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The aim of this paper is to provide a selected advanced review on semiparametric regression which is an emergent promising field of researches in functional data analysis. As a deliberate strategy, we decided to focus our discussion on the single functional index regression (SFIR) model in order to fix the ideas about the stakes linked with infinite dimensional problems and about the methodological challenges that one has to solve when building statistical procedure: one of the most challenging issue being the question of dimensionality effects reduction. This will be the first (and the main) part of this discussion and a complete survey of the literature on SFIR model will be presented. In a second attempt, other semiparametric models (and more generally, other dimension reduction models) will be shortly discussed with the double goal of presenting the state of art and of defining challenging tracks for the future. At the end, we will discuss how additive modeling is an appealing idea for more complicated models involving multifunctional predictors and some tracks for the future will be pointed in this setting. This article is categorized under:Statistical Models > Semiparametric ModelsData: Types and Structure > Time Series, Stochastic Processes, and Functional DataStatistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods [ABSTRACT FROM AUTHOR]

In this paper, we study the Gerber–Shiu (G-S) function for the classical risk model, in which the discount rate is generalized from a constant to a random variable. The discounted interest force accumulated process is modeled by a Poisson process and a Gaussian process for the G-S function. In terms of the standard techniques in ruin theory, we derive the integro-differential equation and the defective renewal equation satisfied by the G-S function. Then, the asymptotic formula for the G-S function is obtained using the renewal theory. [ABSTRACT FROM PUBLISHER]

This article defines a new measure of central tendency (called the "iteratile") by iterating a function which maps a triple of data into a triple of the median, mean, and trimean (sorted). An explicit formula is given with proof, along with brief discussion of potential applications. [ABSTRACT FROM AUTHOR]

This paper deals with the steady-state behavior of an M/G/1 queue with two types of general heterogeneous service to the arriving customers and Bernoulli feedback. We first derive the steady-state probability generating functions for the queue size distributions at a random epoch as well as at a departure epoch. Next, we derive the mean queue size at random epoch and the mean waiting time. Also, we obtain the mean busy period of this model and discuss some important particular cases. [ABSTRACT FROM AUTHOR]

The problem of optimal estimation of the linear functional Aξ = Σk=0∞ a(k)ξ(-k) depending on the unknown values of a stochastic sequence ξ(m) with nth stationary increments from observations of the sequence ξ(m) + η(m) at points m = 0,-1,-2,..., where ξ(m) is a stationary sequence uncorrelated with η(m), is considered. Formulas for calculating the mean square error and the spectral characteristic of the optimal linear estimate of the functional are derived in the case where spectral densities of stochastic sequences are exactly known and admit the canonical factorizations. In the case of spectral uncertainty, where spectral densities are not known exactly, but sets of admissible spectral densities are specified, the minimax-robust method is applied. Formulas and relations that determine the least favourable spectral densities and the minimax-robust spectral characteristics are proposed for the given sets of admissible spectral densities. The filtering problem for a class of cointegrated sequences is investigated. [ABSTRACT FROM AUTHOR]

Optimal design of experiment for logistic models has been examined and applied in a wide range of applications. The optimality of the designs is mostly determined by using general equivalence theorem with no attention paid to the extent at which the design can be useful for determining the predictive capability of the model. This paper addressed the predictive capability of optimal design model for two variable quadratic logistic regression model through prediction error variance(PEV). The PEV is a useful way to determining the predictive capability of a model in optimal design. The study used some initial guess parameters to represent any position of parameter in the design space through a simulation study of 10000 experimental runs. The design was optimal when the PEV value is less than one at nine equally weighted support points. The result of the analysis was able to identify the design that is good for prediction among all the designs obtained and conclude that prediction error variance should be used to test the stability of optimal design of experiment for two variable quadratic logistic models. [ABSTRACT FROM AUTHOR]

The quest to generate distributions with more desirable and flexible properties for the modeling of data has led to an intense focus on the development of new families that are generalizations of existing distributions by researchers. A new family of distributions called the chen generated family is developed in this study. Its statistical properties such as the quantile, moments, incomplete moments, stochastic ordering and order statistics are derived by using the method of maximum likelihood, estimators for the parameters of the new family are developed. Three special distributions, Chen Burr III, Chen Kumaraswamy and Chen Weibull, are proposed from the new family, though it can generalize other distributions. A demonstration of the usefulness of the new family is performed using real dataset. [ABSTRACT FROM AUTHOR]