Asymptotic properties of the MAMSE adaptive likelihood weights

Plante, Jean‐François

doi:10.1016/j.jspi.2008.10.001

Cited by 7 publications

(16 citation statements)

References 13 publications

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“…They are used to define the MAMSE weighted empirical distribution functions

{\overset{F}{true}}_{n} (x) = \sum_{i = 1}^{m} μ_{n, i} {\overset{F}{true}}_{i, n_{i}} (x) and {\overset{G}{true}}_{n} (x) = \sum_{i = 1}^{m} γ_{n, i} {\overset{G}{true}}_{i, k_{i}} (x),

which are estimates of F 1 and G 1 , respectively. If

n_{1} \to \infty

and the other sample sizes are nondecreasing,

\sup_{x} | {\overset{F}{true}}_{n} (x) - F_{1} (x) | \to 0

almost surely and similarly for

{\overset{G}{true}}_{n} (x)

k_{1} \to \infty

as shown by Plante (). No assumptions need to be made on the distributions in populations 2 to m , but as a consequence, the rate of convergence of these suprema is undetermined.…”

Section: Mamse Weights and The Combination Of Roc Curvesmentioning

confidence: 80%

“…The MAMSE criterion compares the empirical distributions obtained from the different samples to adapt the magnitude of their contributions while making no assumptions on their similarities (or lack thereof). The MAMSE weighted empirical distribution function that are shown to be consistent by Plante () will be used to define a nonparametric estimate of the ROC curve. Under mild regularity assumptions, he also shows that the maximum weighted likelihood estimate (MWLE) is consistent.…”

Section: Introductionmentioning

confidence: 99%

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Combining ROC curves using MAMSE weighted distributions

Plante

Débordès

2018

Can J Statistics

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The receiver operating characteristic (ROC) curve can be used to evaluate the properties of a diagnostic test from the distribution of a variable on the healthy and diseased populations. The minimum averaged mean squared error (MAMSE) weights were developed to handle data from different sources by adjusting the relative contribution of each data source. The authors use the MAMSE weights to infer the ROC curve of a diagnostic test based on raw data from multiple studies. The proposed estimates are consistent and Monte Carlo simulations show favourable finite sample performance. The method is illustrated in a case study where progesterone level is used to detect ectopic pregnancies and abortions from other natural causes. The Canadian Journal of Statistics 46: 298–315; 2018 © 2018 Statistical Society of Canada

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“…They are used to define the MAMSE weighted empirical distribution functions

{\overset{F}{true}}_{n} (x) = \sum_{i = 1}^{m} μ_{n, i} {\overset{F}{true}}_{i, n_{i}} (x) and {\overset{G}{true}}_{n} (x) = \sum_{i = 1}^{m} γ_{n, i} {\overset{G}{true}}_{i, k_{i}} (x),

which are estimates of F 1 and G 1 , respectively. If

n_{1} \to \infty

and the other sample sizes are nondecreasing,

\sup_{x} | {\overset{F}{true}}_{n} (x) - F_{1} (x) | \to 0

almost surely and similarly for

{\overset{G}{true}}_{n} (x)

k_{1} \to \infty

as shown by Plante (). No assumptions need to be made on the distributions in populations 2 to m , but as a consequence, the rate of convergence of these suprema is undetermined.…”

Section: Mamse Weights and The Combination Of Roc Curvesmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Combining ROC curves using MAMSE weighted distributions

Plante

Débordès

2018

Can J Statistics

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“…, C m is identical to C 1 . This behaviour is observed and discussed with other versions of the MAMSE weights in Plante (2008Plante ( , 2009a. The study of the asymptotic distribution of √ N k Ĉ μ k − C 1 would require a description of the similarities between the C i , an endeavour that will not be undertaken in this paper.…”

Section: Theorem 3 We Have Uniform Convergence Of the Mamse-weighted mentioning

confidence: 95%

“…In this context, adaptive weights can trade potential bias for reduced variance. We therefore extend the MAMSE weights of Plante (2008Plante ( , 2009a by replacing the empirical distribution functions in their definition with empirical copulas.…”

Section: Heterogeneous Copulas: Adaptive Weightsmentioning

confidence: 99%

“…Whenever the dependence structure in the groups are likely to be similar, using data from all the groups wisely could provide a favorable tradeoff between bias and variance. Rather than keeping only the much smaller sample from each group of interest, we then suggest to use an extension of the Minimum Averaged Mean Squared Error (MAMSE) weights of Plante (2008Plante ( , 2009a to borrow strength adaptively from the other groups.…”

Section: Introductionmentioning

confidence: 99%

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Rank correlation under categorical confounding

Plante

2017

J Stat Distrib App

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Rank correlation is invariant to bijective marginal transformations, but it is not immune to confounding. Assuming a categorical confounding variable is observed, the author proposes weighted coefficients of correlation for continuous variables developed within a larger framework based on copulas. While the weighting is clear under the assumption that the dependence is the same within each group implied by the confounder, the author extends the Minimum Averaged Mean Squared Error (MAMSE) weights to borrow strength between groups when the dependence may vary across them. Asymptotic properties of the proposed coefficients are derived and simulations are used to assess their finite sample properties.

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A predictive approach to measuring the strength of statistical evidence for single and multiple comparisons

Bickel

2011

Can J Statistics

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The normalized maximum likelihood (NML) is a recent penalized likelihood that has properties that justify defining the amount of discrimination information (DI) in the data supporting an alternative hypothesis over a null hypothesis as the logarithm of an NML ratio, namely, the alternative hypothesis NML divided by the null hypothesis NML. The resulting DI, like the Bayes factor but unlike the P‐value, measures the strength of evidence for an alternative hypothesis over a null hypothesis such that the probability of misleading evidence vanishes asymptotically under weak regularity conditions and such that evidence can support a simple null hypothesis. Instead of requiring a prior distribution, the DI satisfies a worst‐case minimax prediction criterion. Replacing a (possibly pseudo‐) likelihood function with its weighted counterpart extends the scope of the DI to models for which the unweighted NML is undefined. The likelihood weights leverage side information, either in data associated with comparisons other than the comparison at hand or in the parameter value of a simple null hypothesis. Two case studies, one involving multiple populations and the other involving multiple biological features, indicate that the DI is robust to the type of side information used when that information is assigned the weight of a single observation. Such robustness suggests that very little adjustment for multiple comparisons is warranted if the sample size is at least moderate. The Canadian Journal of Statistics 39: 610–631; 2011. © 2011 Statistical Society of Canada

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Asymptotic properties of the MAMSE adaptive likelihood weights

Cited by 7 publications

References 13 publications

Combining ROC curves using MAMSE weighted distributions

Combining ROC curves using MAMSE weighted distributions

Rank correlation under categorical confounding

A predictive approach to measuring the strength of statistical evidence for single and multiple comparisons

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