bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some Statistical Methods for Bivariate Circular Data
Authors: Rivest Louis-Paul 
Published: December 2018

Summary
A function of the smallest singular value of the cross product matrix between two circular unit vectors is suggested as a measure of correlation. It possesses most of the desirable properties for a correlation coefficient given by Jupp and Mardia (1980). The concept of cluster dependence is introduced. A good predictor of one unit vector given the other is shown to depend on the type of dependence observed. The wrapped bivariate normal is characterized.
Saddlepoint Approximations for Permutation Tests and Confidence Intervals
Authors: Robinson J. 
Published: December 2018

Summary
Asymptotic approximations for the tail probabilities of certain statistics with complex moment generating functions are obtained by the usual methods of large deviation theory. It is pointed out that this approximation should be adequate over the entire range but of particular use for extreme tails. Approximations to the significance levels for one and two sample permutation tests are obtained and these tests are inverted to obtain approximate confidence intervals. These methods are applied to some numerical examples and the results are compared with the exact values and with approximations obtained from Edgeworth expansions.
Asymptotically Distribution-Free Simultaneous Confidence Region of Treatment Differences in a Randomized Complete Block Design
Authors: Wei L. J. 
Published: December 2018

Summary
For a randomized complete block design with additive block effects, an asymptotically distribution-free simultaneous confidence region of pairwise treatment differences is presented. The corresponding confidence bound has an explicit form and is easily obtained. Asymptotic relative efficiency comparisons with other known confidence regions are made to show the advantage of the proposed procedure. The case of treatment against control is also discussed.
On the Trace Efficiency for Control of Reinforced Balanced Incomplete Block Designs
Authors: Constantine Gregory M. 
Published: December 2018

SUMMARY
It is shown that in any block design containing a set of treatments and a control the average variance of the best linear unbiased estimates of the elementary contrasts with the control is proportional to the trace of the inverse of a suitable principal minor of the information matrix. A BIB design with blocks reinforced by the control is then proved to minimize this average variance over all the designs which contain the control once in every block. The result extends to the setting of two-way elimination of heterogeneity when the control appears bk -1 times, and any other variety appears rk -1 times, in each row. This latter balance can be achieved whenever a BIB design exists and the numerical conditions allow.
Some Minimum Variance Block Designs for Estimating Treatment Differences
Authors: Jacroux Mike 
Published: December 2018

SUMMARY
In this paper we consider experimental settings requiring usage of a block design in which v treatments are to be tested in b blocks of size k. A block design is called MV-optimal in such a setting if the maximal variance with which it estimates elementary treatment differences is minimal among all available designs. MV-optimal designs are particularly useful in exploratory experiments where as much information as possible is desired on the effects of all treatments being studied. Some sufficient conditions are derived which can be used to establish the MV-optimality of certain types of generalized group divisible designs as defined in Jacroux (1982) and some easy methods for constructing such MV-optimal designs are given.
Bayesian “Confidence Intervals” for the Cross-Validated Smoothing Spline
Authors: Wahba Grace 
Published: December 2018

SUMMARY
We consider the model Y(ti)=g(ti) + ∈i, i = 1, 2, …, n, where g(t), t ∈ [0, 1] is a smooth function and the {∈i} are independent N(0, σ2) errors with σ2 unknown. The cross-validated smoothing spline can be used to estimate g non-parametrically from observations on Y(ti), i= 1, 2, …, n, and the purpose of this paper is to study confidence intervals for this estimate. Properties of smoothing splines as Bayes estimates are used to derive confidence intervals based on the posterior covariance function of the estimate. A small Monte Carlo study with the cubic smoothing spline is carried out to suggest by example to what extent the resulting 95 per cent confidence intervals can be expected to cover about 95 per cent of the true (but in practice unknown) values of g(ti), i= 1,2,…,n. The method was also applied to one example of a two-dimensional thin plate smoothing spline. An asymptotic theoretical argument is presented to explain why the method can be expected to work on fixed smooth functions (like those tried), which are “smoother” than the sample functions from the prior distributions on which the confidence interval theory is based.
Recursive Estimation in Non-Linear Time Series Models of Autoregressive Type
Authors: Aase Knut K. 
Published: December 2018

SUMMARY
An adaptive estimation principle is considered for non-standard time series models; non-linear autoregressive processes in one dimension. Because of the recursive nature of the resulting estimator, it is computationally appealing, especially when a time series is considered as a flow of data. The least squares estimator is, for example, quite likely to be inferior. Asymptotic properties are derived under fairly weak assumptions, and special applications are considered. Monte Carlo simulations are used for illustration.
An Asymptotic Expansion Associated with the Maximum Likelihood Estimators in Arma Models
Authors: Tanaka Katsuto 
Published: December 2018

SUMMARY
A technique is given for the Edgeworth type asymptotic expansion for the joint as well as marginal and conditional distributions of the maximum likelihood estimators in autoregressive moving-average (ARMA) models. Our methodology is illustrated and results on the expansions for some simple ARMA models are presented.
Asymptotic Results on the Greenwood Statistic and Some of its Generalizations
Authors: Rao J. S. , Kuo Morgan 
Published: December 2018

SUMMARY
There has been a renewed interest in the Greenwood statistic for goodness of fit and its percentage points. See Burrows (1979), Currie (1981) and Stephens (1981). This statistic, which is based on the sum of squares of the sample spacings, is known to be locally most powerful among all tests based symmetrically on the simple one-step spacings. This paper discusses some generalizations of this statistic based on higher-order or m-step spacings and shows them to be asymptotically more efficient. It is also shown that the limiting efficiency increases further if the test is based on overlapping m-step spacings as opposed to the disjoint (or non-overlapping) m-step spacings.
Testing Misspecification in Vector Time Series Models with Exogenous Variables
Authors: Poskitt D. S. , Tremayne A. R. 
Published: December 2018

SUMMARY
In this paper we consider the application of hypothesis testing procedures to ARMAX systems. The score, or Lagrangian multiplier, principle is used to obtain mis-specification tests appropriate to these models. The structure of the information or sensitivity matrix is investigated in order to discuss the identifiability of alternative models and is used to show the existence of a set of admissible alternatives that are locally equivalent to one another. This notion is then developed to suggest why the score test is to be regarded as a pure significance test.
Efficient Nonparametric Estimation of Mixture Proportions
Authors: Hall Peter , Titterington D. M. 
Published: December 2018

SUMMARY
By constructing a sequence of multinomial approximations and related maximum likelihood estimators, we derive a Cramér-Rao lower bound for nonparametric estimators of the mixture proportions and thereby characterize asymptotically optimal estimators. For the case of the sampling model M2 of Hosmer (1973) it is shown that the sequence of maximum likelihood estimators, which can be obtained explicitly, is asymptotically optimal in this sense. The results hold true even when the multinomial approximations involve cells chosen adaptively, from the data, in a well-specified way.
Likelihood Analysis of Spatial Point Patterns
Authors: Ogata Yosihiko , Tanemura Masaharu 
Published: December 2018

SUMMARY
The likelihood procedure for estimating the pairwise interaction potential function is developed for statistical analysis of homogeneous spatial point patterns. Approximation methods of the normalizing factor of Gibbs canonical distribution are discussed both to estimate a scale parameter and to measure the softness (or hardness) of repulsive interactions. The approximations are useful up to a considerably high density. The validity of our procedure is demonstrated by some computer experiments. Some real data are analysed.
On the Asymptotic Distribution of the Location Linear Discriminant Function
Authors: Vlachonikolis Ioannis G. 
Published: December 2018

SUMMARY
The location linear discriminant function forms the basis of the optimal Bayes classification rule when the data contain both binary and continuous variables (Krzanowski, 1975). When the unknown parameters are replaced by their sample estimates, the resulting “estimative” rule has an exact distribution which is too complicated for numerical use. We present here an asymptotic expansion of this distribution and study its performance under various assumptions about the parameters.
Spline Smoothing in a Partly Linear Model
Authors: Heckman Nancy E. 
Published: December 2018

SUMMARY
Suppose that Yi = X'iβ + f(ti) + εi, 1 ≤ i ≤ n, where β, f, and εi are unknown, but the m-th derivative of f is square integrable. Estimates of β and f are given which minimize the sum of the residual sum of squares and a roughness penalty. It is shown that these estimates are Bayes under a diffuse prior on β and f, and that, under mild conditions on Xi, ti, εi, and the roughness penalty, the estimate of β is consistent and asymptotically normal.
The Analysis of Lattice Square Designs
Authors: Williams E. R. , Ratcliff D. , Ewijk P. H. 
Published: December 2018

SUMMARY
This paper presents a general definition for lattice square designs and gives a unified approach to the analysis of the class of restricted lattice square designs. This class includes as special cases all the lattice square designs covered in the books by Cochran and Cox (1957) and Federer (1955)
Two-Sample Problem with Bivariate Exchangeable Observations
Authors: Wei L. J. 
Published: December 2018

SUMMARY
In comparing two groups of subjects, suppose that each subject has two observations which are probabilistically exchangeable. Univariate rank tests which utilize this symmetry property are proposed for testing the equality of the two groups. Efficiencies of these tests are discussed. Point and interval estimators of the location shift parameter are obtained through the proposed rank tests. Examples are also provided to illustrate the proposed procedures.
Some Prediction Properties of Balanced Half-Sample Variance Estimators in Single-Stage Sampling
Authors: Valliant Richard 
Published: December 2018

SUMMARY
The balanced half-sample (BHS) method of variance estimation is a widely used technique in complex sample surveys. Large-sample prediction properties of the BHS method are given here for the separate ratio and regression estimators. Results are obtained when a large number of units are sampled and divided into two groups within each stratum. An empirical study examines the conditional and unconditional performance of the BHS method when estimating mean squared errors and constructing confidence intervals. The study also includes comparisons with the jackknife and the linearization estimators.
Identification of Nonzero Elements in the Polynomial Matrices of Mixed Varma Processes
Authors: Koreisha S. G. , Pukkila T. M. 
Published: December 2018

SUMMARY
The parameter density is the polynomial matrices of vector autoregressive moving average (VARMA) time series models is generally very low. Thus, estimation of fully parameterized high order models or of models with many variables is an ineffective, if not impractical, way of utilizing computing power. In the article we present methods for identifying the nonzero elements in VARMA(1,1) models, and show how these procedures can be used to construct models of higher order.
Affine Invariant Rank Methods in the Bivariate Location Model
Authors: Brown B. M. , Hettmansperger T. P. 
Published: December 2018

SUMMARY
The generalized multivariate median of Oja (Statist. and Prob. Letters 1(1983), 327–332) is used to define a multivariate notion of quantile, or rank, and to define a measure of scatter of multivariate linear models. The latter, when applied to the one- and two-sample bivariate location models, yields affine invariant analogues of the Wilcoxon rank-sum and signed-rank tests, and of the corresponding estimates.
Minimum Contrast Estimation for Spectral Densities of Stationary Processes
Authors: Taniguchi Masanobu 
Published: December 2018

SUMMARY
Let {z(n)} be a stationary process with mean zero and true spectral density g(λ). In this paper we approximate g(λ) by a parametric family f θ(λ) and propose a minimum contrast estimator θ^ which minimizes D(fθ,g^N)=∫−ππK{fθ(λ)/g^N(λ)}dλ with respect to θ, where K(.) is an appropriate function and ĝ N(λ) is a nonparametric spectral estimator of g(λ). We give the asymptotic distribution of θ^ and sufficient conditions such that θ^ is asymptotically efficient. Also, we show that for various spectra f θ(λ), if we choose K(.) in D(f θ, g) appropriately, we obtain a non-iterative efficient estimator of θ in explicit form.
Estimation and Model Identification for Continuous Spatial Processes
Authors: Vecchia A. V. 
Published: December 2018

SUMMARY
Formal parameter estimation and model identification procedures for continuous domain spatial processes are introduced. The processes are assumed to be adequately described by a linear model with residuals that follow a second-order stationary Gaussian random field and data are assumed to consist of noisy observations of the process at arbitrary sampling locations. A general class of two-dimensional rational spectral density functions with elliptic contours is used to model the spatial covariance function. An iterative estimation procedure alleviates many of the computational difficulties of conventional maximum likelihood estimation for non-lattice data. The procedure is applied to several generated data sets and to an actual ground-water data set.
A Method for the Estimation and Identification of Transfer Function Models
Authors: Poskitt D. S. 
Published: December 2018

SUMMARY
This paper proposes an approach to the simultaneous identification and estimation of transfer function models. An estimation procedure is advanced consisting of a sequence of four ordinary least squares calculations and the asymptotic properties of each step are presented, consistency and asymptotic efficiency being shown. A strategy for the identification of the model structure based on a selection criterion that arises naturally from the last step of the estimation algorithm is also investigated. Consideration is given to the numerical implementation of the techniques discussed, and finally a practical example is employed to illustrate the methods.
Arma Models with Double-Exponentially Distributed Noise
Authors: Damsleth Eivind , El-Shaarawi A. H. 
Published: December 2018

SUMMARY
The marginal and bivariate distributions of the observations generated from a standard autoregressive moving average scheme are derived, assuming the noise to have a double-exponential (Laplace) distribution. The distributions may differ substantially from their Gaussian counterparts. The AR(1) model with double-exponential noise is applied to a series of weekly measurements of sulphate concentration and is shown to give a significantly better fit when compared with the Gaussian model.
Bayes Estimation for the Marshall–Olkin Exponential Distribution
Authors: Peña Edsel A. , Gupta Arjun K. 
Published: December 2018

SUMMARY
Bayes estimators of the parameters of the Marshall–Olkin exponential distribution are obtained when random samples from series and parallel systems are available. The estimators are with respect to the quadratic loss function, and the prior distribution allows for prior dependence among the components of the parameter vector. Exact and approximate highest posterior density credible ellipsoids for the parameters are also obtained. In contrast with series sampling, the Bayes estimators under parallel sampling are not in closed form, and numerical procedures are required to obtain estimates. Bayes estimators of the reliability functions are also given. The gain in asymptotic precision of parallel estimates over series estimates is also ascertained theoretically.
Models for Exceedances Over High Thresholds
Authors: Davison A. C. , Smith R. L. 
Published: December 2018

SUMMARY
We discuss the analysis of the extremes of data by modelling the sizes and occurrence of exceedances over high thresholds. The natural distribution for such exceedances, the generalized Pareto distribution, is described and its properties elucidated. Estimation and model-checking procedures for univariate and regression data are developed, and the influence of and information contained in the most extreme observations in a sample are studied. Models for seasonality and serial dependence in the point process of exceedances are described. Sets of data on river flows and wave heights are discussed, and an application to the siting of nuclear installations is described.
Local Minima in Cross-Validation Functions
Authors: Hall Peter , Marron J. S. 
Published: December 2018

SUMMARY
The method of least squares cross-validation for choosing the bandwidth of a kernel density estimator has been the object of considerable research, through both theoretical analysis and simulation studies. The method involves the minimization of a certain function of the bandwidth. One of the less attractive features of this method, which has been observed in simulation studies but has not previously been understood theoretically, is that rather often the cross-validation function has multiple local minima. The theoretical results of this paper provide an explanation and quantification of this empirical observation, through modelling the cross-validation function as a Gaussian stochastic process. Asymptotic analysis reveals that the degree of wiggliness of the cross-validation function depends on the underlying density through a fairly simple functional, but dependence on the kernel function is much more complicated. A simulation study explores the extent to which the asymptotic analysis describes the actual situation. Our techniques may also be used to obtain other related results—e.g. to show that spurious local minima of the cross-validation function are more likely to occur at too small values of the bandwidth, rather than at too large values.
Modelling Extreme Multivariate Events
Authors: Coles Stuart G. , Tawn Jonathan A. 
Published: December 2018

SUMMARY
The classical treatment of multivariate extreme values is through componentwise ordering, though in practice most interest is in actual extreme events. Here the point process of observations which are extreme in at least one component is considered. Parametric models for the dependence between components must satisfy certain constraints. Two new techniques for generating such models are presented. Aspects of the statistical estimation of the resulting models are discussed and are illustrated with an application to oceanographic data.
Bayesian Inference for Medical Screening Tests: Approximations Useful for the Analysis of Acquired Immune Deficiency Syndrome
Authors: Johnson Wesley O. , Gastwirth Joseph L. 
Published: December 2018

SUMMARY
In this paper, we develop large sample Bayesian methods for assessing the accuracy of screening tests that are used to detect antibodies to the human immunodeficiency virus in donated blood, and for assessing the prevalence of the disease in the population sampled from. We obtain approximate joint and marginal posterior distributions for the predictive values positive and negative of a test and, additionally, we obtain approximate predictive distributions for the number of future individuals that will test positively or be truly positive out of a new sample or population of interest. We illustrate our methods with data from Canada and the UK.
A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation
Authors: Sheather S. J. , Jones M. C. 
Published: December 2018

SUMMARY
We present a new method for data-based selection of the bandwidth in kernel density estimation which has excellent properties. It improves on a recent procedure of Park and Marron (which itself is a good method) in various ways. First, the new method has superior theoretical performance; second, it also has a computational advantage; third, the new method has reliably good performance for smooth densities in simulations, performance that is second to none in the existing literature. These methods are based on choosing the bandwidth to (approximately) minimize good quality estimates of the mean integrated squared error. The key to the success of the current procedure is the reintroduction of a non-stochastic term which was previously omitted together with use of the bandwidth to reduce bias in estimation without inflating variance.
Diagnostics in Categorical Data Analysis
Authors: Andersen Erling B. 
Published: December 2018

SUMMARY
Diagnostics as measures of model deviations and of the influence of particular data sets are used extensively in modern regression analysis. For contingency tables, and more generally for the parametric multinomial distribution, it is not the influence of individual observations which is of interest, but rather the contribution to a lack of model fit or to the values of the parameter estimates from a single cell in the table, which must be evaluated. Hence diagnostics for contingency tables take somewhat different forms. In this paper such diagnostics are discussed and their applicability is illustrated with data sets analysed by the Goodman RC association model.
A Nonparametric Estimation Procedure for a Periodically Observed Three-State Markov Process, with Application to Aids
Authors: Frydman Halina 
Published: December 2018

SUMMARY
Estimation in a three-state Markov process with irreversible transitions in the presence of interval-censored data is considered. A nonparametric maximum likelihood procedure for the estimation of the cumulative transition intensities is presented. A self-consistent estimator of the parameters is defined and it is shown that the maximum likelihood estimator is a self-consistent estimator. This extends the idea of self-consistency introduced by Efron to the estimation of more than one parameter. An algorithm, based on self-consistency equations, is provided for the computation of the estimators. This algorithm is a generalization of an algorithm by Turnbull which yields an estimator of a distribution function for interval-censored univariate data. The methods are applied to Aids data.
On the Removal of Skewness by Transformation
Authors: Hall Peter 
Published: December 2018

SUMMARY
We suggest empirical transformations for removing most of the skewness of an asymmetric statistic. These transformations may be used as the basis for accurate confidence procedures or hypothesis tests and can be employed in conjunction with either a normal approximation or the bootstrap. Our approach differs from those of other researchers in that the transformation is monotone and invertible.