bluuebunny/crossref_metadata_2025_split huggingface dataset:
Bayesian Inference for a Normal Dispersion Matrix and its Application to Stochastic Multiple Regression Analysis
Authors: Chen Chan-Fu 
Published: December 2018

Summary
This paper discusses Bayesian inference procedures for a normal dispersion matrix. Structural information for the prior mean of the dispersion matrix is incorporated into the analysis through a Normal-Wishart prior distribution. Many of the resulting Bayes estimates are invariant, consistent and asymptotically efficient. Using this procedure, a coherent Bayesian argument for stochastic multiple regression analysis is developed, where dependent and independent variables are jointly random, without experimental control. It is shown that ordinary least squares, a general form of ridge regression, and factor analysis regression methods can be represented as special cases within this general framework. The preliminary report of a simulation study indicates that the Bayesian regression techniques demonstrate substantial improvements over least squares, even using frequentist criteria. Finally, the related problem of joint estimation of the normal population mean and dispersion matrix is briefly discussed in Section 5. The resulting Bayes estimate for the population mean is shown to be closely related to Stein estimates.
Complete Latin Squares and Related Experimental Designs
Authors: Freeman G. H. 
Published: December 2018

Summary
A description is given of complete latin squares, which are squares with all ordered pairs of elements occurring next to each other once each in rows and columns, and of their uses as experimental designs. The existence of complete latin squares for all even numbers has been known for more than 30 years. Squares with various types of symmetry are considered here, all possible squares being described with side 4, 6, 8 and 10, together with some of side 12, 14, 16 and 18. These are put into genera whose members can all be obtained from each other by one or more of the processes of interchanging rows and columns, rearranging rows or reading the square in reverse. Where no complete latin squares exist, quasi-complete latin squares are considered in which all unordered pairs occur twice in rows and twice in columns. Such squares exist for all odd numbers, as well as even numbers greater than 4, and examples are given up to size 9.
Some Algebraic Properties of Ridge Coefficients
Authors: McDonald Gary C. 
Published: December 2018

Summary
This note is concerned with one parameter ridge estimators in a multiple linear regression context as described by Hoerl and Kennard (Technometrics, 12 (1970), pp. 55-68). These estimators are rational functions of the ridge parameter, and some properties concerning sign changes and asymptotic behaviour are noted. Further properties of these estimators are derived assuming that the x'x matrix possesses intraclass (or uniform) correlation structure. Some of these characteristics, e.g. the order of the ridge coefficients and their rates-of-change, are unrelated to the degree of multicollinearity; while others, e.g. existence and location of sign changes, are explicitly related to multicollinearity.
The G/G/1 Queueing System with a Particular Queue Discipline
Authors: Fakinos D. 
Published: December 2018

SUMMARY
This paper considers the G/G/1 queueing system under the assumption of a last-come, first served queue discipline where each customer begins service immediately upon his arrival. At the next arrival, the previous service is interrupted but no loss of service is involved. It is shown, among other things, that the equilibrium distribution of the number of customers in the system (when the system is considered exclusively at arrival epochs) is geometric.
On the Theory of Bilinear Time Series Models
Authors: Rao T. Subba 
Published: December 2018

SUMMARY
The theory of bilinear time series models is considered in this paper. The sufficient conditions for asymptotic stationarity of the bilinear time series models are derived, and the expressions for the variance and covariance are obtained. The conditions for the invertibility of the model are also included. The estimation of the parameters of the scalar bilinear time series model is considered. The bilinear models are fitted to sunspot numbers and also to a P-wave of a nuclear explosion. The forecasting of sunspot numbers is also considered.
The Statistical Analysis of Compositional Data
Authors: Aitchison J. 
Published: December 2018

Summary
The simplex plays an important role as sample space in many practical situations where compositional data, in the form of proportions of some whole, require interpretation. It is argued that the statistical analysis of such data has proved difficult because of a lack both of concepts of independence and of rich enough parametric classes of distributions in the simplex. A variety of independence hypotheses are introduced and interrelated, and new classes of transformed-normal distributions in the simplex are provided as models within which the independence hypotheses can be tested through standard theory of parametric hypothesis testing. The new concepts and statistical methodology are illustrated by a number of applications.
Inference for the Linear Model Using a Likelihood Based on Ranks
Authors: Pettitt A. N. 
Published: December 2018

Summary
An approximation to the marginal likelihood of the ranks of a set of observations is used to analyse data. The observations, after some arbitrary monotone transformation, are assumed to be independently normally distributed with means related by a linear model. An approximate posterior distribution for the parameters of the linear model is given and used to find predictive distributions for the ordering of future observations. A numerical example is given. Appendices give mathematical details of the approximation.
Methods for Analysing Spatial Processes of Several Types of Points
Authors: Lotwick H. W. , Silverman B. W. 
Published: December 2018

Summary
Two approaches are described to the analysis of spatial patterns consisting of several types of points. The first approach uses a method of asymptotically unbiased estimation of the second moment distribution; the second uses methods based on regions of empty space in the patterns. Some distributional results are given in each case, and a method of Monte Carlo testing conditional on the marginal structure is described. The methods are illustrated by being applied to some physiological data.
Assessing Sensitivity to an Unobserved Binary Covariate in an Observational Study with Binary Outcome
Authors: Rosenbaum P. R. , Rubin D. B. 
Published: December 2018

SUMMARY
This paper proposes a simple technique for assessing the range of plausible causal conclusions from observational studies with a binary outcome and an observed categorical covariate. The technique assesses the sensitivity of conclusions to assumptions about an unobserved binary covariate relevant to both treatment assignment and response. A medical study of coronary artery disease is used to illustrate the technique.
On Sprent's Generalized Least-Squares Estimator
Authors: Mak Tak K. 
Published: December 2018

Summary
This paper studies the asymptotic properties of Sprent's (1966) generalized least-squares estimator of the slope parameter in a functional relationship model which allows errors at different data points be correlated. Consistency is established and the asymptotic variance derived. When the Joint distribution of the errors is normal, in which case Sprent's estimator coincides with the maximum likelihood estimator, the asymptotic variance formula is further simplified and the limiting distribution of the estimator is also shown to be normal. The variance expression obtained under the normality assumption differs from that of Dolby (1972) derived by inverting the information matrix, and the latter procedure is known to be generally invalid in functional relationship problems due to the presence of incidental parameters (Patefield, 1978). An estimator of the asymptotic variance is also suggested.
A Unified Method for Constructing PBIB Designs Based on Triangular and L
2 Schemes
Authors: Cheng Ching-Shui , Constantine G. M. , Hedayat A. S. 
Published: December 2018

SUMMARY
A general and simple method for constructing triangular and L 2 type partially balanced incomplete block (PBIB) designs is presented. This method unifies several well-known methods and produces many new series of designs. The idea is based on a well-known relation between triangular and L 2 type PBIB designs and line graphs. Triangular or L 2 type PBIB designs can often be obtained by suitably “symmetrizing” a given initial block.
Robust Non-Parametric Function Fitting
Authors: HÄrdle W. , Gasser T. 
Published: December 2018

SUMMARY
A robust non-parametric function fitting method is introduced. The estimate is motivated from the theory of M-estimation and of kernel estimation of regression functions. Consistency and asymptotic normality are shown. Bias and variance rates are the same as those previously obtained by Gasser and Müller (1979) for linear smoothers. The estimate satisfies a minimax property, i.e. it minimizes the maximal asymptotic variance as the error distributions vary over a suitable contamination neighbourhood.
Estimation of the Mean of a Selected Negative Exponential Population
Authors: Sackrowitz Harold , Samuel-Cahn Ester 
Published: December 2018

SUMMARY
Let Xi be independent, negative exponentially distributed with unknown expectation λi, i = 1, …, k. Let J and M denote the (random) indices of the maximal and minimal observation, respectively. The paper considers estimation of the random quantities λJ and λM. The loss function is (a – λM)2/λ2 M for λM, and correspondingly for λJ. UMVUE and minimax estimators are shown to exist and are exhibited, and certain other reasonable estimators are discussed.
A Predictive Model Selection Criterion
Authors: Martini A. San , Spezzaferri F. 
Published: December 2018

SUMMARY
A procedure for model selection is presented which chooses the model that gives the best prediction of the future observation. The predictive distributions associated with each model are compared by means of the logarithmic utility function. For two nested normal linear models, the choice criterion is the product of the posterior odds ratio and a factor depending on the design point of the future observation. Taking appropriate mean values, a criterion is obtained which is independent of the particular design point. This average criterion differs from the ones proposed by Akaike, Schwarz and others in that it adjusts the likelihood ratio statistic by taking into account not only the difference in dimensionality, but also the estimated distance of the two models.
Quasi-Complete Latin Squares: Construction and Randomization
Authors: Bailey R. A. 
Published: December 2018

SUMMARY
A general method for constructing quasi-complete Latin squares based on groups is given. This method leads to a relatively straightforward way of counting the number of inequivalent quasi-complete Latin squares of side at most 9. Randomization of such designs is discussed, and an explicit construction for valid randomization sets of quasi-complete Latin squares whose side is an odd prime power is given. It is shown that, contrary to common belief, randomization using a subset of all possible quasi-complete Latin squares may be valid while that using the whole set is not.
Jackknifing Differentiable Statistical Functionals
Authors: Parr William C. 
Published: December 2018

SUMMARY
The purpose of this paper is to give a general unified view of “how smooth” a statistic needs to be for the jackknife to work. We give general sufficient conditions for the jackknife to produce consistent bias and variance estimators, and for linear combinations of the pseudovalues to be asymptotically normal. Regularity conditions are stated in terms of the existence of strong Fréchet differentials of the functional version of the statistic being jackknifed.
Kernels for Nonparametric Curve Estimation
Authors: Gasser T. , MÜller H-G. , Mammitzsch V. 
Published: December 2018

SUMMARY
The choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated. Explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error, IMSE (the present proof of the optimality of the latter kernels is restricted up to order k = 5). These kernels are also of interest for the nonparametric estimation of probability densities and spectral densities. A finite sample study indicates that higher order kernels – asymptotically improving the rate of convergence – may become attractive for realistic finite sample size. Suitably modified kernels are considered for estimating at the extremities of the data, in a way which allows to retain the order of the bias found for interior points.
Using Bricks to Build Block Designs
Authors: Jones Byron 
Published: December 2018

SUMMARY
A method is suggested for constructing incomplete block designs in which uncorrelated estimates of contrasts of interest have variances in a specified ratio. The designs are built up by using sets of blocks called bricks. Many of the constructed designs have blocks of different sizes. The choice between competing designs is made by choosing the one that maximizes the weighted sum of the effective replications. An example is given to illustrate the method.
Stochastic Models of Computer Communication Systems
Authors: Kelly F. P. 
Published: December 2018

SUMMARY
This paper describes some examples of the stochastic models found useful in the design and analysis of advanced computer and communication systems. Our major theme might be termed the control of contention. As illustrations of this theme we discuss concurrency control procedures for databases, dynamic channel assignment for cellular radio, and random access schemes for the control of a broadcast channel. We emphasize asymptotic properties of product-form distributions and we present some new results on the stability of acknowledgement based random access schemes.
Asymptotic Normality of Goodness-Of-Fit Statistics for Sparse Product Multinomials
Authors: Dale Jocelyn R. 
Published: December 2018

SUMMARY
The asymptotic distribution of the Pearson X 2 and likelihood ratio G 2 goodness-of-fit statistics is derived for k independent, non-identically distributed multinomials, as k approaches infinity, with expected cell frequencies bounded. The application is to large datasets of counts with many zero cells. Conditions are given under which the limiting distributions are normal for originating probabilities (i) known and (ii) dependent on a common, finite-dimensional parameter. A logistic regression model is given which satisfies (ii). Finally, skewness is discussed as a measure of closeness of moderate upper percentage points of X 2 to normal percentiles.
On the Rate of Convergence of Orthogonal Series Density Estimators
Authors: Hall Peter 
Published: December 2018

SUMMARY
We derive a lower bound to the rate of convergence of nonparametric density estimators on compact sets, and show that it is achieved by estimators based on orthogonal series. Unlike earlier work on this type of problem, the bound depends on the size of Fourier coefficients rather than explicitly on smoothness assumptions.
Orientation Statistics Without Parametric Assumptions
Authors: Prentice Michael J. 
Published: December 2018

SUMMARY
Maximum likelihood estimation using the matrix von Mises-Fisher distribution in orientation statistics leads to unacceptably complicated likelihood equations, essentially because of the inconvenient form of the normalizing constant in the probability distribution. For the case of 3 × 2 or 3 × 3 orientations, the main cases of practical importance, an alternative approach is developed here by transforming the data into unsigned four-dimensional directions and using known results on the sampling properties of the spectral decomposition of the resulting sample moment of inertia matrix. It is demonstrated that the necessary computations are relatively simple by applying some of the techniques to a set of vectorcardiogram data.
Recovery of Row and Column Information in Row-Column Designs with Adjusted Orthogonality
Authors: Eccleston J. A. , John J. A. 
Published: December 2018

SUMMARY
The analysis of row-column designs which satisfy the property of adjusted orthogonality is considered. For such designs a series of results are derived which relate the information matrix, its inverse, the estimator of the treatment effects and the adjusted treatment sum of squares to those of its component designs. It is also shown that estimators of the stratum variances required for the recovery of information from between rows and between columns can be obtained by a relatively simple method.
Consistency of Deviance-Based M Estimators
Authors: Lenth Russell V. , Green Peter J. 
Published: December 2018

SUMMARY
In a general estimation problem, the deviance function generates statistics that are similar to squared standardized residuals. A deviance-based M estimator (DBME) is defined as an adaptively weighted maximum-likelihood estimator, where the weights depend upon the deviances. In both a single-parameter and a regression setting, we give some general conditions under which a DMBE is consistent. For a suitable weighting scheme, these conditions are satisfied in many continuous Cramer-Rao-regular families and in related linear or nonlinear regression cases. The conditions fail (and the estimator is inconsistent) in most discrete families.
Saddlepoint Expansions for Directional Test Probabilities
Authors: Skovgaard Ib M. 
Published: December 2018

SUMMARY
An expansion is derived for the conditional tail probability of a multivariate random variable given its direction from the expected value. In particular, if the score function of a statistical model is chosen as this variable, such a conditional probability gives a test for a simple hypothesis, which is asymptotically equivalent to the likelihood ratio test. The expansion is of the large deviation type and is derived through the use of saddlepoint methods. Thus the relative error of the test probability is O(n –1) uniformly in a bounded set for an average of n independent replications. The approximation is based on the cumulant transform for the random variable, but is otherwise a simple expression in terms of chi-squared distributions. In the one-dimensional case it reduces to the expansion obtained by Lugannani and Rice. Numerical examples show an excellent fit, comparable with other saddlepoint expansions, when the dimension is low, even for very small sample sizes, but for higher dimensions more replications are required to give a similar approximation.
A Note on the Existence of Maximum Likelihood Estimates in Linear Regression Models Using Interval-Censored Data
Authors: Hamada M. , Tse S. K. 
Published: December 2018

SUMMARY
For a class of linear regression models with interval-censored data, including the exponential regression model as a special case, a necessary and sufficient condition is given for the existence of the maximum likelihood estimator (MLE). The condition is especially simple to check for simple linear regression. This result is useful for comparing the small sample properties of MLEs from different special cases of interval-censored data.
A Review of Bootstrap Confidence Intervals
Authors: Diciccio Thomas J. , Romano Joseph P. 
Published: December 2018

SUMMARY
A survey of bootstrap procedures for constructing confidence regions is given. In particular, several distinct bootstrap methods are considered, with emphasis on the mathematical correctness of these procedures. The percentile, bias-corrected percentile and accelerated bias-corrected percentile methods, developed by Efron, are reviewed in both parametric and nonparametric situations. A procedure related to the accelerated bias-corrected method, which avoids explicit calculation of the analytical corrections required in Efron's method, is also introduced. In the context of a functional approach for the construction of confidence regions, the bootstrap is motivated as a method to estimate the distributions of approximate pivots. Finally, iterative bootstrap methods are discussed as means to improve coverage accuracy.
Bayes Methods for Outliers in Exponential Samples
Authors: Pettit L. I. 
Published: December 2018

SUMMARY
A Bayesian approach to the modelling of outliers is presented and examined in relation to members of the exponential family in general, and the exponential distribution in particular. The approach is appropriate when the analyst's prior knowledge is such that any aberrant observations will be surprising with high probability. It is shown that the most surprising observation, as measured by the predictive ordinate, must lie on the ‘outside’ of the sample. Bayes factors for models with and without outliers are given for exponential samples. It is shown that masking and swamping cannot occur. An exponential regression problem is considered.
On the Distribution of a Studentized Quantile
Authors: Hall Peter , Sheather Simon J. 
Published: December 2018

SUMMARY
The asymptotic variance of a sample quantile depends on the value of the population density at the population quantile. Therefore Studentizing a sample quantile involves density estimation, either explicitly or implicitly. One popular way of Studentizing is to use the Siddiqui–Bloch–Gastwirth estimator, whose construction depends crucially on the choice of a smoothing parameter m. We examine the effect which the selection of m has on the level error of tests or confidence intervals based on Studentized quantiles and show that, if we wish to minimize this error, m should be of a smaller order of magnitude than is recommended by squared error theory. The cases of one- and two-sided procedures are distinctly different, the former being less sensitive to the choice of m.
Bahadur Efficiency of Two-Sample Tests Based on One-Sample Sign Statistics
Authors: Tableman Mara , Hettmansperger Thomas P. 
Published: December 2018

SUMMARY
This paper discusses the two-sample test of location based on the comparison of two distribution-free one-sample confidence intervals derived from sign statistics. This test procedure, first introduced by Hettmansperger (1984), rejects the null hypothesis of equal population medians when the two intervals are disjoint. He presents three different ways to select the two one-sample intervals and one choice leads to Mood's test. All solutions have the same Pitman efficiency. This paper shows that the choices can be distinguished on the basis of Bahadur's efficiency. We formulate the problem in terms of (asymptotically) fixed width confidence intervals. In this context various median tests (including Mood's test) arise as special cases and they yield different performance. The solution that specifies equal asymptotic lengths for the one-sample intervals (which is different from Mood's test) is recommended.
Estimating Weighted Integrals of the Second-Order Intensity of a Spatial Point Process
Authors: Berman Mark , Diggle Peter 
Published: December 2018

SUMMARY
This paper considers the nonparametric estimation of the integral J=∫0Ttλ2(t)φ(t)dt
where λ2(t) is the unknown second-order intensity function of a two-dimensional stationary isotropic point process observed in some region and φ(t) is known for t ϵ [0, T]. An unbiased estimator of J is derived, and a computationally fast approximation to it is proposed. The estimator is then used to obtain a kernel method for smoothing point process data, a new estimator of the Fourier transform of the second-order intensity and some tests for spatial association between a point process and another stochastic process.