Application of a delta-method for random operators to testing equality of two covariance operators

This article explores a method of creating confidence bounds for information-theoretic measures in linguistics, such as entropy, Kullback-Leibler Divergence (KLD), and mutual information. We show that a useful measure of uncertainty can be derived from simple statistical principles, namely the asymptotic distribution of the maximum likelihood estimator (MLE) and the delta method. Three case studies from phonology and corpus linguistics are used to demonstrate how to apply it and examine its robustness against common violations of its assumptions in linguistics, such as insufficient sample size and non-independence of data points.

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An approximate point-based alternative for the estimation of variance under big BAF sampling

Forest Ecosystems ◽

10.1186/s40663-021-00304-0 ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Thomas B. Lynch ◽

Jeffrey H. Gove ◽

Timothy G. Gregoire ◽

Mark J. Ducey

Keyword(s):

Forest Inventory ◽

Variance Estimation ◽

Basal Area ◽

Volume Estimation ◽

Delta Method ◽

Sampling Point ◽

Variance Estimator ◽

Computer Simulation Studies ◽

New Formula ◽

Estimation Of Variance

Abstract Background A new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation. Methods The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula. Results Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas. Conclusions A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of $\frac {1}{n}$ 1 n where n is the number of sample points.

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Dental Expenditure by Household Income in Korea over the Period 2008–2017: A Review of the National Dental Insurance Reform

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph18083859 ◽

2021 ◽

Vol 18 (8) ◽

pp. 3859

Author(s):

Hosung Shin ◽

Han-A Cho ◽

Bo-Ra Kim

Keyword(s):

Health Insurance ◽

Concentration Index ◽

Dental Health ◽

Age Groups ◽

The Elderly ◽

Dental Service ◽

Delta Method ◽

Dental Services ◽

Insurance Reform ◽

Health Insurance Reform

Since 2009, the National Health Insurance in Korea (NHI) has been implementing a series of policies to expand the scope of dental benefits. This study reviewed the changes in co-payments and dental use patterns before (2008 to 2012) and after (2013 to 2017) the NHI’s dental health insurance reform. The study used Korea Health Panel data of 7681 households (16,493 household members) from a 10-year period (2008–2017). Dental expenditures and equivalent income using square root of household size were analyzed. Dental services were categorized into 13 types and a concentration index and 95% confidence interval using the delta method was calculated to identify income-related inequalities by a dental service. Dental expenditures and the number of dental services used increased significantly, while the proportion of out-of-pocket spending by the elderly decreased. The expenditure ratio for implant services to total dental expenditures increased substantially in all age groups, but the ratio of expenditures for dentures and fixed bridges decreased relatively. The concentration index of implant services was basically in favor of the rich, but there was no longer a significant bias favoring the better-off after the reforms. The dental health insurance reform in Korea appears to contribute not only to lowering the ratio of out-of-pocket to total dental expenses per episode in the elderly but also to improving the inequality of dental expenses.

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Angoff's delta method revisited: Improving DIF detection under small samples

British Journal of Mathematical and Statistical Psychology ◽

10.1111/j.2044-8317.2011.02025.x ◽

2011 ◽

Vol 65 (2) ◽

pp. 302-321 ◽

Cited By ~ 9

Author(s):

David Magis ◽

Bruno Facon

Keyword(s):

Delta Method ◽

Small Samples

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Exact parametric causal mediation analysis for a binary outcome with a binary mediator

Statistical Methods & Applications ◽

10.1007/s10260-021-00562-w ◽

2021 ◽

Author(s):

Marco Doretti ◽

Martina Raggi ◽

Elena Stanghellini

Keyword(s):

Logistic Regression ◽

Direct Effect ◽

Mediation Analysis ◽

Delta Method ◽

Binary Outcome ◽

Effect Decomposition ◽

Causal Mediation ◽

Regression Parameters ◽

Causal Mediation Analysis ◽

Parametric Expression

AbstractWith reference to causal mediation analysis, a parametric expression for natural direct and indirect effects is derived for the setting of a binary outcome with a binary mediator, both modelled via a logistic regression. The proposed effect decomposition operates on the odds ratio scale and does not require the outcome to be rare. It generalizes the existing ones, allowing for interactions between both the exposure and the mediator and the confounding covariates. The derived parametric formulae are flexible, in that they readily adapt to the two different natural effect decompositions defined in the mediation literature. In parallel with results derived under the rare outcome assumption, they also outline the relationship between the causal effects and the correspondent pathway-specific logistic regression parameters, isolating the controlled direct effect in the natural direct effect expressions. Formulae for standard errors, obtained via the delta method, are also given. An empirical application to data coming from a microfinance experiment performed in Bosnia and Herzegovina is illustrated.

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The Delta-Method

Weak Convergence and Empirical Processes - Springer Series in Statistics ◽

10.1007/978-1-4757-2545-2_35 ◽

1996 ◽

pp. 372-400 ◽

Cited By ~ 2

Author(s):

Aad W. van der Vaart ◽

Jon A. Wellner

Keyword(s):

Delta Method

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Q-Matrix Refinement Based on Item Fit Statistic RMSEA

Applied Psychological Measurement ◽

10.1177/0146621618813104 ◽

2018 ◽

Vol 43 (7) ◽

pp. 527-542 ◽

Cited By ~ 2

Author(s):

Chunhua Kang ◽

Yakun Yang ◽

Pingfei Zeng

Keyword(s):

Search Algorithm ◽

Delta Method ◽

Mean Square ◽

Simulation Studies ◽

Response Data ◽

Item Fit ◽

Dina Model ◽

Q Matrix ◽

Diagnosis Model ◽

Effectiveness And Efficiency

A Q-matrix, which reflects how attributes are measured for each item, is necessary when applying a cognitive diagnosis model to an assessment. In most cases, the Q-matrix is constructed by experts in the field and may be subjective and incorrect. One efficient method to refine the Q-matrix is to employ a suitable statistic that is calculated using response data. However, this approach is limited by its need to estimate all items in the Q-matrix even if only some are incorrect. To address this challenge, this study proposes an item fit statistic root mean square error approximation (RMSEA) for validating a Q-matrix with the deterministic inputs, noisy, “and” (DINA) model. Using a search algorithm, two simulation studies were performed to evaluate the effectiveness and efficiency of the proposed method at recovering Q-matrices. Results showed that using RMSEA can help define attributes in a Q-matrix. A comparison with the existing Delta method and residual sum of squares (RSS) method revealed that the proposed method had higher mean recovery rates and can be used to identify and correct Q-matrix misspecifications. When no error exists in the Q-matrix, the proposed method does not modify the correct Q-matrix.

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