Efficient generation of random vectors by using the ratio-of-uniforms method with ellipsoidal envelopes

Stochastic simulation is widely used to validate procedures and provide guidance for both theoretical and practical problems. Random variate generation is the basis of stochastic simulation. Applying the ratio-of-uniforms method to generate random vectors requires the ability to generate points uniformly in a suitable region of the space. Starting from the observation that, for many multivariate distributions, the multidimensional objective region can be covered by a hyper-ellipsoid more tightly than by a hyper-rectangle, a new algorithm to generate from multivariate distributions is proposed. Due to the computational saving it can produce, this method becomes an appealing statistical tool to generate random vectors from families of standard and nonstandard multivariate distributions. It is particularly interesting to generate from densities known up to a multiplicative constant, for example, from those arising in Bayesian computation. The proposed method is applied and its efficiency is shown for some classes of distributions.     

A ratio-of-uniforms method for generating exponential power variates

A ratio-of-uniforms method of generating exponential power variates is presented. It is compared to an established generalized rejection method developed by Tadikamalla (1980) and shown to be faster and more easily implemented.     

Some computational aspects of the generalized von Mises distribution

This article deals with some important computational aspects of the generalized von Mises distribution in relation with parameter estimation, model selection and simulation. The generalized von Mises distribution provides a flexible model for circular data allowing for symmetry, asymmetry, unimodality and bimodality. For this model, we show the equivalence between the trigonometric method of moments and the maximum likelihood estimators, we give their asymptotic distribution, we provide bias-corrected estimators of the entropy, the Akaike information criterion and the measured entropy for model selection, and we implement the ratio-of-uniforms method of simulation.     

Sampling Methods for Wallenius' and Fisher's Noncentral Hypergeometric Distributions

Several methods for generating variates with univariate and multivariate Walleniu' and Fisher's noncentral hypergeometric distributions are developed. Methods for the univariate distributions include: simulation of urn experiments, inversion by binary search, inversion by chop-down search from the mode, ratio-of-uniforms rejection method, and rejection by sampling in the τ domain. Methods for the multivariate distributions include: simulation of urn experiments, conditional method, Gibbs sampling, and Metropolis-Hastings sampling. These methods are useful for Monte Carlo simulation of models of biased sampling and models of evolution and for calculating moments and quantiles of the distributions.     

Construction of more Flexible and Efficient P–rep Designs

Early generation variety trials are very important in plant and tree breeding programs. Typically many entries are tested, often with very few resources available. Unreplicated trials using control plots are popular and it is common to repeat the trials at a number of locations. An alternative is to use partially replicated (p–rep) designs, where a proportion of the test entries are replicated at each location. We extend a method for the generation of p–rep designs based on α–arrays to allow for a much broader class of designs to be constructed. Updating procedures for the average efficiency factor and its upper bound are developed for application to the computer generation of efficient p–rep designs.     

On simulation of weak records

In the present paper, we discuss algorithms of generation of weak records. These generation algorithms are based on two different methods. In the case, when the inverse function for the underlying distribution function can be obtained explicitly, the corresponding generation algorithms are built on the inverse-transform method. In the case, when the inverse function cannot be obtained explicitly, the algorithms are based on the rejection method. Generation algorithms of our paper are supplied with illustrative examples.     

Generating random variates from D-distributions via substitution sampling

Laud et al. (1993) describe a method for random variate generation from D-distributions. In this paper an alternative method using substitution sampling is given. An algorithm for the random variate generation from SD-distributions is also given.     

Matrix generators for pseudo-random vector generation

In this paper a method for the direct generation of pseudo-random vectors is considered. Thereby the n-th pseudo-random vector is recursively generated from the (n?1)-th pseudo-random vector by multiplication with a matrix. The period lengths of this generator type are examined and characterized. Furthermore it is shown that some popular pseudo-random number generators can be regarded as special cases of this method.     

Identification of outlier bootstrap samples

SUMMARY We define a variation of Efron's method II based on the outlier bootstrap sample concept. A criterion for the identification of such samples is given, with which a variation in the bootstrap sample generation algorithm is introduced. The results of several simulations are analyzed in which, in comparison with Efron's method II, a higher degree of closeness to the estimated quantities can be observed.     

Some aspects of probability forecasting

The problems of assessing, comparing and combining probability forecasts for a binary events sequence are considered. A Gaussian threshold model (analytically of closed form) is introduced which allows generation of different probability forecast sequences valid for the same events. Chi - squared type test statistics, and also a marginal-conditional method are proposed for the assessment problem, and an asymptotic normality result is given. A graphical method is developed for the comparison problem, based upon decomposing arbitrary proper scoring rules into certain elementary scoring functions. The special role of the logarithmic scoring rule is examined in the context of Neyman - Pearson theory.     

Using wavelets for data generation

Wavelets are proposed as a non-parametric data generation tool. The idea behind the suggested method is decomposition of data into its details and later reconstruction by summation of the details randomly to generate new data. A Haar wavelet is used because of its simplicity. The method is applied to annual and monthly streamflow series taken from Turkey and USA. It is found to give good results for non-skewed data, as well as in the presence of auto-correlation.     

Generating multivariate continuous data via the notion of nearest neighbors

Taylor and Thompson [15] introduced a clever algorithm for simulating multivariate continuous data sets that resemble the original data. Their approach is predicated upon determining a few nearest neighbors of a given row of data through a statistical distance measure, and subsequently combining the observations by stochastic multipliers that are drawn from a uniform distribution to generate simulated data that essentially maintain the original data trends. The newly drawn values are assumed to come from the same underlying hypothetical process that governs the mechanism of how the data are formed. This technique is appealing in that no density estimation is required. We believe that this data-based simulation method has substantial potential in multivariate data generation due to the local nature of the generation scheme, which does not have strict specification requirements as in most other algorithms. In this work, we provide two R routines: one has a built-in simulator for finding the optimal number of nearest neighbors for any given data set, and the other generates pseudo-random data using this optimal number.     

Simulation studies:do data generation techniques play favourites?

When comparing the performances of several classification procedures utilizing simulated data, it is necessary to ensure that the method of data generation does not unfairly favor one or more of the procedures. This study was undertaken to examine the influence of five methods of generation of data with dichotomous independent variables and an ordinal response. One generation method considered was model-free and four were model-based; it was hypothesized that the model-based generation techniques would unfairly favor their respective underlying models. In the three outcome category situation, it was found that the interaction between generation procedure and classification model, although statistically significant, was always very small. Thus, these results indicate that the choice of generation procedure may usually be made based on issues other than potential interaction between generation procedure and classification model.     

Non-parametric Bayesian inference through MCMC method for Y-linked two-sex branching processes with blind choice

ABSTRACT

Dirichlet-process-based non-parametric Bayesian inference is developed for a Y-linked two-sex branching process with blind choice. This stochastic model is suitable for analysing the evolution of the number of carriers of two alleles of a Y-linked gene in a two-sex monogamous population where each female chooses her partner from among the male population without caring about his type (i.e. the allele he carries). The only data assumed to be available are the total number of females and males (regardless of their types) up to some generation and the numbers of each type of male in the last generation. A simulation method which is based on a Dirichlet process and a Gibbs sampler is developed to estimate the posterior distributions of the model's main parameters. Finally, the computational efficiency of the algorithm is illustrated with example simulations and an application to real data.     

Data-driven sensitivity analysis to detect missing data mechanism with applications to structural equation modelling

Missing data are a common problem in almost all areas of empirical research. Ignoring the missing data mechanism, especially when data are missing not at random (MNAR), can result in biased and/or inefficient inference. Because MNAR mechanism is not verifiable based on the observed data, sensitivity analysis is often used to assess it. Current sensitivity analysis methods primarily assume a model for the response mechanism in conjunction with a measurement model and examine sensitivity to missing data mechanism via the parameters of the response model. Recently, Jamshidian and Mata (Post-modelling sensitivity analysis to detect the effect of missing data mechanism, Multivariate Behav. Res. 43 (2008), pp. 432–452) introduced a new method of sensitivity analysis that does not require the difficult task of modelling the missing data mechanism. In this method, a single measurement model is fitted to all of the data and to a sub-sample of the data. Discrepancy in the parameter estimates obtained from the the two data sets is used as a measure of sensitivity to missing data mechanism. Jamshidian and Mata describe their method mainly in the context of detecting data that are missing completely at random (MCAR). They used a bootstrap type method, that relies on heuristic input from the researcher, to test for the discrepancy of the parameter estimates. Instead of using bootstrap, the current article obtains confidence interval for parameter differences on two samples based on an asymptotic approximation. Because it does not use bootstrap, the developed procedure avoids likely convergence problems with the bootstrap methods. It does not require heuristic input from the researcher and can be readily implemented in statistical software. The article also discusses methods of obtaining sub-samples that may be used to test missing at random in addition to MCAR. An application of the developed procedure to a real data set, from the first wave of an ongoing longitudinal study on aging, is presented. Simulation studies are performed as well, using two methods of missing data generation, which show promise for the proposed sensitivity method. One method of missing data generation is also new and interesting in its own right.     

Computer generation of random variates from the tail of t and normal distributions

An algorithm is developed for the efficient generation of random variates from the tail of a t-distribution. This is specialised to the case of a Normal distribution. Theoretical measures of efficiency are derived. Computer timings for the algorithms are given, and, in the Normal case, compared with existing tail generation procedures.     

基于潜变量的新生代农民工人力资本测度研究

新生代农民工作为城市新增劳动力的主要来源,其人力资本水平的提升,对促进供给侧结构性改革、增强经济持续增长动力具有重要意义。为了研究新生代农民工人力资本的构成、测度及现状等问题,从健康资本、经验资本和技能资本三个维度建立指标体系,构建了基于潜变量的新生代农民工人力资本的测度模型。通过问卷调查,采用偏最小二乘方法对新生代农民工的人力资本水平进行了测度,结果表明:新生代农民工健康资本对于技能资本的形成具有积极作用,健康资本通过技能资本对收入产生影响,技能资本和经验资本的差异直接导致其收入的差异,新生代农民工技能资本和经验资本仍然偏低。因此,提升新生代农民工人力资本应该突破学历教育的局限,转向适应产业发展需求的职业技能培训和技术经验的积累上。     

An application of nonparametric regression to missing data in large market surveys

Non-response (or missing data) is often encountered in large-scale surveys. To enable the behavioural analysis of these data sets, statistical treatments are commonly applied to complete or remove these data. However, the correctness of such procedures critically depends on the nature of the underlying missingness generation process. Clearly, the efficacy of applying either case deletion or imputation procedures rests on the unknown missingness generation mechanism. The contribution of this paper is twofold. The study is the first to propose a simple sequential method to attempt to identify the form of missingness. Second, the effectiveness of the tests is assessed by generating (experimentally) nine missing data sets by imposed MCAR, MAR and NMAR processes, with data removed.     

Universal methods for generating random variables with a given characteristic function

Universal generators for absolutely-continuous and integer-valued random variables are introduced. The proposal is based on a generalization of the rejection technique proposed by Devroye [The computer generation of random variables with a given characteristic function. Computers and Mathematics with Applications. 1981;7:547–552]. The method involves a dominating function solely requiring the evaluation of integrals which depend on the characteristic function of the underlying random variable. The proposal gives rise to simple algorithms which may be implemented in a few code lines and which may show noticeable performance even if some classical families of distributions are considered.     

Solving Survo puzzles using matrix combinatorial products

We investigate combinatorial matrix problems that are related to restricted integer partitions. They arise from Survo puzzles, where the basic task is to fill an m×n table by integers 1, 2,?…?, mn, so that each number appears only once, when the column sums and the row sums are fixed. We present a new computational method for solving Survo puzzles with binary matrices that are recoded and combined using the Hadamard, Kronecker, and Khatri–Rao products. The idea of our method is based on using the matrix interpreter and other data analytic tools of Survo R, which represents the newest generation of the Survo computing environment, recently implemented as a multiplatform, open source R package. We illustrate our method with detailed examples.