On robustness of maximum likelihood estimates for Poisson-lognormal models

Weems, Kimberly S.; Smith, Paul J.

doi:10.1016/j.spl.2003.11.003

Cited by 9 publications

(5 citation statements)

References 8 publications

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“…comm.). Also known as mixed Poisson regression models, these models assume that the conditional distribution of the response is Poisson distributed with a random mean, which is dependent on the normally-distributed random effects (Weems and Smith 2004). We included a random effect on each individual visit to each wetland (WETLAND*TIME OF DAY*TIME OF SEASON) and random effects on wetland (WET-LAND), survey point (POINT), the interaction of wetland and time of day (WETLAND*TIME OF DAY), and the interaction of wetland and time of season (WETLAND*TIME OF SEASON) to further account for variation in the model.…”

Section: Methodsmentioning

confidence: 99%

Influence of season and time of day on marsh bird detections

Harms¹,

Dinsmore²

2014

The Wilson Journal of Ornithology

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Call-broadcast surveys are frequently used to elicit responses of secretive marsh birds and produce greater detection rates than passive surveys. However, little is known about how detection rates of birds from these surveys differ by season and time of day. We conducted call-broadcast surveys for eight focal species at 56 wetlands throughout Iowa from 15 May-13 June 2010 (early season) and from 15 June-10 July 2010 (late season). Our focal species were Pied-billed Grebe (Podilymbus podiceps), American Bittern (Botaurus lentiginosus), Least Bittern (Ixobrychus exilis), King Rail (Rallus elegans), Virginia Rail (Rallus limicola), Sora (Porzana carolina), Common Gallinule (Gallinula chloropus), and American Coot (Fulica americana). Surveys were conducted in the early morning (30 mins before sunrise to 3 hrs after sunrise) and late evening (3 hrs before sunset to 30 mins after sunset) in accordance with the North American Marsh Bird Monitoring Protocol. We evaluated marsh bird detection rates as a function of a) time of day (morning and evening survey periods), b) season (early and late in the breeding season), and c) wetland size for four species with the greatest detection rates (Pied-billed Grebe, Least Bittern, Virginia Rail, and Sora). We also evaluated the above effects for two species groups; all eight species pooled and all rails pooled. We found significant (P < 0.05) effects on the number of detections for Pied-billed Grebe in response to time of day, time of season, and wetland size; Sora, Virginia Rail, all rails, and all species had an effect of time of season only. Understanding seasonal and time-of-day differences in detection rates, as well as area dependence of secretive marsh birds, will refine existing monitoring protocols by allowing researchers to maximize detection probabilities of target species. ABSTRACT.-Call-broadcast surveys are frequently used to elicit responses of secretive marsh birds and produce greater detection rates than passive surveys. However, little is known about how detection rates of birds from these surveys differ by season and time of day. We conducted call-broadcast surveys for eight focal species at 56 wetlands throughout Iowa from 15 May-13 June 2010 (early season) and from 15 June-10 July 2010 (late season). Our focal species were Piedbilled Grebe (Podilymbus podiceps), American Bittern (Botaurus lentiginosus), Least Bittern (Ixobrychus exilis), King Rail (Rallus elegans), Virginia Rail (Rallus limicola), Sora (Porzana carolina), Common Gallinule (Gallinula chloropus), and American Coot (Fulica americana). Surveys were conducted in the early morning (30 mins before sunrise to 3 hrs after sunrise) and late evening (3 hrs before sunset to 30 mins after sunset) in accordance with the North American Marsh Bird Monitoring Protocol. We evaluated marsh bird detection rates as a function of a) time of day (morning and evening survey periods), b) season (early and late in the breeding season), and c) wetland size for four species with the greatest detection rates (Pied...

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Section: Methodsmentioning

confidence: 99%

Influence of season and time of day on marsh bird detections

Harms¹,

Dinsmore²

2014

The Wilson Journal of Ornithology

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“…But, the MLE does struggle if the underlying data is contaminated. This lack of robustness has been observed in the literature for different known models, e.g., in Xu and Reid (2011), Weems and Smith (2004) or Genton and Ma (1999). Here, we start with an example of Poisson process to show that the classical MLE fails when there is even a minute contamination in the data.…”

Section: Introductionmentioning

confidence: 74%

Robust and Efficient Parameter Estimation for Discretely Observed Stochastic Processes

Hore¹,

Ghosh²

2022

Preprint

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In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference methods based on the maximum likelihood (ML) principle are susceptible to minor deviations from assumed model or data contamination due to their well known lack of robustness. Since the alternative non-parametric procedures often lose significant efficiency, in this paper, we develop a robust parameter estimation procedure for discretely observed data from a parametric stochastic process model which exploits the nice properties of the popular density power divergence measure in the framework of minimum distance inference. In particular, here we define the minimum density power divergence estimators (MDPDE) for the independent increment and the Markov processes. We establish the asymptotic consistency and distributional results for the proposed MDPDEs in these dependent stochastic process set-ups and illustrate their benefits over the usual ML estimator for common examples like Poisson process, drifted Brownian motion and auto-regressive models.

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“…But, the MLE does struggle if the underlying data is contaminated. This lack of robustness has been observed in the literature for different known models, e.g., in [8], [9] or [10]. Here, we start with an example of Poisson process to show that the classical MLE fails when there is even a minute contamination in the data.…”

Section: Introductionmentioning

confidence: 74%

“…, p, where ∇ denotes the (first order) gradient with respect to θ, ∇ kl represents the second order partial derivative with respect to the indicated components (k, l) of θ and the associated expectation and variance are considered with respect to different densities for the IIP and MP set-ups as described above. In particular, for the IIP models, the variance can be taken inside the summation in the expression of Ω n (t) in (9). Now our goal is to establish the asymptotic normality and consistency of the MDPDE for both the IIP and MP models.…”

Section: Accordingly If We Denotementioning

confidence: 99%

Robust and Efficient Parameter Estimation for Discretely Observed Stochastic Processes

Hore

Ghosh

2022

Preprint

View full text Add to dashboard Cite

In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference methods based on the maximum likelihood (ML) principle are susceptible to minor deviations from assumed model or data contamination due to their well known lack of robustness. Since the alternative non-parametric procedures often lose significant efficiency, in this paper, we develop a robust parameter estimation procedure for discretely observed data from a parametric stochastic process model which exploits the nice properties of the popular density power divergence measure in the framework of minimum distance inference. In particular, here we define the minimum density power divergence estimators (MDPDE) for the independent increment and the Markov processes. We establish the asymptotic consistency and distributional results for the proposed MDPDEs in these dependent stochastic process setups and illustrate their benefits over the usual ML estimator for common examples like Poisson process, drifted Brownian motion and auto-regressive models.

show abstract

On robustness of maximum likelihood estimates for Poisson-lognormal models

Cited by 9 publications

References 8 publications

Influence of season and time of day on marsh bird detections

Influence of season and time of day on marsh bird detections

Robust and Efficient Parameter Estimation for Discretely Observed Stochastic Processes

Robust and Efficient Parameter Estimation for Discretely Observed Stochastic Processes

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