First-passage densities of controlled Gaussian processes

Whittle has proved a theorem that gives the optimal control of Gaussian processes in terms of the mathematical expectation of a function of the time and the place where the uncontrolled processes hit the boundary of the stopping region for the first time. In this paper we obtain formulae for the joint probability density function of the first hitting time and place and, in the time-invariant case, for the moment generating function of the first exit time of the optimally controlled processes. Two particular one-dimensional cases are considered.     

Analysis of Panel Count Data with Dependent Observation Times

In this article, a semiparametric approach is proposed for the regression analysis of panel count data. Panel count data commonly arise in clinical trials and demographical studies where the response variable is the number of multiple recurrences of the event of interest and observation times are not fixed, varying from subject to subject. It is assumed that two processes exist in this data: the first is for a recurrent event and the second is for observation time. Many studies have been done to estimate mean function and regression parameters under the independency between recurrent event process and observation time process. In this article, the same statistical inference is studied, but the situation where these two processes may be related is also considered. The mixed Poisson process is applied for the recurrent event processes, and a frailty intensity function for the observation time is also used, respectively. Simulation studies are conducted to study the performance of the suggested methods. The bladder tumor data are applied to compare previous studie' results.     

中国农村贫困变动：1981—2005 —基于不同贫困线标准和指数的对比分析

 本文以中国官方贫困线和世界银行公布的国际贫困线为标准,利用中国农村家庭的收入分配分组数据,测算了1980年以来的四种贫困指数。研究发现,虽然农村贫困状况总体上呈下降趋势,但基于不同贫困线标准衡量的贫困程度相差悬殊,这使农村反贫困政策的制定和调整变得更加复杂;脱贫时间指数的构成中,由于不平等所延长的脱贫时间,相对而言明显提高,这说明收入分配的恶化已经成为反贫困的严重障碍,这种变化趋势值得高度关注。     

Asymptotic expansions and the reliability of tests in accelerated failure time models

This paper gives matrix formilae for the O(n^-1 ) cerrecti0n applicable to asymptotically efficient conditional moment tests. These formulae only require expectations of functions involving, at most, second order derivatives of the log-likelihood; unlike those previously providcd by Ferrari and Corddro(1994). The correction is used to assess the reliability of first order asymptotic theory for arbitrary residual-based diagnostics in a class of accelerated failure time models: this correction is always parameter free, depending only on the number of included covariates in the regression design. For all but one of the tests considered, first order theory is found to be extremely unreliable, even in quite large samples, although this may not be widely appreciated by applied workers.     

Gaussian models for degradation processes-part I: Methods for the analysis of biomarker data

We present two stochastic models that describe the relationship between biomarker process values at random time points, event times, and a vector of covariates. In both models the biomarker processes are degradation processes that represent the decay of systems over time. In the first model the biomarker process is a Wiener process whose drift is a function of the covariate vector. In the second model the biomarker process is taken to be the difference between a stationary Gaussian process and a time drift whose drift parameter is a function of the covariates. For both models we present statistical methods for estimation of the regression coefficients. The first model is useful for predicting the residual time from study entry to the time a critical boundary is reached while the second model is useful for predicting the latency time from the infection until the time the presence of the infection is detected. We present our methods principally in the context of conducting inference in a population of HIV infected individuals.     

The generalized Poisson-binomial distribution and the computation of its distribution function

The Poisson-binomial distribution is useful in many applied problems in engineering, actuarial science and data mining. The Poisson-binomial distribution models the distribution of the sum of independent but non-identically distributed random indicators whose success probabilities vary. In this paper, we extend the Poisson-binomial distribution to a generalized Poisson-binomial (GPB) distribution. The GPB distribution corresponds to the case where the random indicators are replaced by two-point random variables, which can take two arbitrary values instead of 0 and 1 as in the case of random indicators. The GPB distribution has found applications in many areas such as voting theory, actuarial science, warranty prediction and probability theory. As the GPB distribution has not been studied in detail so far, we introduce this distribution first and then derive its theoretical properties. We develop an efficient algorithm for the computation of its distribution function, using the fast Fourier transform. We test the accuracy of the developed algorithm by comparing it with enumeration-based exact method and the results from the binomial distribution. We also study the computational time of the algorithm under various parameter settings. Finally, we discuss the factors affecting the computational efficiency of the proposed algorithm and illustrate the use of the software package.     

Some results on residual life and inactivity time at random time

In this article, we enhance the study of residual life at random time (RLRT) and inactivity time at random time (ITRT). To this aim, first we provide some stochastic orderings results among ITRT in two-sample problems when they failed at two different random times. Then, we develop some sufficient conditions which lead to the stochastic comparisons of RLRT and ITRT based on variance residual life order. The results are expected to be useful in reliability theory, forensic science, queue theory, and actuarial science.     

On the functional central limit theorem for first passage time of nonlinear semi-Markov reward processes

Abstract

In this article we examine the functional central limit theorem for the first passage time of reward processes defined over a finite state space semi-Markov process. In order to apply this process for a wider range of real-world applications, the reward functions, considered in this work, are assumed to have general forms instead of the constant rates reported in the other studies. We benefit from the martingale theory and Poisson equations to prove and establish the convergence of the first passage time of reward processes to a zero mean Brownian motion. Necessary conditions to derive the results presented in this article are the existence of variances for sojourn times in each state and second order integrability of reward functions with respect to the distribution of sojourn times. We finally verify the presented methodology through a numerical illustration.     

Discrete time cold standby repairable system: Combinatorial analysis

ABSTRACT

In this article, we obtain exact expression for the distribution of the time to failure of discrete time cold standby repairable system under the classical assumptions that both working time and repair time of components are geometric. Our method is based on alternative representation of lifetime as a waiting time random variable on a binary sequence, and combinatorial arguments. Such an exact expression for the time to failure distribution is new in the literature. Furthermore, we obtain the probability generating function and the first two moments of the lifetime random variable.     

Statistical methods for regular monitoring data

Summary.  Meteorological and environmental data that are collected at regular time intervals on a fixed monitoring network can be usefully studied combining ideas from multiple time series and spatial statistics, particularly when there are little or no missing data. This work investigates methods for modelling such data and ways of approximating the associated likelihood functions. Models for processes on the sphere crossed with time are emphasized, especially models that are not fully symmetric in space–time. Two approaches to obtaining such models are described. The first is to consider a rotated version of fully symmetric models for which we have explicit expressions for the covariance function. The second is based on a representation of space–time covariance functions that is spectral in just the time domain and is shown to lead to natural partially nonparametric asymmetric models on the sphere crossed with time. Various models are applied to a data set of daily winds at 11 sites in Ireland over 18 years. Spectral and space–time domain diagnostic procedures are used to assess the quality of the fits. The spectral-in-time modelling approach is shown to yield a good fit to many properties of the data and can be applied in a routine fashion relative to finding elaborate parametric models that describe the space–time dependences of the data about as well.     

A second-order fuzzy time series model for stock price analysis

It is difficult to model stock market because of its uncertainty. Many methods have been introduced to tackle these difficulties, in which fuzzy time series has shown its advantages in dealing with fuzzy and uncertainty data. In recent years, many researchers have applied the fuzzy time series to analyze and forecast the stock price, and how to improve the accuracy of forecasting has attracted many researchers. In this paper, the data are first preprocessed and a new way to divide the universe of discourse is given, after which the data are fuzzified applying the triangular membership function, then three-layer back propagation (BP) neural network is established. Finally, the generalized inverse fuzzy number formula is applied to defuzzify the relation obtained with the prediction results. The proposed method is applied to predict the stock price of State Bank of India (SBI) and Dow-Jones Industrial Average (DJIA). The experimental results show that the proposed method can greatly improve the accuracy of forecasting. Furthermore, the proposed method is not sensitive to its parameters.     

Estimating the intensity function of a power law process at the current time: time truncated case

The power law process, a nonhomogeneous Poisson process with intensity function µ(t) = (β/θ)(t/θ) , is frequently used to model the occurence of events in time. Often, an important quantity is the value of the intensity function at the current time, that is, the time when data collection is ceased. In this article, the problem of estimating this quantity is addressed when the data are time truncated, that is, when data collection is stopped at a predetermined time T. The class of multiples of the conditional MLE is suggested, and some members are analyzed. In addition, the class of estimators formed by first performing a preliminary test of significance on the parameter β is analyzed. Expressions for the bias and MSE of these estimators are derived and evaluated for several values of the parameters     

The multidimensional markov chain with prespecified asymptotic means,and (auto-)covariances

In this paper a method is presented to construct random time series which, starting from their present values, converge to stationary time series with a priori specified mean values, standard deviations, correlations and autocorrelations. The method is applied to simulate time series of price-inflation, wage-inflation, and interest rates, whose mean values, standard deviations, correlations and autocorrelations converge to the values which are estimated from historical data This application is a circular part of a Decision Support System which assists management of pension funds in analysing new methods of calculating pension premiums.     

The win ratio: Impact of censoring and follow‐up time and use with nonproportional hazards

The win ratio has been studied methodologically and applied in data analysis and in designing clinical trials. Researchers have pointed out that the results depend on follow‐up time and censoring time, which are sometimes used interchangeably. In this article, we distinguish between follow‐up time and censoring time, show theoretically the impact of censoring on the win ratio, and illustrate the impact of follow‐up time. We then point out that, if the treatment has long‐term benefit from a more important but less frequent endpoint (eg, death), the win ratio can show that benefit by following patients longer, avoiding masking by more frequent but less important outcomes, which occurs in conventional time‐to‐first‐event analyses. For the situation of nonproportional hazards, we demonstrate that the win ratio can be a good alternative to methods such as landmark survival rate, restricted mean survival time, and weighted log‐rank tests.     

The transition from university to work: a multilevel approach to the analysis of the time to obtain the first job

The aim of the paper is to characterize the factors that determine the transition from university to work as well as to evaluate the effectiveness of universities and course programmes with respect to the labour market outcomes of their graduates. The study is focused on the analysis of the time to obtain the first job, taking into account the graduates' characteristics and the effects pertaining to course programmes and universities. For this a three-level discrete time survival model is used, where the logit of the hazard—conditionally on the random effects at course programme and university level—is a linear function of the covariates. The analysis is accomplished by using a large data set from a survey on job opportunities for the 1992 Italian graduates.     

On the real representation of quaternion random variables

For the first time, the matrix-variate quaternion normal and quaternion Wishart distributions are derived from first principles, that is, from their real counterparts, exposing the relations between their respective densities and characteristic functions. Applications of this theory in hypothesis testing are presented, and the density function of Wilks’ statistic is derived for quaternion Wishart matrices.     

A class of mean residual life regression models with censored survival data

When describing a failure time distribution, the mean residual life is sometimes preferred to the survival or hazard rate. Regression analysis making use of the mean residual life function has recently drawn a great deal of attention. In this paper, a class of mean residual life regression models are proposed for censored data, and estimation procedures and a goodness-of-fit test are developed. Both asymptotic and finite sample properties of the proposed estimators are established, and the proposed methods are applied to a cancer data set from a clinic trial.     

A Method for Estimating Time Dependent Intervention Benefits under Arbitrarily Varying Age and Exogenous Components of Hazard

A method for estimating the dependence of intrinsic intervention benefits on time elapsed since the intervention took place is proposed. The method is aimed at intervention programs against diseases where one or all of the following components of hazard intensity may undergo important and unknown variations: 1) the intervention benefits to a subject are a function of the time elapsed since the intervention took place, or since inception for a continuing treatment, 2) the subjects vulnerability is an unknown function of their age, 3) the exogenous or environmental baseline intensity, to which all are assumed subjected, fluctuates arbitrarily with calendar time. During the time span of a study, these variables interact in a complex way, possibly masking the real contribution of the intervention. However, with very general assumptions about how hazard components interact, the cumulative hazards of subpopulations treated at different times in the past are shown to be described mathematically by a convolution of the time elapsed dependent intervention benefit function with the age and calendar time dependent baseline intensity. Starting from the cumulative hazards of untreated and treated subpopulations that had the intervention at different times in the past, a method of deconvolution through regularization is proposed to reconstruct the time elapsed dependence of the intervention benefit function. The regularization technique used is of the penalized least square smoothing type, it is applied to the solution of Volterra integral equations of the first kind under noisy inputs. Simulations, to test for the reconstruction of different modes of time elapsed variation of the intervention benefits, are carried out on realistically noisy data sets taken to be available at a limited number of time points. The stability of the estimated reconstructions, to measurement errors, is examined through repeated simulations with random noise added to inputs. The method is applied to a Brazilian data set where BCG vaccination resulted in a small reduction in the cumulated risk of leprosy infection.     

Availability analysis for general repairable systems with repair time threshold

Availability analysis is an important issue in many practical fields. This paper investigates the availability for general repairable systems with repair time threshold. Based on practical applications, a repair time threshold is introduced. If the period of a repair is less than a predefined time threshold, then the system may be considered as working during this period, i.e., the effect of the repair could be neglected. Otherwise, if the period of a repair is longer than the given threshold, then the system is considered as working from the beginning of the system failure until the repair time exceeding the threshold, i.e., the time point of the system down could be delayed. We consider both constant and random repair time threshold. This paper valuates the user-perceived availability, when the user does not experience any service interruption because the duration of repair is too short. The results can be applied in reliability engineering, queueing theory and many other fields. A numerical example for ventilator system is presented to demonstrate the application of the developed approach.     

First and Second Derivatives in Time Series Classification Using DTW

In our previous work, we developed a new distance function based on a derivative and showed that our algorithm is effective. In contrast to well-known measures from the literature, our approach considers the general shape of a time series rather than standard distance of function (value) comparison. The new distance was used in classification with the nearest neighbor rule. Now we improve on our previous technique by adding the second derivative. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on 47 time series datasets from a wide variety of application domains. Our experiments show that this new method provides a significantly more accurate classification on the examined datasets.