Efficiency of Some Estimators for a Generalized Poisson Autoregressive Process of Order 1

Various models have been proposed in the literature to study non-negative integer-valued time series. In this paper, we study estimators for the generalized Poisson autoregressive process of order 1, a model developed by Alzaid and Al-Osh [1]. We compare three estimation methods, the methods of moments, quasi-likelihood and conditional maximum likelihood and study their asymptotic properties. To compare the bias of the estimators in small samples, we perform a simulation study for various parameter values. Using the theory of estimating equations, we obtain expressions for the variance-covariance matrices of those three estimators, and we compare their asymptotic efficiency. Finally, we apply the methods derived in the paper to a real time series.

Estimation of Poisson-Generalized Pareto Compound Extreme Value Distribution by Probability-Weighted Moments and Empirical Analysis

This paper puts forward a Poisson-generalized Pareto (Poisson-GP) distribution. This new form of compound extreme value distribution expands the existing application of compound extreme value distribution, and can be applied to predicting financial risk, large insurance settlement and high-grade earthquake, etc. Compared with the maximum likelihood estimation (MLE) and compound moment estimation (CME), probability-weighted moment estimation (PWME) is used to estimate the parameters of the distribution function. The specific formulas are presented. Through Monte Carlo simulation with sample sizes 10, 20, 50, 100, 1 000, it is concluded that PWME is an efficient method and it behaves steadily. The mean square errors (MSE) of estimators by PWME are much smaller than those of estimators by CME, and there is no significant difference between PWME and MLE. Finally, an example of foreign exchange rate is given. For Dollar/Pound exchange rates from 1990-01-02 to 2006-12-29, this paper formulates the distribution function of the largest loss among the investment losses exceeding a certain threshold by Poisson-GP compound extreme value distribution, and obtains predictive values at different confidence levels.

Quasi-Negative Binomial: Properties, Parametric Estimation, Regression Model and Application to RNA-SEQ Data

Background: The Poisson and the Negative Binomial distributions are commonly used to model count data. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial has a variance larger than the mean and therefore both models are appropriate to model over-dispersed count data. Objectives: A new two-parameter probability distribution called the Quasi-Negative Binomial Distribution (QNBD) is being studied in this paper, generalizing the well-known negative binomial distribution. This model turns out to be quite flexible for analyzing count data. Our main objectives are to estimate the parameters of the proposed distribution and to discuss its applicability to genetics data. As an application, we demonstrate that the QNBD regression representation is utilized to model genomics data sets. Results: The new distribution is shown to provide a good fit with respect to the “Akaike Information Criterion”, AIC, considered a measure of model goodness of fit. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling count data exhibiting overdispersion, arising in various fields of scientific investigation such as genomics and biomedicine.

Statistical Analysis for the Birnbaum-Saunders Fatigue Life Distribution under Type-Ⅱ Bilateral Censoring and Multiply Type-II Censoring

In present paper, we obtain the inverse moment estimations of parameters of the Birnbaum-Saunders fatigue life distribution based on Type-Ⅱ bilateral censored samples and multiply Type-Ⅱ censored sample. In this paper, we also get the interval estimations of the scale parameters.

BAS-ADAM:An ADAM Based Approach to Improve the Performance of Beetle Antennae Search Optimizer

In this paper,we propose enhancements to Beetle Antennae search(BAS)algorithm,called BAS-ADAIVL to smoothen the convergence behavior and avoid trapping in localminima for a highly noin-convex objective function.We achieve this by adaptively adjusting the step-size in each iteration using the adaptive moment estimation(ADAM)update rule.The proposed algorithm also increases the convergence rate in a narrow valley.A key feature of the ADAM update rule is the ability to adjust the step-size for each dimension separately instead of using the same step-size.Since ADAM is traditionally used with gradient-based optimization algorithms,therefore we first propose a gradient estimation model without the need to differentiate the objective function.Resultantly,it demonstrates excellent performance and fast convergence rate in searching for the optimum of noin-convex functions.The efficiency of the proposed algorithm was tested on three different benchmark problems,including the training of a high-dimensional neural network.The performance is compared with particle swarm optimizer(PSO)and the original BAS algorithm.

The mechanism and heterogeneity of environmental regulations'impact on the technological progress of dairy farming

The study analyses the theoretical mechanism through which environmental regulation affects the dairy industry’s technological progress,with a particular focus on how the effect is conditional on farm size.Using the input–output data of dairy farms of different sizes from 2009 to 2019 in 10 Chinese provinces/autonomous regions in China and the quantitative measurement index of environmental regulation,the study estimates environmental regulation’s heterogeneous influences on the dairy industry’s technological progress by dynamic panel data models.The empirical results suggest that,first,environmental regulation has a U-type influence on the technological progress of dairy farming.The U-type influence means moving from pollution control’s high cost and low technology progress to the high profit and high innovation input generated by optimizing the breeding structure.Second,the promotion of dairy farming technology depends on farm size.The effect of environmental regulation on technological progress in moderately large-farms showed a U-type relationship.In contrast,the effect in free-range and large-size dairy farms showed a linear and positive relationship.The government should further strengthen environmental regulation based on advancing moderately large-farms in compliance with market mechanisms in the long run.Particular attention should be paid to the forms of environmental regulation so that dairy cattle breeding technology can break through the inflection point of the“U”curve as soon as possible and ensure the significance of the rising stage.Along the way,technical support should be provided for realizing environmental protection and economic growth.

Modeling Liver Cancer and Leukemia Data Using Arcsine-Gaussian Distribution

The main objective of this paper is to discuss a general family of distributions generated from the symmetrical arcsine distribution.The considered family includes various asymmetrical and symmetrical probability distributions as special cases.A particular case of a symmetrical probability distribution from this family is the Arcsine–Gaussian distribution.Key statistical properties of this distribution including quantile,mean residual life,order statistics and moments are derived.The Arcsine–Gaussian parameters are estimated using two classical estimation methods called moments and maximum likelihood methods.A simulation study which provides asymptotic distribution of all considered point estimators,90%and 95%asymptotic confidence intervals are performed to examine the estimation efficiency of the considered methods numerically.The simulation results show that both biases and variances of the estimators tend to zero as the sample size increases,i.e.,the estimators are asymptotically consistent.Also,when the sample size increases the coverage probabilities of the confidence intervals increase to the nominal levels,while the corresponding length decrease and approach zero.Two real data sets from the medicine filed are used to illustrate the flexibility of the Arcsine–Gaussian distribution as compared with the normal,logistic,and Cauchy models.The proposed distribution is very versatile to fit real applications and can be used as a good alternative to the traditional gaussian distribution.

Research on Ruin Probability of Risk Model Based on AR(1)Time Series

The insurance industry typically exploits ruin theory on collected data to gain more profits.However,state-of-art approaches fail to consider the dependency of the intensity of claim numbers,resulting in the loss of accuracy.In this work,we establish a new risk model based on traditional AR(1)time series,and propose a fine-gained insurance model which has a dependent data structure.We leverage Newton iteration method to figure out the adjustment coefficient and evaluate the exponential upper bound of the ruin probability.We claim that our model significantly improves the precision of insurance model and explores an interesting direction for future research.

Degree-Based Moment Estimation for Ordered Networks

The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations(e.g., the measurement of the relationship between people from worst to best in social networks). In this paper, the authors study the asymptotic property of the moment estimator based on the degrees of vertices in ordered networks whose edges are ordered random variables. In particular, the authors establish the uniform consistency and the asymptotic normality of the moment estimator when the number of parameters goes to infinity. Simulations and a real data example are provided to illustrate asymptotic results.

A Class of Stochastic Diferential Equations with the Time Average

Stochastic diferential equations with the time average have received increasing attentions in recent years since they can ofer better explanations for some fnancial models.Since the time average is involved in this class of stochastic diferential equations,in this paper,the linear growth condition and the Lipschitz condition are diferent from the classical conditions.Under the special linear growth condition and the special Lipschitz condition,this paper establishes the existence and uniqueness of the solution.By using the Lyapunov function,this paper also establishes the existence and uniqueness under the local Lipschitz condition and gives the p-th moment estimate.Finally,a scalar example is given to illustrate the applications of our results.

Correlated squared returns

Joint densities for a sequential pair of returns with weak autocorrelation and strong correlation in squared returns are formulated.The marginal return densities are either variance gamma or bilateral gamma.Two-dimensional matching of empirical characteristic functions to its theoretical counterpart is employed for dependency parameter estimation.Estimations are reported for 3920 daily return sequences of one thousand days.Path simulation is done using conditional distribution functions.The paths display levels of squared return correlation and decay rates for the squared return autocorrelation function that are comparable to these magnitudes in daily return data.Regressions of log characteristic functions at different time points are used to estimate time scaling coefficients.Regressions of these time scaling coefficients on squared return correlations support the view that autocorrelation in squared returns slows the rate of passage of economic time.An analysis of financial markets for 2020 in comparison with 2019 displays a post-COVID slowdown in financial markets.