Empirical-likelihood-based confidence interval for the mean with a heavy-tailed distribution

Inspired by L.Peng’s work on estimating the mean of heavy-tailed distribution in the case of completed data. we propose an alternative estimator and study its asymptotic normality when it comes to the right truncated random variable. A simulation study is executed to evaluate the finite sample behavior on the proposed estimator

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A Semi-Markov Leaky Integrate-and-Fire Model

Mathematics ◽

10.3390/math7111022 ◽

2019 ◽

Vol 7 (11) ◽

pp. 1022

Author(s):

Giacomo Ascione ◽

Bruno Toaldo

Keyword(s):

Markov Process ◽

Waiting Times ◽

Markov Property ◽

Fire Model ◽

Integrate And Fire ◽

Heavy Tailed Distribution ◽

Semi Markov Process ◽

The Mean ◽

Heavy Tailed ◽

Mean Variance

In this paper, a Leaky Integrate-and-Fire (LIF) model for the membrane potential of a neuron is considered, in case the potential process is a semi-Markov process. Semi-Markov property is obtained here by means of the time-change of a Gauss-Markov process. This model has some merits, including heavy-tailed distribution of the waiting times between spikes. This and other properties of the process, such as the mean, variance and autocovariance, are discussed.

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BETTER CONFIDENCE INTERVALS FOR IMPORTANCE SAMPLING

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024910006200 ◽

2010 ◽

Vol 13 (08) ◽

pp. 1279-1291

Author(s):

HALIS SAK ◽

WOLFGANG HÖRMANN ◽

JOSEF LEYDOLD

Keyword(s):

Confidence Interval ◽

Credit Risk ◽

Confidence Intervals ◽

Importance Sampling ◽

Standard Method ◽

Weight Distribution ◽

Numerical Examples ◽

Closed Form Solutions ◽

The Mean ◽

Heavy Tailed

It is well known that for highly skewed distributions the standard method of using the t statistic for the confidence interval of the mean does not give robust results. This is an important problem for importance sampling (IS) as its final distribution is often skewed due to a heavy tailed weight distribution. In this paper, we first explain Hall's transformation and its variants to correct the confidence interval of the mean and then evaluate the performance of these methods for two numerical examples from finance which have closed-form solutions. Finally, we assess the performance of these methods for credit risk examples. Our numerical results suggest that Hall's transformation or one of its variants can be safely used in correcting the two-sided confidence intervals of financial simulations.

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Novel empirical likelihood inference for the mean difference with right-censored data

Statistical Methods in Medical Research ◽

10.1177/09622802211041767 ◽

2021 ◽

pp. 096228022110417

Author(s):

Kangni Alemdjrodo ◽

Yichuan Zhao

Keyword(s):

Confidence Interval ◽

Confidence Intervals ◽

Censored Data ◽

Empirical Likelihood ◽

Likelihood Method ◽

Right Censored Data ◽

Empirical Likelihood Method ◽

Chi Squared ◽

Coverage Accuracy ◽

The Mean

This paper focuses on comparing two means and finding a confidence interval for the difference of two means with right-censored data using the empirical likelihood method combined with the independent and identically distributed random functions representation. In the literature, some early researchers proposed empirical link-based confidence intervals for the mean difference based on right-censored data using the synthetic data approach. However, their empirical log-likelihood ratio statistic has a scaled chi-squared distribution. To avoid the estimation of the scale parameter in constructing confidence intervals, we propose an empirical likelihood method based on the independent and identically distributed representation of Kaplan–Meier weights involved in the empirical likelihood ratio. We obtain the standard chi-squared distribution. We also apply the adjusted empirical likelihood to improve coverage accuracy for small samples. In addition, we investigate a new empirical likelihood method, the mean empirical likelihood, within the framework of our study. The performances of all the empirical likelihood methods are compared via extensive simulations. The proposed empirical likelihood-based confidence interval has better coverage accuracy than those from existing methods. Finally, our findings are illustrated with a real data set.

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Mean Empirical Likelihood Inference for Response Mean with Data Missing at Random

Discrete Dynamics in Nature and Society ◽

10.1155/2020/8893594 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12

Author(s):

Hanji He ◽

Guangming Deng

Keyword(s):

Empirical Likelihood ◽

Missing At Random ◽

Confidence Regions ◽

Likelihood Inference ◽

High Dimensional ◽

Finite Sample ◽

The Mean ◽

Data Missing ◽

Consistency And Asymptotic Normality ◽

The Impact

We extend the mean empirical likelihood inference for response mean with data missing at random. The empirical likelihood ratio confidence regions are poor when the response is missing at random, especially when the covariate is high-dimensional and the sample size is small. Hence, we develop three bias-corrected mean empirical likelihood approaches to obtain efficient inference for response mean. As to three bias-corrected estimating equations, we get a new set by producing a pairwise-mean dataset. The method can increase the size of the sample for estimation and reduce the impact of the dimensional curse. Consistency and asymptotic normality of the maximum mean empirical likelihood estimators are established. The finite sample performance of the proposed estimators is presented through simulation, and an application to the Boston Housing dataset is shown.

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