scholarly journals Functional delta-method for the bootstrap of quasi-Hadamard differentiable functionals

2016 ◽  
Vol 10 (1) ◽  
pp. 1181-1222 ◽  
Author(s):  
Eric Beutner ◽  
Henryk Zähle
Keyword(s):  
Delta Method ◽  
Functional Delta Method

TESTING FOR A CHANGE IN CORRELATION AT AN UNKNOWN POINT IN TIME USING AN EXTENDED FUNCTIONAL DELTA METHOD

2011 ◽  
Vol 28 (3) ◽  
pp. 570-589 ◽  
Author(s):  
Dominik Wied ◽  
Walter Krämer ◽  
Herold Dehling
Keyword(s):  
Monte Carlo ◽  
Stock Returns ◽  
Structural Changes ◽  
Null Distribution ◽  
Delta Method ◽  
Local Power ◽  
Finite Sample ◽  
Empirical Correlations ◽  
Functional Delta Method ◽  
Unknown Point

We propose a new test against a change in correlation at an unknown point in time based on cumulated sums of empirical correlations. The test does not require that inputs are independent and identically distributed under the null. We derive its limiting null distribution using a new functional delta method argument, provide a formula for its local power for particular types of structural changes, give some Monte Carlo evidence on its finite-sample behavior, and apply it to recent stock returns.

scholarly journals A NONPARAMETRIC HELLINGER METRIC TEST FOR CONDITIONAL INDEPENDENCE

2008 ◽  
Vol 24 (4) ◽  
pp. 829-864 ◽  
Author(s):  
Liangjun Su ◽  
Halbert White
Keyword(s):  
Monte Carlo Simulation ◽  
Exchange Rates ◽  
Conditional Independence ◽  
Nonparametric Test ◽  
Delta Method ◽  
Mixing Conditions ◽  
Test Statistic ◽  
Finite Samples ◽  
Functional Delta Method ◽  
Simulation Results

We propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities, f(y|x,z) and f(y|x), which is identically zero under the null. We use the functional delta method to expand the test statistic around the population value and establish asymptotic normality under β-mixing conditions. We show that the test is consistent and has power against alternatives at distance n−1/2h−d/4. The cases for which not all random variables of interest are continuously valued or observable are also discussed. Monte Carlo simulation results indicate that the test behaves reasonably well in finite samples and significantly outperforms some earlier tests for a variety of data generating processes. We apply our procedure to test for Granger noncausality in exchange rates.

scholarly journals Bootstrapping Average Value at Risk of Single and Collective Risks

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 96
Author(s):  
Eric Beutner ◽  
Henryk Zähle
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Delta Method ◽  
Average Value ◽  
Independent Observations ◽  
Functional Delta Method ◽  
Average Value At Risk ◽  
Statistical Functionals ◽  
Differentiable Statistical Functionals

Almost sure bootstrap consistency of the blockwise bootstrap for the Average Value at Risk of single risks is established for strictly stationary β -mixing observations. Moreover, almost sure bootstrap consistency of a multiplier bootstrap for the Average Value at Risk of collective risks is established for independent observations. The main results rely on a new functional delta-method for the almost sure bootstrap of uniformly quasi-Hadamard differentiable statistical functionals, to be presented here. The latter seems to be interesting in its own right.

scholarly journals Quasi-Hadamard differentiability of general risk functionals and its application

2015 ◽  
Vol 32 (1) ◽  
Author(s):  
Volker Krätschmer ◽  
Alexander Schied ◽  
Henryk Zähle
Keyword(s):  
Limit Theorems ◽  
Risk Measures ◽  
Delta Method ◽  
Fine Tuning ◽  
Coherent Risk Measures ◽  
Coherent Risk ◽  
Hadamard Differentiability ◽  
Functional Delta Method ◽  
Statistical Functionals

AbstractWe apply a suitable modification of the functional delta method to statistical functionals that arise from law-invariant coherent risk measures. To this end we establish differentiability of the statistical functional in a relaxed Hadamard sense, namely with respect to a suitably chosen norm and in the directions of a specifically chosen “tangent space”. We show that this notion of quasi-Hadamard differentiability yields both strong laws and limit theorems for the asymptotic distribution of the plug-in estimators. Our results can be regarded as a contribution to the statistics and numerics of risk measurement and as a case study for possible refinements of the functional delta method through fine-tuning the underlying notion of differentiability.

Large-sample confidence intervals of information-theoretic measures in linguistics

2020 ◽  
Vol 6 (1) ◽  
pp. 19-54
Author(s):  
Ryan Ka Yau Lai ◽  
Youngah Do
Keyword(s):  
Maximum Likelihood ◽  
Corpus Linguistics ◽  
Delta Method ◽  
Confidence Bounds ◽  
Likelihood Estimator ◽  
Information Theoretic ◽  
Leibler Divergence ◽  
Information Theoretic Measures ◽  
Data Points ◽  
Measure Of Uncertainty

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.

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

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.

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

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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