)))$ in a new model with observations $Y_{i} \sim F_{u (z_{i}^{t} β_{0})}$ , where $z_{i} \in ℝ^{p}$ are regressors, $β_{0} \in ℝ^{p}$ is a structural parameter and $u : ℝ \to ℝ$ a structural function of the new model. Sufficient conditions for the consistency of ${\hat{β}}_{n}$ are derived, motivated by the sufficiency conditions for the simpler “parent estimator” ${\hat{θ}}_{n}$ . The result is a general method of consistent estimation in a class of nonlinear (pseudolinear) statistical...