forecasting cause age specific mortality using two random processes mortality forecasts are critical information for assessing the health of a population and are necessary for making informed decisions about how best to direct health related resources and activities timeliness in making health statistics available is crucial to identify and address current health problems being motivated to meet these needs we propose a method to forecast the number of cause age specific deaths through a two random processes model unlike the previous methods the new method incorporates both cross sectional and longitudinal correlations into our model without a high dimensional problem a bootstrap confidence interval is presented to measure the validity of our model and to detect an unusual occurrence of deaths our data analysis demonstrates that our method gives promising results compared with the true final counts

regression analysis for a functional response functional responses are encountered when units are observed over time although the whole function itself is not observed a sufficiently large number of evaluations as is common with modern recording equipment are assumed to be available functional regression analysis relates the smooth functional response y t to known covariates x by a linear combination of parameter functions t which are to be estimated the model takes the standard form y t x t t t this approach provides an alternative to standard longitudinal data methods used in the biological sciences where less and noisier data necessitate parametric modeling the methodology is illustrated by an application in ergonomics

degree based entropies of networks revisited studies on the information content of graphs and networks have been initiated in the late fifties based on the seminal work due to shannon and rashevsky various graph parameters have been used for the construction of entropy based measures to characterize the structure of complex networks based on shannon s entropy in cao et al extremality of degree based graph entropies inform sci 278 2014 22 33 we studied graph entropies which are based on vertex degrees by using so called information functionals as a matter of fact there has been very little work to find their extremal values when considered shannon entropy based graph measures we pursue with this line of research by proving further extremal properties of the degree based graph entropies

on the zeros of the partial hosoya polynomial of graphs abstract the partial hosoya polynomial or briefly the partial h polynomial can be used to construct the well known hosoya polynomial the ith coefficient of this polynomial defined for an arbitrary vertex u of a graph g is the number of vertices at distance i from u the aim of this paper is to determine the partial h polynomial of several well known graphs and then to investigate the location of their zeros to pursue we characterize the structure of graphs with the minimum and the maximum modulus of the zeros of partial h polynomial finally we define another graph polynomial of the partial h polynomial see 9 also we determine the unique positive root of this polynomial for particular graphs

modeling hazard rates as functional data for the analysis of cohort lifetables and mortality forecasting as world populations age the analysis of demographic mortality data and demographic predictions of future mortality have met with increasing interest the study of mortality patterns and the forecasting of future mortality with its associated impacts on social welfare health care and societal planning has become a more pressing issue an ideal set of data to study patterns of change in long term mortality is the well known historical swedish cohort mortality data because of its high quality and long span of more than two centuries we explore the use of functional data analysis to model these data and to derive mortality forecasts specifically we address the challenge of flexibly modeling these data while including the effect of the birth year by regarding log hazard functions derived from observed cohort lifetables as random functions a functional model for the analysis of these cohort log hazard functions extending functional principal component approaches by introducing time varying eigenfunc

properties of principal component methods for functional and longitudinal data analysis the use of principal component methods to analyze functional data is appropriate in a wide range of different settings in studies of functional data analysis it has often been assumed that a sample of random functions is observed precisely in the continuum and without noise while this has been the traditional setting for functional data analysis in the context of longitudinal data analysis a random function typically represents a patient or subject who is observed at only a small number of randomly distributed points with nonnegligible measurement error nevertheless essentially the same methods can be used in both these cases as well as in the vast number of settings that lie between them how is performance affected by the sampling plan in this paper we answer that question we show that if there is a sample of n functions or subjects then estimation of eigenvalues is a semiparametric problem with root n consistent estimators even if only a few observations are made of each function and if each observation is encumbered by noise however estimation of eigenfunctions becomes a nonparametric problem when observations are sparse the optimal convergence rates in this case are those which pertain to more familiar function estimation settings we also describe the effects of sampling at regularly spaced points as opposed to random points in particular it is shown that there are often advantages in sampling randomly however even in the case of noisy data there is a threshold sampling rate depending on the number of functions treated above which the rate of sampling either randomly or regularly has negligible impact on estimator performance no matter whether eigenfunctions or eigenvectors are being estimated

understanding exponential smoothing via kernel regression exponential smoothing is the most common model free means of forecasting a future realization of a time series it requires the specification of a smoothing factor which is usually chosen from the data to minimize the average squared residual of previous one step ahead forecasts in this paper we show that exponential smoothing can be put into a nonparametric regression framework and gain some interesting insights into its performance through this interpretation we also use theoretical developments from the kernel regression field to derive for the first time asymptotic properties of exponential smoothing forecasters

the weight distribution of cosets sullivan s 1967 inequality between the weight distribution function of a binary linear code and the weight distribution function of a proper subset of the code is generalized to linear codes over arbitrary finite fields

nonparametric regression analysis of longitudinal data abstract nonparametric methods are developed for estimating the dose effect when a response consists of correlated observations over time measured in a dose response experiment the methods can also be applied to data collected from a completely randomized design experiment methods are developed for the detection and description of the effects of dose time and their interaction the methods allow for individual variation in the timing and number of observations a generalization allowing baseline covariates to be incorporated is addressed these results may be used in an exploratory fashion in the process of building a random effects model for longitudinal data

modeling and forecasting u s mortality abstract time series methods are used to make long run forecasts with confidence intervals of age specific mortality in the united states from 1990 to 2065 first the logs of the age specific death rates are modeled as a linear function of an unobserved period specific intensity index with parameters depending on age this model is fit to the matrix of u s death rates 1933 to 1987 using the singular value decomposition svd method it accounts for almost all the variance over time in age specific death rates as a group whereas e 0 has risen at a decreasing rate over the century and has decreasing variability k t declines at a roughly constant rate and has roughly constant variability facilitating forecasting k t which indexes the intensity of mortality is next modeled as a time series specifically a random walk with drift and forecast the method performs very well on within sample forecasts and the forecasts are insensitive to reductions in the length of the base period from 90 to 30

graph distance measures based on topological indices revisited graph distance measures based on topological indices have been already explored by dehmer et al also inequalities for those graph distance measures have been proved in this paper we continue studying such comparative graph measures based on the well known wiener index graph energy and randic index respectively we prove extremal properties of the graph distance measures for some special classes of graphs to demonstrate useful properties of the measures we also discuss numerical results to conclude the paper we state some open problems

analysis of oldest old mortality lifetables revisited ing the hazard function we provide rigorous asymptotic results for the smoothing of lifetables and show that the transformation approach is supported by both asymptotic and simulation results we also demonstrate how the information contained in many samples of lifetables as typically obtained in aging experiments can be summarized in a twodimensional hazard surface

from lifetables to hazard rates the transformation approach summary we address the problem of estimating hazard rates from lifetable data the central issue is a discretisation bias which is caused by the aggregation of lifetimes which occurs in lifetable data smoothing raw mortalities directly derived from lifetable data leads to severe biases whenever the true hazard rate is large we propose here a new transformation of smoothed lifetable data which is superior to previous approaches this is demonstrated by means of large sample arguments and a simulation study in which several recent approaches are compared we demonstrate the application of the proposed methods to assess the mortality of medflies

functional quasi likelihood regression models with smooth random effects summary we propose a class of semiparametric functional regression models to describe the influence of vector valued covariates on a sample of response curves each observed curve is viewed as the realization of a random process composed of an overall mean function and random components the finite dimensional covariates influence the random components of the eigenfunction expansion through single index models that include unknown smooth link and variance functions the parametric components of the single index models are estimated via quasi score estimating equations with link and variance functions being estimated nonparametrically we obtain several basic asymptotic results the functional regression models proposed are illustrated with the analysis of a data set consisting of egg laying curves for 1000 female mediterranean fruit flies medflies

a history of graph entropy measures this survey seeks to describe methods for measuring the entropy of graphs and to demonstrate the wide applicability of entropy measures setting the scene with a review of classical measures for determining the structural information content of graphs we discuss graph entropy measures which play an important role in a variety of problem areas including biology chemistry and sociology in addition we examine relationships between selected entropy measures illustrating differences quantitatively with concrete examples

an accelerated time model for response curves abstract we propose a nonparametric method of data analysis for situations where the data consist of a sample of curves and a covariate is present we assume the observed curves to be time accelerated versions of a basic underlying stochastic process and assume the time acceleration factor for each observed process determining the eigenzeit to be a smooth function of the covariate we discuss an iterative procedure to estimate the components of the model nonparametrically using cross validation to determine smoothing parameters using a leave one curve out technique our example concerns time courses of mortality for a sample of cohorts of fruit flies

inference for density families using functional principal component analysis we consider t 1 t samples of iid observations x1t xntt from unknown population densities ft to characterize differences and similarities of ft we assume their expansions into the first l principal components from the given observations xit we study inference on the components and on their required number l a detailed asymptotic theory is presented our method is applied in the analysis of yearly cross sectional samples of british households interpretation of the estimated principal components and their scores provides new insights into the evolution and interplay of household income and age distributions from 1968 1988 from estimating their required numbersl we draw conclusions on the dimensionality of mixture models for describing the densities

hosoya entropy of fullerene graphs abstract entropy based methods are useful tools for investigating various problems in mathematical chemistry computational physics and pattern recognition in this paper we introduce a general framework for applying shannon entropy to fullerene graphs and used it to investigate their properties we show that important physical properties of these molecules can be determined by applying hosoya entropy to their corresponding graphs

network entropies based on independent sets and matchings entropy based measures have been used to characterize the structure of complex networks various graph entropies based on different graph parameters have been proposed and studied so it has been intricate to decide which measure is the right one for solving a particular problem in this paper we introduce graph entropy measures based on independent sets and matchings of graphs the values of entropies of some special graphs are calculated and we draw several conclusions regrading the usability of the measures based on our findings we conclude that it should be demanding studying extremal values of the novel entropies