Machine Learning Vasicek Model Calibration with Gaussian Processes

In this article, we calibrate the Vasicek interest rate model under the risk neutral measure by learning the model parameters using Gaussian processes for machine learning regression. The calibration is done by maximizing the likelihood of zero coupon bond log prices, using mean and covariance functions computed analytically, as well as likelihood derivatives with respect to the parameters. The maximization method used is the conjugate gradients. The only prices needed for calibration are zero coupon bond prices and the parameters are directly obtained in the arbitrage free risk neutral measure.     

Prediction intervals for farima processes by bootstrap methods

In this paper we introduce a procedure to compute prediction intervals for FARIMA (p d q) processes, taking into account the variability due to model identification and parameter estimation. To this aim, a particular bootstrap technique is developed. The performance of the prediction intervals is then assessed and compared to that of stand­ard bootstrap percentile intervals. The methods are applied to the time series of Nile River annual minima.     

Estimation for a first-order bifurcating autoregressive process with heavy-tail innovations

Asymptotics of an alternative extreme-value estimator for the autocorrelation parameter in a first-order bifurcating autoregressive (BAR) process with non-gaussian innovations are derived. This contrasts with traditional estimators whose asymptotic behavior depends on the central part of the innovation distribution. Within any BAR model, the main concern is addressing the complex dependency between generations. The inability of traditional methods to handle this dependency motivated an alternative procedure. With the combination of an extreme-value approach and a clever blocking argument, the dependency issue within the BAR process was resolved, which in turn allowed us to derive the limiting distribution for the proposed estimator through the use of regular variation and non-stationary point processes. Finally, the implications of our extreme-value approach are discussed with an extensive simulation study that not only assesses the reliability of our proposed estimate but also presents the findings for a new estimator of an unknown location parameter θ and its implications.     

1906-1908年的郑孝胥与预备立宪公会

考虑到我国未来年度的OD分布预测中的路网构成变化、区域经济布局变动、区域经济增长速度差异等一些具有时变性和特殊性因素，采用在“四阶段法”运量预测基础上改进而成的“三阶段法”进行高速铁路短期客运量预测。首先采用组合预测模型进行趋势运量预测，然后采用多元LOGIT模型进行方式分担，最后采用弹性系数诱增模型进行诱增运量预测。以京沪高铁为例，采用“三阶段法”预测了2014年和2015年京沪高铁本线及跨线单向客流量。     

基于学分绩点与综合素质测评的换算模型建立

学生综合素质测评体系的完善对有效实施大学生综合素质测评工作以及指导大学生健康发展有重要意义,其中,学生综合素质测评体系的关键在于学分绩点与综合素质测评的换算模型的转化。通过分析高校现行学分绩点测评公式,发现其存在的主要缺陷是转化公式不满足统计学原理,并指出学分绩点测评的换算公式应建立在对特定学生群体特征参数群数值分析的基础上。以西南石油大学某专业学生某学年的成绩分布数据进行验证,采取统计原理、常数变异法和不动点原理进行建模,利用求导方法对学分绩点测评中的特征参数群进行层次划分,然后对每段划分积分,通过归一化来确定变异项,得出新的换算模型。结果表明新模型能更好地反映学生的学习成绩在综合素质测评中的地位。     

Sums of powers of binomial coefficients

An asymptotic series for sums of powers of binomial coefficients is derived, the general term being defined and usable with a computer symbolic language. Sums of squares of coefficients in the symmetric case are shown to have a link with classical moment problems, but this property breaks down for cubes and higher powers. Problems of remainders for the asymptotic series are mentioned. Using the reflection formula for I'(.), a continuous form for a binomial function is set up, and this becomes oscillatory outstde the usual range. A new contmued fraction emerges for the logarithm of an adjusted sum of binomial squares. The note is a contribution to the problem of the interpretation of asymptotic series and processes for their convergence acceleration.     

On characterizing the normal and poisson distributions

Multivariate normal, correlated multivariate Poisson and multiple Poisson distributions are characterized, in the class of exponential-type distributions, by the properties of the linear combinations of the variables, the properties of their cumulants and the recurance relation between the cumulants.     

Sequential estimation problems for negative exponential populations

The literature on sequential estimation problems for negative exponential populations has been reviewed here, We attempt to bring in all the published and unpublished materials known to us in a fairly coherent fashion. Both the concepts and theoretical findings are discussed.     

Simulations of Some Doubly Stochastic Poisson Point Processes

Computer simulations of point processes are important either to verify the results of certain theoretical calculations that can be very awkward at times or to obtain practical results when these calculations become almost impossible. One of the most common methods for the simulation of nonstationary Poisson processes is random thinning. Its extension when the intensity becomes random (doubly stochastic Poisson processes) depends on the structure of this intensity. If the random density takes only discrete values, which is a common situation in many physical problems where quantum mechanics introduces discrete states, it is shown that the thinning method can be applied without error. We study in particular the case of binary density and present the kind of theoretical calculations that then become possible. The results of various experiments realized with data obtained by simulation show a fairly good agreement with the theoretical calculations.     

The economic design of multivariate binomial EWMA VSSI control charts

Since multi-attribute control charts have received little attention compared with multivariate variable control charts, this research is concerned with developing a new methodology to employ the multivariate exponentially weighted moving average (MEWMA) charts for m-attribute binomial processes; the attributes being the number of nonconforming items. Moreover, since the variable sample size and sampling interval (VSSI) MEWMA charts detect small process mean shifts faster than the traditional MEWMA, an economic design of the VSSI MEWMA chart is proposed to obtain the optimum design parameters of the chart. The sample size, the sampling interval, and the warning/action limit coefficients are obtained using a genetic algorithm such that the expected total cost per hour is minimized. At the end, a sensitivity analysis has been carried out to investigate the effects of the cost and the model parameters on the solution of the economic design of the VSSI MEWMA chart.