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The lasso and elastic net methods are the popular technique for parameter estimation and variable selection. Moreover, the adaptive lasso and elastic net methods use the adaptive weights on the penalty function based on the lasso and elastic net estimates. The adaptive weight is related to the power order of the estimator. Normally, these methods focus to estimate parameters in terms of linear regression models that are based on the dependent variable and independent variable as a continuous scale. In this paper, we compare the lasso and elastic net methods and the higher-order of the adaptive lasso and adaptive elastic net methods for classification on high dimensional data. The classification is used to classify the categorical data for dependent variable dependent on the independent variables, which is called the logistic regression model. The categorical data are considered a binary variable, and the independent variables are used as the continuous variable. The high dimensional data are represented when the number of independent variables is higher than the sample sizes. For this research, the simulation of the logistic regression is considered as the binary dependent variable and 20, 30, 40, and 50 as the independent variables when the sample sizes are less than the number of the independent variables. The independent variables are generated from normal distribution on several variances, and the dependent variables are obtained from the probability of logit function and transforming it to predict the binary data. For application in real data, we express the classification of the type of leukemia as the dependent variables and the subset of gene expression as the independent variables. The criterion of these methods is to compare by the average percentage of predicted accuracy value. The results are found that the higher-order of adaptive lasso method is satisfied with large dispersion, but the higher-order of adaptive elastic net method outperforms on small dispersion. [ABSTRACT FROM AUTHOR]

We consider the problem of the first passage time T of an inhomogeneous geometric Brownian motion through a constant threshold, for which only limited results are available in the literature. In the case of a strong positive drift, we get an approximation of the cumulants of T of any order using the algebra of formal power series applied to an asymptotic expansion of its Laplace transform. The interest in the cumulants is due to their connection with moments and the accounting of some statistical properties of the density of T like skewness and kurtosis. Some case studies coming from neuronal modeling with reversal potential and mean reversion models of financial markets show the goodness of the approximation of the first moment of T. However hints on the evaluation of higher order moments are also given, together with considerations on the numerical performance of the method. [ABSTRACT FROM AUTHOR]

A complex multi-state redundant system with preventive maintenance subject to multiple events is considered. The online unit can undergo several types of failure: both internal and those provoked by external shocks. Multiple degradation levels are assumed as both internal and external. Degradation levels are observed by random inspections and, if they are major, the unit goes to a repair facility where preventive maintenance is carried out. This repair facility is composed of a single repairperson governed by a multiple vacation policy. This policy is set up according to the operational number of units. Two types of task can be performed by the repairperson, corrective repair and preventive maintenance. The times embedded in the system are phase type distributed and the model is built by using Markovian Arrival Processes with marked arrivals. Multiple performance measures besides the transient and stationary distribution are worked out through matrix-analytic methods. This methodology enables us to express the main results and the global development in a matrix-algorithmic form. To optimize the model, costs and rewards are included. A numerical example shows the versatility of the model. [ABSTRACT FROM AUTHOR]

The homogeneous branching process with migration and continuous time is considered. We investigated the distribution of the period-life τ , i.e., the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time. The probability generating function of the random process, which describes the behavior of the process within the period-life, was obtained. The boundary theorem for the period-life of the subcritical or critical branching process with migration was found. [ABSTRACT FROM AUTHOR]

In this paper, we mainly investigate the weak convergence analysis about the error terms which are determined by the discretization for solving the stochastic differential equation (SDE, for short) in forward-backward stochastic differential equations (FBSDEs, for short), which is on the basis of Itô Taylor expansion, the numerical SDE theory, and numerical FBSDEs theory. Under the weak convergence analysis of FBSDEs, we further establish better error estimates of recent numerical schemes for solving FBSDEs. [ABSTRACT FROM AUTHOR]

The asymptotic behaviour of the tail expectation E (S n ξ) α { S n ξ > x } is investigated, where exponent α is a nonnegative real number and S n ξ = ξ 1 + ... + ξ n is a sum of dominatedly varying and not necessarily identically distributed random summands, following a specific dependence structure. It turns out that the tail expectation of such a sum can be asymptotically bounded from above and below by the sums of expectations E ξ i α { ξ i > x } with correcting constants. The obtained results are extended to the case of randomly weighted sums, where collections of random weights and primary random variables are independent. For illustration of the results obtained, some particular examples are given, where dependence between random variables is modelled in copulas framework. [ABSTRACT FROM AUTHOR]

This paper introduces a fuel-switching price to the Alberta market, which is designed for encouraging power plant companies to switch from coal to natural gas when they produce electricity; this has been successfully applied to the European market. Moreover, we consider an energy-switching price which considers power switch from natural gas to wind. We modeled these two prices using five mean reverting processes including a Regime-switching processes, Lévy-driven Ornstein–Uhlenbeck process and Inhomogeneous Geometric Brownian Motion, and estimate them based on multiple procedures such as Maximum likelihood estimation and Expectation-Maximization algorithm. Finally, this paper proves previous results applied to the Albertan Market where the jump modeling technique is needed when modeling fuel-switching data. In addition, it not only gives promising conclusions on the necessity of introducing Regime-switching models to the fuel-switching data, but also shows that the Regime-switching model is better fitted to the data. [ABSTRACT FROM AUTHOR]

In this paper, we computed general interval indicators of availability and reliability for systems modelled by time non-homogeneous semi-Markov chains. First, we considered duration-dependent extensions of the Interval Reliability and then, we determined an explicit formula for the availability with a given window and containing a given point. To make the computation of the window availability, an explicit formula was derived involving duration-dependent transition probabilities and the interval reliability function. Both interval reliability and availability functions were evaluated considering the local behavior of the system through the recurrence time processes. The results are illustrated through a numerical example. They show that the considered indicators can describe the duration effects and the age of the multi-state system and be useful in real-life problems. [ABSTRACT FROM AUTHOR]

We consider a Metropolis–Hastings method with proposal N (x , h G (x) − 1) , where x is the current state, and study its ergodicity properties. We show that suitable choices of G (x) can change these ergodicity properties compared to the Random Walk Metropolis case N (x , h Σ) , either for better or worse. We find that if the proposal variance is allowed to grow unboundedly in the tails of the distribution then geometric ergodicity can be established when the target distribution for the algorithm has tails that are heavier than exponential, in contrast to the Random Walk Metropolis case, but that the growth rate must be carefully controlled to prevent the rejection rate approaching unity. We also illustrate that a judicious choice of G (x) can result in a geometrically ergodic chain when probability concentrates on an ever narrower ridge in the tails, something that is again not true for the Random Walk Metropolis. [ABSTRACT FROM AUTHOR]