Rao–Cramer Type Inequalities for Mean Squared Error of Prediction

Nayak, Tapan K.

doi:10.1198/000313002317572763

Cited by 9 publications

(3 citation statements)

References 13 publications

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“…There are two notes concerning . First, application of Theorem 1 in Nayak (2002) shows that the last line is the lower bound for MSPE. Therefore, is asymptotically most efficient.…”

Section: Ecological Inferencementioning

confidence: 99%

A Model‐Based Approach for Making Ecological Inference from Distance Sampling Data

Johnson¹,

Laake²,

Hoef³

2010

Biometrics

114

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Summary. We consider a fully model-based approach for the analysis of distance sampling data. Distance sampling has been widely used to estimate abundance (or density) of animals or plants in a spatially explicit study area. There is, however, no readily available method of making statistical inference on the relationships between abundance and environmental covariates. Spatial Poisson process likelihoods can be used to simultaneously estimate detection and intensity parameters by modeling distance sampling data as a thinned spatial point process. A model-based spatial approach to distance sampling data has three main benefits: it allows complex and opportunistic transect designs to be employed, it allows estimation of abundance in small subregions, and it provides a framework to assess the effects of habitat or experimental manipulation on density. We demonstrate the model-based methodology with a small simulation study and analysis of the Dubbo weed data set. In addition, a simple ad hoc method for handling overdispersion is also proposed. The simulation study showed that the model-based approach compared favorably to conventional distance sampling methods for abundance estimation. In addition, the overdispersion correction performed adequately when the number of transects was high. Analysis of the Dubbo data set indicated a transect effect on abundance via Akaike's information criterion model selection. Further goodness-of-fit analysis, however, indicated some potential confounding of intensity with the detection function.

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“…There are two notes concerning . First, application of Theorem 1 in Nayak (2002) shows that the last line is the lower bound for MSPE. Therefore, is asymptotically most efficient.…”

Section: Ecological Inferencementioning

confidence: 99%

A Model‐Based Approach for Making Ecological Inference from Distance Sampling Data

Johnson¹,

Laake²,

Hoef³

2010

Biometrics

114

View full text Add to dashboard Cite

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“…It develops by generalizing the results of point estimation to prediction problems (see for instance Yatracos (1992), Bosq and Blanke (2007) and Bosq (2007)). For instance some authors have studied the extension of the Cramér-Rao inequality to the case of statistical prediction problems (Yatracos (1992), Miyata (2001), Nayak (2002), Onzon (2011)). In the univariate case and for an unbiased predictor p(X) it has the form (1.1) E θ (p(X) − r(X, θ)) 2 E θ (∂ θ r(X, θ))…”

Section: Introductionmentioning

confidence: 99%

Asymptotically efficient prediction for LAN families

Onzon

2013

Preprint

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In a previous paper (Bosq and Onzon ( 2012)) we did a first generalization of the concept of asymptotic efficiency for statistical prediction, i.e. for the problems where the unknown quantity to infer is not deterministic but random. However, in some instances, the assumptions we made were not easy to verify. Here we give proofs of similar results based on quite a different set of assumptions. The model is required to be a LAN family, which allows to use the convolution theorem of Hájek and Le Cam. The results are applied to the forecasting of a bivariate Ornstein-Uhlenbeck process, for which the assumptions of (Bosq and Onzon ( 2012)) are tricky to verify.

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“…A lower bound of Cramér-Rao type has been proved for the QEP with conditions of point differentiability of the family of the densities of the distributions of the model with respect to the parameter and conditions of differentiability under the integral sign (Yatracos (1992), Nayak (2002), Bosq and Blanke (2007)). The bound has also been proved for conditions of L 2 -differentiability of the family of distributions of the model (Miyata (2001), Onzon (2012)).…”

mentioning

confidence: 99%

Efficient prediction in $L^2$-differentiable families of distributions

Onzon¹

2013

Preprint

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A proof of the Cramér-Rao inequality for prediction is presented under conditions of L 2 -differentiability of the family of distributions of the model. The assumptions and the proof differ from those of Miyata ( 2001) who also proved this inequality under L 2differentiability conditions. It is also proved that an efficient predictor (i.e. which risk attains the bound) exists if and only if the family of distributions is of a special form which can be seen as an extension of the notion of exponential family. This result is also proved under L 2 -differentiability conditions.

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Rao–Cramer Type Inequalities for Mean Squared Error of Prediction

Cited by 9 publications

References 13 publications

A Model‐Based Approach for Making Ecological Inference from Distance Sampling Data

A Model‐Based Approach for Making Ecological Inference from Distance Sampling Data

Asymptotically efficient prediction for LAN families

Efficient prediction in $L^2$-differentiable families of distributions

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