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Confidence sets
"... • If the random set S(X) satisfies IPθ{S(X) ∋ θ} ≥ 1 − α for all θ ∈ Θ, S is a 1 − α confidence set. • Probability meaningful only before the datum is observed: If X = x, either S(x) ∋ θ or not. • Connected confidence set for real parameter: confidence interval (CI).Background Univariate location ..."
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• If the random set S(X) satisfies IPθ{S(X) ∋ θ} ≥ 1 − α for all θ ∈ Θ, S is a 1 − α confidence set. • Probability meaningful only before the datum is observed: If X = x, either S(x) ∋ θ or not. • Connected confidence set for real parameter: confidence interval (CI).Background Univariate
Modulation Estimators and Confidence Sets
 ANN. STATIST
, 1999
"... An unknown signal plus white noise is observed at n discrete time points. Within a large convex class of linear estimators of , we choose the estimator b that minimizes estimated quadratic risk. By construction, b is nonlinear. This estimation is done after orthogonal transformation of the data to ..."
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Cited by 50 (11 self)
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one such asymptotic minimax property with the JamesStein estimator. We describe computational algorithms for b and construct confidence sets for the unknown signal. These confidence sets are centered at b , have correct asymptotic coverage probability, and have relatively small risk as set
Nonparametric confidence set estimation
 Math. Methods Statist
, 2003
"... Abstract: The problem of adaptive estimation of regression function from noisy observations is considered in the paper. We provide an adaptive confidence set ˆ BN of level 1 − α, 0 < α < 1, for the unknown function f. Here ˆ BN is a L2ball of (random) diameter τN, centered at the wavelet adap ..."
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Cited by 14 (0 self)
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Abstract: The problem of adaptive estimation of regression function from noisy observations is considered in the paper. We provide an adaptive confidence set ˆ BN of level 1 − α, 0 < α < 1, for the unknown function f. Here ˆ BN is a L2ball of (random) diameter τN, centered at the wavelet
Clustering Confidence Sets
"... We propose a method for clustering a large set of observed objects with different noise levels based on their confidence set estimates rather than their point estimates. The minimal and maximal distances between confidence sets provide confidence intervals for the true distances between objects. The ..."
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We propose a method for clustering a large set of observed objects with different noise levels based on their confidence set estimates rather than their point estimates. The minimal and maximal distances between confidence sets provide confidence intervals for the true distances between objects
Nonoptimality of Randomized Confidence Sets
, 1988
"... Randomized confidence sets are used in classical decision theory as a device to obtain optimality results. In particular, in discrete distributions, a uniformly most accurate unbiased (UMA U) confidence set is based on an auxiliary randomizer that is independent of the data. Such procedures are sho ..."
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Randomized confidence sets are used in classical decision theory as a device to obtain optimality results. In particular, in discrete distributions, a uniformly most accurate unbiased (UMA U) confidence set is based on an auxiliary randomizer that is independent of the data. Such procedures
ADAPTIVE NONPARAMETRIC CONFIDENCE SETS
, 2006
"... We construct honest confidence regions for a Hilbert spacevalued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited in sc ..."
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Cited by 16 (0 self)
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We construct honest confidence regions for a Hilbert spacevalued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited
Confidence Sets for Network Structure
"... Latent variable models are frequently used to identify structure in dichotomous network data, in part because they give rise to a Bernoulli product likelihood that is both well understood and consistent with the notion of exchangeable random graphs. In this article we propose conservative confidence ..."
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Cited by 2 (0 self)
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confidence sets that hold with respect to these underlying Bernoulli parameters as a function of any given partition of network nodes, enabling us to assess estimates of residual network structure, that is, structure that cannot be explained by known covariates and thus cannot be easily verified by manual
Confidence Sets for Asset . . .
, 2007
"... This paper addresses the estimation of confidence sets for asset correlation for credit risk assessment using rating transition data. Research on the estimation of asset correlation with rating transition data has focused on the point estimation of the correlation without giving any consideration wi ..."
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This paper addresses the estimation of confidence sets for asset correlation for credit risk assessment using rating transition data. Research on the estimation of asset correlation with rating transition data has focused on the point estimation of the correlation without giving any consideration
Confidence Sets for Network Structure
, 2011
"... Abstract: Latent variable models are frequently used to identify structure in dichotomous network data, in part, because they give rise to a Bernoulli product likelihood that is both well understood and consistent with the notion of exchangeable random graphs. In this article, we propose conservativ ..."
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conservative confidence sets that hold with respect to these underlying Bernoulli parameters as a function of any given partition of network nodes, enabling us to assess estimates of residual network structure, that is, structure that cannot be explained by known covariates and thus cannot be easily verified
Confidence Sets for Asset Correlation
, 2007
"... This paper addresses the estimation of confidence sets for asset correlation for credit risk assessment using rating transition data. Research on the estimation of asset correlation with rating transition data has focused on the point estimation of the correlation without giving any consideration wi ..."
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This paper addresses the estimation of confidence sets for asset correlation for credit risk assessment using rating transition data. Research on the estimation of asset correlation with rating transition data has focused on the point estimation of the correlation without giving any consideration
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