European Journal of Statistics

Quasi-likelihood and Quasi-Bayes Estimation in Noncommutative Fractional SPDEs

2023-07-05T22:05:50+08:00

We study the quasi-likelihood and quasi Bayes estimator of the drift parameter in the stochastic partial differential equations when the process is observed at the arrival times of a Poisson process. Unlike the previous work, no commutativity condition is assumed between the operators in the equation. We use a two stage estimation procedure. We first estimate the intensity of the Poisson process. Then we plug-in this estimate in the quasi-likelihood to estimate the drift parameter. Under certain non-degeneracy assumptions on the operators, we obtain the consistency and the asymptotic normality of the estimators.

New Sine Inverted Exponential Distribution: Properties, Simulation and Application

2023-11-07T00:07:42+08:00

The New Sine Inverted Exponential Distribution, a new distribution model with just one parameter, is suggested in this study. The suggested model has several statistical qualities and reliability properties that have been constructed and explored. The MLE estimations of the parameters were determined using R's adequacy model package. To calculate the bias of the model parameter and the root mean square error, a simulation study was done. The simulation study revealed that the proposed model is well-behaved. The findings also showed that the suggested model outperforms the current listed models on two real datasets when performance was compared.

ANOVA F Test of Non-Null Hypothesis

2023-12-28T09:44:54+08:00

ANOVA, a test of a null hypothesis, is limited in assessing the statistical significance of differences. This paper considers an ANOVA F test of the non-null hypothesis for comparing k group means. A margin is chosen for the difference of means between each group and the kth group. A non-null hypothesis is defined to be the difference equal to the margin instead of zero. Data are thus prepared under the non-null hypothesis. Then follows the derivation of the one-way ANOVA non-null F test and its power. It reduces to the classical F test on setting the margin equal to zero. The observed size of it is identical to that of the F test and is near the nominal level of significance. The observed power is close to the power in balanced designs. With the non-null F test, it enables inferences to extend to the equivalence of group means or the clinical significance of differences. An example is taken to analyze both non-inferiority trials and k-sample equivalence trials.

Estimation of Optimal Lock-Down and Vaccination Rate of a Stochastic SIR Model: A Mathematical Approach

2023-12-03T11:09:07+08:00

This paper utilizes a stochastic Susceptible-Infected-recovered (SIR) model with a nonlinear incidence rate to estimate the optimal lock-down intensity and vaccination rate under the COVID-19 pandemic environment. We use a Feynman-type path integral control approach to determine a Fokker-Plank type equation of this system. Since we assume the availability of information on the COVID-19 pandemic is complete and perfect, we show the existence of a unique fixed point. A non-linear incidence rate is used because, it can be raised from saturation effects that if the proportion of infected agents is very high so that exposure to the pandemic is inevitable, then the transmission rate responds slower than linearity to the increase in the number of infections. The simulation study shows that with higher diffusion coefficients susceptible and recovery curves keep the downward trends while the infection curve becomes ergodic. Finally, we perform a data analysis using UK data at the beginning of 2021 and compare it with our theoretical results.

Improved Monitoring of Early-Warning Signs of an AMOC Collapse

2023-08-21T14:47:06+08:00

This paper reviews a recent study predicting that the Atlantic Meridional Overturning Current circulation may collapse in the middle of this century and concludes that there are too many uncertainties to allow a reliable prediction. Even if the model used in that study is fairly adequate, its predictions depend heavily on the quality of the involved approximations, the choice of the circulation proxy, the method of trend estimation, the size of the rolling window used for the estimation of the second moments, the determination of the start time of ramping, etc. Forced to set lower targets, the focus is consequently shifted to the improved detection of early-warning signs like an increase in variance and autocorrelation. Two new estimation procedures are introduced. The first concerns the estimation of the trend and includes a new criterion for comparing the quality of different estimates. The second is a procedure for detecting changes in the first-order autocorrelation without any delay caused by an estimation window. The results obtained with these methods suggest that the autocorrelation increases erratically rather than steadily which would make forecasting based on extrapolation impossible.

Enhancing Multiple Frame Surveys: Improved Calibration and Efficient Bootstrap Techniques

2023-11-03T07:43:53+08:00

In recent years, multiple frame surveys have gained significant attention due to their applicability in capturing special or challenging-to-sample populations. This paper introduces two methodological advancements, the calibrated multiplicity estimator and without-replacement bootstrap techniques, in the field of multiple frame surveys. A comprehensive simulation study assesses their performance. The calibrated multiplicity estimator is demonstrated to outperform the multiplicity estimator, particularly in terms of mean squared error, with a ratio ranging from 0.6 to 0.8. Furthermore, the study shows that without-replacement bootstrap techniques perform favorably compared to their with-replacement counterparts. Future research directions include conducting more extensive simulations with real-world data and establishing the theoretical properties of the proposed estimator. This paper contributes to the growing body of knowledge on multiple frame surveys and their estimation methods.