bluuebunny/crossref_metadata_2025_split huggingface dataset:
Tests of Fit Based on Normalized Spacings
Authors: Lockhart R. A. , O'Reilly F. J. , Stephens M. A. 
Published: December 2018

SUMMARY
Normalized spacings provide useful tests of fit for many suitably regular continuous distributions; attractive features of the tests are that they can be used with unknown parameters and also with samples which are censored (Type 2) on the left and/or right. A transformation of the spacings leads, under the null hypothesis, to a set of z-values in (0, 1); however, these are not uniformly distributed except for spacings from the exponential or uniform distributions. Statistics based on the mean or the median of the z-values have already been suggested for tests for the Weibull (or equivalently the extreme-value) distribution; we now add the Anderson-Darling statistic. Asymptotic theory of the test statistics is given in general, and specialized to the normal, logistic and extreme-value distributions. Monte Carlo results show the asymptotic points can be used for relatively small samples. Also, a Monte Carlo study on power of the normal tests is given, which shows the Anderson-Darling statistic to be powerful against a wide range of alternatives; the mean and median can be non-consistent or even biased.
Penalized Likelihood Estimation of Hazard and Intensity Functions
Authors: Senthilselvan A. 
Published: December 2018

SUMMARY
A nonparametric estimate is proposed for the hazard function using penalized likelihood methods. The estimate turns out to be a hyperbolic spline function which is continuous with its first derivative discontinuous only at a finite number of points. It always assumes positive values, unlike Anderson and Senthilselvan’s (1980) quadratic spline estimate. This method is modified for the estimation of the intensity function of a nonstationary Poisson process. An example is given for comparison of the new estimator with the estimator of Anderson and Senthilselvan (1980).
Stochastic Complexity
Authors: Rissanen Jorma 
Published: December 2018

SUMMARY
It is argued that all the useful information in observed data that can be extracted with a selected class of modeled distributions, will be obtained if we calculate the stochastic complexity, defined to be the shortest description length of the data. The same quantity also determines the greatest lower bound for prediction errors when the data are sequentially predicted. An abstract definition of stochastic complexity is given along with two fundamental theorems which justify the notion. Further, three explicit model selection criteria to approximate the stochastic complexity are described and the associated optimal models are interpreted to define asymptotically sufficient statistics for the data.
Design of Experiments for Studying Intergenotypic Competition
Authors: Azais J. M. 
Published: December 2018

SUMMARY
A method of construction and randomization of designs for experiments for studying intergenotypic competition is given. These designs are like row complete latin squares, but they include border plots, which are necessary under field conditions. These border plots permit intra-block randomization without destroying the neighbour-balance property. In several cases it is proved that the design is connected even under a general competition model.
Control of Stochastic Loss Networks, with Applications
Authors: Zachary Stan 
Published: December 2018

SUMMARY
We consider the application of the policy improvement routine of Markov decision theory to the control of a stochastic loss network which can process calls of differing types requiring differing resources. The objective is the minimisation of the cost of lost calls. In practice the derivation of exactly optimal policies is computationally intractable, and we identify circumstances in which nearly optimal policies may reasonably be computed. Examples are fully connected telephone networks and cellular radio networks.
Limit Distribution of a High Order Markov Chain
Authors: Adke S. R. , Deshmukh S. R. 
Published: December 2018

SUMMARY
The limit distribution of a Markov chain of order k &gt; 1 is obtained under conditions weaker than those assumed by Raftery (1985). The results are shown to be valid also for arbitrary state space Markov sequences of order k &gt; 1.
Gittins Procedures for Bandits with Delayed Responses
Authors: Eick Stephen G. 
Published: December 2018

SUMMARY
This paper introduces the multi-armed delayed response bandit with geometric discounting. The existence of dynamic allocation indices is shown when the discount factor is less than 1/2 or when the information bank size is zero. For the multi-armed delayed response bandit, the arm indicated by the dynamic allocation procedure or Gittins procedure is optimal when all information bank sizes are zero. A computational method for calculating indices is presented. The idea is to approximate the optimal strategy using a class of strategies whose worths are easy to calculate.
Nonparametric Estimation of the Probability of a Long Delay in the M/G/1 Queue
Authors: Gaver D. P. , Jacobs P. A. 
Published: December 2018

SUMMARY
A Poisson stream of customers with known arrival rate λ approaches a single server having independent identically distributed service times with unknown distribution. A nonparametric estimator of the probability of a long customer delay is obtained from an asymptotic renewal theoretic result giving an exponential approximation to the tail of the virtual waiting time distribution for a stable M/G/1 queue. Asymptotic properties of the estimator are obtained. Results of a simulation study of the small sample size behaviour are given.
Detecting Periodic Components in a White Gaussian Time Series
Authors: Chiu Shean-Tsong 
Published: December 2018

SUMMARY
A family of tests for periodic components in a white Gaussian series is proposed. The test is based on a statistic which is proportional to the ratio of the maximum periodogram to a trimmed mean of the periodograms. The asymptotic distributions of the statistics are obtained. It is shown that the proposed test and Fisher's test have the same asymptotic powers against the alternative of a sinusoidal wave at a non-zero Fourier frequency. The simulation results suggest that the proposed test is more powerful than Fisher's test against the alternatives of multiple peaks. The problem of detecting multiple peaks is also discussed.
Hierarchical Interaction Models
Authors: Edwards David 
Published: December 2018

SUMMARY
Lauritzen and Wermuth have proposed a class of models for mixed qualitative and continuous data, defined by two properties: that the continuous variables are normally distributed given the qualitative variables and that a set of conditional independence relations hold between specified pairs of variables. These models, called graphical association models, include graphical log-linear models for contingency tables and covariance selection models for correlation matrices. The present paper examines an extension to this class called hierarchical interaction models. A compact form for model representation is described and an estimation algorithm is given. Some properties of the models concerning marginalization and conditioning are examined. The class includes and generalizes hierarchical log-linear models, standard fixed effect analysis of variance (ANOVA), multivariate ANOVA and multivariate regression models. Two applications are given.
Balanced Design of Bootstrap Simulations
Authors: Graham R. L. , Hinkley D. V. , John P. W. M. , Shi S. 
Published: December 2018

SUMMARY
Davison et al. (1986) have shown that finite bootstrap simulations can be improved by forcing balance in the aggregate of simulated data sets. Their methods yield first-order balance, which principally affects bootstrap estimation of bias. Here we extend the methodology to second-order balance, which principally affects bootstrap estimation of variance. The particular techniques involve Latin square and balanced incomplete block designs. Numerical examples are given to illustrate both the positive and the negative features of the balanced simulations.
Robust Bayesian Analysis with ϵ-Contaminations Partially Known
Authors: Moreno E. , Cano J. A. 
Published: December 2018

SUMMARY
Prior distributions of the form π=(1−ϵ)π0+ϵq,π0 being the base elicited prior, q being contamination and ϵ reflecting the amount of error in π0 that is deemed possible, are considered. It is assumed that π0 is completely specified and that only some quantiles of q are known. As π varies over this class, the ranges of the posterior mean and of the posterior probabilities of an arbitrary set are determined. Some examples including hypotheses testing related to a bivariate normal likelihood are given.
Recursive Order Estimation of Autoregressions Without Bounding the Model Set
Authors: Hemerly E. M. , Davis M. H. A. 
Published: December 2018

SUMMARY
In a recent paper, we proved that Rissanen's 'predictive least squares' (PLS) criterion for model selection provides strongly consistent order estimates for autoregressive (AR) processes, i.e. the PLS order estimate p̂(n) based on the first n data points converges almost surely to p 0 as n → ∞ when the data are generated by an AR process of order p 0, and p 0 is known to belong to the finite model set M = {1, 2, ..., K}, K &lt; ∞. In the present paper we strengthen this result by showing that strong consistency is maintained even if K is allowed to increase with rate O((log n)γ), for any γ&lt;12, thus removing the need to specify an a priori upper bound.
One-Step Bootstrapping for Smooth Iterative Procedures
Authors: Schucany William R. , Wang Suojin 
Published: December 2018

SUMMARY
Resampling techniques have the potential to provide useful information about the sampling distribution of estimators of many population characteristics. Ambitious schemes such as the bootstrap and iterated bootstrap imply a substantial increase in computational effort. For some iterative procedures, such as generalized least squares or the EM algorithm, it is possible to avoid fully iterating each bootstrap replication to convergence. By analysing expansions of the defining equation, we can extract asymptotically correct bootstrap estimates from a single step for each replication. In this paper we demonstrate the large sample validity of this computationally efficient approach and illustrate its small sample applicability. Whether or not the adjustment represents an adequate replacement for full iteration depends on the nature of the problem and the desired accuracy for the bootstrap quantiles. If subsequent iterations are adjusted, then greater enhancement of the rate is achieved and the practical increase in accuracy is significant.
Practical Use of Higher Order Asymptotics for Multiparameter Exponential Families
Authors: Pierce Donald A. , Peters Dawn 
Published: December 2018

SUMMARY
Recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families, especially in generalized linear models. The aim here is to clarify and explore these. Attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family. Excellent approximations to exact conditional inferences are often available, in terms of simple adjustments to the signed square root of the likelihood ratio statistic. The focus is on distinguishing between two aspects of the adjustments: one reducing effects of nuisance parameter estimation and the other adjusting for little information regarding the parameter of interest. Numerical results are given for some Poisson and multinomial models.
Bivariate Threshold Methods for Extremes
Authors: Joe Harry , Smith Richard L. , Weissman Ishay 
Published: December 2018

SUMMARY
An extension of the threshold method for extreme values is developed, to consider the joint distribution of extremes of two variables. The methodology is based on the point process representation of bivariate extremes. Both parametric and nonparametric models are considered. The simplest case to handle is that in which both marginal distributions are known. For the more realistic case in which the marginal distributions are unknown, a mixed parametric-nonparametric method is proposed. The techniques are illustrated with data on sulphate and nitrate levels taken from a major study of acid rain.
Single-Factor Analysis by Minimum Message Length Estimation
Authors: Wallace C. S. , Freeman P. R. 
Published: December 2018

SUMMARY
The minimum message length (MML) technique is applied to the problem of estimating the parameters of a multivariate Gaussian model in which the correlation structure is modelled by a single common factor. Implicit estimator equations are derived and compared with those obtained from a maximum likelihood (ML) analysis. Unlike ML, the MML estimators remain consistent when used to estimate both the factor loadings and the factor scores. Tests on simulated data show the MML estimates to be on average more accurate than the ML estimates when the former exist. If the data show little evidence for a factor, the MML estimate collapses. It is shown that the condition for the existence of an MML estimate is essentially that the log-likelihood ratio in favour of the factor model exceeds the value expected under the null (no-factor) hypotheses.
A Characterization of Exponential Distributions Through Conditional Independence
Authors: Liang Ta Chen , Balakrishnan N. 
Published: December 2018

SUMMARY
Let Y 1, Y 2, . . ., Yn be mutually independent non-negative random variables having an absolutely continuous distribution function Fi(y) over its support [0, ∞) and the corresponding density function f i(y) &gt; 0 for y &gt; 0. Let A denote the event that Yi – Y i+1 &gt; 0 for all i = 1, 2, . . ., n – 1. Then we show that, conditional on the event A, Yi – Y i+1 and Y i+1 are independent for all i = 1, 2,. . ., k if and only if Yi (i = 1, 2, . . ., k) are exponentially distributed random variables, where 1 ≤ k ≤ n – 1. We note that the k exponential distributions can have different scale parameters.
The Use of a Canonical Form in the Construction of Locally Optimal Designs for Non-Linear Problems
Authors: Ford I. , Torsney B. , Wu C. F. J. 
Published: December 2018

SUMMARY
Optimal experimental designs for non-linear problems depend on the values of the underlying unknown parameters in the model. For various reasons there is interest in providing explicit formulae for the optimal designs as a function of the unknown parameters. This paper shows that, for a certain class of generalized linear models, the problem can be reduced to a canonical form. This simplifies the underlying problem and designs are constructed for several contexts with a single variable using geometric and other arguments.
Distribution Estimation Using Concomitants of Order Statistics, with Application to Monte Carlo Simulation for the Bootstrap
Authors: Do Kim-Anh , Hall Peter 
Published: December 2018

SUMMARY
We show that a simulation method suggested by Efron for approximating bootstrap distributions is closely related to techniques based on concomitants of order statistics and develop its asymptotic properties from that viewpoint. We prove that the method produces Monte Carlo approximations with variance and mean-squared error decreasing like B− 1 n− 1/2, where B denotes the number of simulations and n equals the sample size. Therefore Efron's method can be a competitor with techniques such as balanced resampling, importance resampling and antithetic resampling, where variance and mean-squared error decrease like B −1 with no significant contribution from sample size. However, Efron's method has drawbacks, one being that performance in the tails is not as good as performance towards the centre of the distribution. In this respect, importance resampling has distinct advantages.
Downdating the Moore-Penrose Generalized Inverse for Cross-Validation of Centred Least Squares Prediction
Authors: Dunne T. T. , Stone M. 
Published: December 2018

SUMMARY
Given a p × p symmetric matrix B and a p-vector c outside the range of B, a simple expression is formulated for the action of the Moore-Penrose generalized inverse B + on a vector b in the range of B, in terms of b, c and (B + cc‱)+. A special case of this formula gives a ‘downdating’ formula for the vector of least squares regression coefficients based on the Moore-Penrose inverse of the centred sum of squares and products matrix. The formula is analogous to that given by A. Albert for uncentred least squares fitting. An explicit downdating formula for the Moore-Penrose inverse B + itself is derived, and then more general downdating expressions for the inverse and the vector B + b when the p-vector c is replaced by a matrix array C of such vectors outside the range of B.
Multidimensional Density Estimation by Tomography
Authors: O'Sullivan Finbarr , Pawitan Yudi 
Published: December 2018

SUMMARY
The paper explores the application of the filtered backprojection algorithm of computerized tomography to statistical smoothing of multidimensional densities. The method makes use of automated one-dimensional density smoothers to obtain an automated smoothed multidimensional density. No structural assumptions such as additivity or log-additivity are used. An important computational aspect of this method is its inherently parallel structure. We demonstrate linear speed-up on a parallel computer architecture. Various practical details are discussed together with some illustrative two-dimensional examples. Asymptotic mean error characteristics of the method are shown to match those of more familiar multivariate kernel-, near-neighbour- and spline-type smoothing techniques.
Robust Likelihood Calculation for Time Series
Authors: Taplin Ross H. 
Published: December 2018

SUMMARY
We propose a computationally efficient method for calculating the likelihoods of a time series under many submodels, each of which assumes a patch of outliers or level shifts. We assume a state space representation of the time series model with a Bayesian-type treatment of anomalies. The calculations form the basis for an efficient and robust estimation procedure. The method is also applicable to linear regression with correlated errors and is illustrated with two examples.
Prediction Rules for Exponential Family State Space Models
Authors: Grunwald Gary K. , Guttorp Peter , Raftery Adrian E. 
Published: December 2018

SUMMARY
We state and prove a simple and general expression for the marginal mean in an exponential family state space model with conjugate state density. We then discuss implications of this result on the choice of parameterization of the observation density, on the interpretation of the predictive density for steady models and on exponentially weighted moving average and trend-free forecasting.
Estimation in Generalized Mixed Models
Authors: McGilchrist C. A. 
Published: December 2018

SUMMARY
Regression models containing fixed and random effects may have a response variable which is not normally distributed. The generalized mixed model includes both discrete and continuous response variables and is developed here for problems in which the regression variables enter linearly into the model. Best linear unbiased predictor methods are extended to maximum likelihood and residual maximum likelihood estimation procedures. Applications in modelling discrete response variables and in survival analysis are discussed.
Grouping Corrections for Circular Goodness-Of-Fit Tests
Authors: Brown B. M. 
Published: December 2018

SUMMARY
Simple corrections are outlined for the application to grouped seasonal data of Watson's and Maag's tests. These tests are circular or seasonal analogues of one-sample and k- (≥2) sample tests, of Cramér–von Mises type, and have several natural advantages over their competitors. The provision of simple grouping corrections may enhance the use of these tests, which otherwise have very good features. The corresponding grouping corrections are also presented for conventional, i.e. non-circular, Cramér–von Mises types of test.
A Note on Posterior Moments for a Normal Mean with Double-Exponential Prior
Authors: Mitchell Ann F. S. 
Published: December 2018

SUMMARY
General results on the behaviour of the posterior mean and variance of the mean of a normal distribution with known variance using a double-exponential prior are derived and complement the conjectures and particular examples given by Pericchi and Smith (1992) and Pericchi and Walley (1991).
A New Index of Fit Based on Mixture Methods for the Analysis of Contingency Tables
Authors: Rudas Tamás , Clogg Clifford C. , Lindsay Bruce G. 
Published: December 2018

SUMMARY
A framework based on mixture methods is proposed for evaluating goodness of fit in the analysis of contingency tables. For a given model H applied to a contingency table P, we consider the two-point mixture P = (1 – π)π 1 + ππ 2, with π the mixing proportion (0 ≤ π ≤ 1) and π 1 and π 2 the tables of probabilities for each latent class or component. In the unstructured approach recommended here, the mixture model applies H to π 1 but does not impose any restrictions on π 2. A contingency table P can generally be represented as such a two-point mixture for an interval of π-values. We define our index of lack of fit, π*, to be the smallest such π, i.e. π* is the fraction of the population that cannot be described by model H. This approach can be contrasted with the structured approach that applies model H to both π 1 and π 2 and leads to conventional latent class models when H is the hypothesis of independence. The case where H is the hypothesis of row–column independence and P is a two-way contingency table is covered in detail, but the procedure is quite general.
Transformations to Reduce Boundary Bias in Kernel Density Estimation
Authors: Marron J. S. , Ruppert D. 
Published: December 2018

SUMMARY
We consider kernel estimation of a univariate density whose support is a compact interval. If the density is non-zero at either boundary, then the usual kernel estimator can be seriously biased. ‘Reflection’ at a boundary removes some bias, but unless the first derivative of the density is 0 at the boundary the estimator with reflection can still be much more severely biased at the boundary than in the interior. We propose to transform the data to a density that has its first derivative equal to 0 at both boundaries. The density of the transformed data is estimated, and an estimate of the density of the original data is obtained by a change of variables. The transformation is selected from a parametric family, which is allowed to be quite general in our theoretical study. We propose algorithms where the transformation is either a quartic polynomial, a β cumulative density function (CDF) or a linear combination of a polynomial and a β CDF. The last two types of transformation are designed to accommodate possible poles at the boundaries. The first two algorithms are tested on simulated data and compared with an adjusted kernel method of Rice. We find that our proposal performs similarly to Rice's for densities with one-sided derivatives at the boundaries. Unlike Rice's method, our proposal is guaranteed to produce non-negative estimates. This can be a distinct advantage when the density is 0 at either boundary. Our algorithm for densities with poles outperforms the Rice adjustment when the density has a pole at a boundary.