bluuebunny/crossref_metadata_2025_split huggingface dataset:
Inference from Accelerated Life Tests Using Filtering in Coloured Noise
Authors: Blackwell Louis M. , Singpurwalla Nozer D. 
Published: December 2018

SUMMARY
We present a new approach for inference from accelerated life tests. Our approach formulates such problems as inference under Kalman filter models with correlated observation errors. We restrict attention to exponential life distributions, and the power rule as a time transformation function. Extensions to other time transformation functions are straightforward; however, extensions to other distributions involve nonlinear filtering and are not considered. The advantages of our formulation are that we are able to incorporate uncertainty in the time transformation function and also are able to allow it to change with the stress. to validate our approach we consider some simulated data; to give it a sense of reality we apply it to actual data.
On the Use of Marginal Likelihood in Time Series Model Estimation
Authors: Wilson G. Tunnicliffe 
Published: December 2018

SUMMARY
In the context of time series regression, with an error model of the ARIMA type, the fitting of the regression can seriously bias the ARIMA model parameter estimates. Moreover, choosing between different error models on the basis of the smallest residual variance may lead to incorrect selection with a high probability, even in samples of moderate size. The marginal likelihood procedure is considered as a solution to these problems and examples are presented in the context of trend estimation, seasonal forecasting and mixed spectrum analysis.
Model Specification in Multivariate Time Series
Authors: Tiao George C. , Tsay Ruey S. 
Published: December 2018

SUMMARY
We propose a method to specify an appropriate yet parsimonious vector autoregressive moving average (ARMA) model for a given multivariate time series. By considering contemporaneous linear transformations of the vector process, we introduce the concept of scalar component models within the vector ARMA framework (a) to reveal possibly hidden simplifying structures of the process, (b) to achieve parsimony in parameterization and (c) to identify the exchangeable models. The simplifying structures are of particular importance in the analysis of multivariate time series because they are often not obvious from the observed data but can be used to gain insights to the process under study. The analytical tool used to search for scalar component models is a canonical correlation analysis of vector processes and the proposed procedures are illustrated via two real examples.
Embedded Models in Three-Parameter Distributions and Their Estimation
Authors: Cheng R. C. H. , Iles T. C. 
Published: December 2018

SUMMARY
Two distinct problems can arise in maximum likelihood estimation in certain three-parameter problems. One problem, associated with the fitting of a threshold parameter, occurs if the fitted distribution has to be very positively skewed. This problem is well known. However, there is a second and unrelated difficulty which occurs quite often in practice and which arises when the distribution is not at all skew. This problem is not so well understood. It is shown in this paper that, within the three-parameter model, there is an embedded two-parameter special case which corresponds to infinite parameter values in the original model. The problem arises when this embedded model is the best fit to the data. The problem is shown to be easily resolved by first carrying out a check to see whether the embedded model should be fitted instead of the three-parameter model. Formal tests for this are discussed. The gamma, inverse Gaussian, log-normal and Weibull distributions are examples where the problem occurs. Numerical examples are provided for illustration.
The Conditional Predictive Ordinate for the Normal Distribution
Authors: Pettit L. I. 
Published: December 2018

SUMMARY
The conditional predictive ordinate (CPO) is a Bayesian diagnostic which detects surprising observations. It has been used in a variety of situations such as univariate samples, the multivariate normal distribution and regression models. Results are presented about the most surprising observation which has minimum CPO. For the multivariate normal distribution it is shown that the most surprising observation must lie at one of the vertices of the convex hull. It is also shown that the observation with maximum Mahalanobis distance from the sample mean must lie on the convex hull. Results are given for the expected number of vertices on the convex hull when the sample is contaminated. An alternative, closely related diagnostic, the ratio ordinate measure, is presented. A numerical comparison of the two measures is given.
A Simple Method for the Adjustment of Profile Likelihoods
Authors: McCullagh Peter , Tibshirani Robert 
Published: December 2018

SUMMARY
We propose a simple adjustment for profile likelihoods. The aim of the adjustment is to alleviate some of the problems inherent in the use of profile likelihoods, such as bias, inconsistency and overoptimistic variance estimates. The adjustment is applied to the profile log-likelihood score function at each parameter value so that its mean is zero and its variance is the negative expected derivative matrix of the adjusted score function. For cases in which explicit calculation of the adjustments is difficult, we give two methods to simplify their computation: An ‘automatic’ simulation method that requires as input only the profile log-likelihood and its first few derivatives; first-order asymptotic expressions. Some examples are provided and a comparison is made with the conditional profile log-likelihood of Cox and Reid.
Alternative Smoothed Bootstraps
Authors: Young G. A. 
Published: December 2018

SUMMARY
Bootstrap estimation of simple population functionals is considered. The smoothed bootstrap (Efron, 1979, 1982) is compared with an alternative estimation procedure based on resampling ideas of Kendall and Kendall (1980). Specific examples of the estimation problem are considered, showing that the competing estimators may display different qualitative behaviours.
Construction of Block Designs Using Mathematical Programming
Authors: Whitaker D. , Triggs C. M. , John J. A. 
Published: December 2018

SUMMARY
The construction of optimal or nearly optimal block designs, using the A-optimality criterion, is formulated as a non-linear 0–1 programme. An approach which ignores the 0–1 constraint is suggested and its feasibility is examined by constructing block designs using the non-linear programming computer package MINOS.
Fisherian Inference in Likelihood and Prequential Frames of Reference
Authors: Dawid A. P. 
Published: December 2018

SUMMARY
In celebration of the centenary of the birth of Sir Ronald Fisher, this paper explores Fisher's conception of statistical inference, with special attention to the importance he placed on choosing an appropriate frame of reference to define the inferential model. In particular, we investigate inferential models which respect the likelihood principle or the prequential principle, and argue that these will typically have an asymptotic sampling theory justification.
Kernel Regression Estimation with Time Series Errors
Authors: Hart Jeffrey D. 
Published: December 2018

SUMMARY
Suppose that data y 1, ..., yn are observed according to the model yi=f((i−12)/n)+ϵi,i=1,…,n, where f is a smooth function and {ϵ1,…,ϵn} is a sample from a zero-mean, covariance stationary time series. The problem of objectively choosing the bandwidth of a kernel estimate for f is addressed. It is shown both theoretically and by simulation that cross-validation produces extremely rough kernel estimates when the data are sufficiently positively correlated. This makes it inadvisable to use residuals from a cross-validated kernel estimate as a means of estimating the covariance function of the errors. Alternative methods of estimating the covariance function are proposed. In a simulation study, incorporating these estimated covariances into a risk estimation procedure leads to more efficient smoothing of positively correlated data.
Bivariate Distributions with Conditionals in Prescribed Exponential Families
Authors: Arnold B. C. , Strauss D. J. 
Published: December 2018

SUMMARY
We characterize the class of bivariate distributions such that the conditional distributions belong to any specified exponential families. The result leads at once to several bivariate families derived by Castillo and Galambos and by Arnold and Strauss, as well as to distributions with Poisson, geometric and other conditionals. We indicate methods to simulate samples from the distributions and estimate their parameters.
An Approximate Bartlett Adjustment for Testing the Goodness of Fit of Multinomial Regression Models
Authors: Lugtenburg D. 
Published: December 2018

SUMMARY
For up to four categories and given sufficient replications per design point (eight or more seem to be enough), an adjusted likelihood ratio statistic for testing the goodness of fit of multinomial regression models is proposed. This adjustment does not depend on the multinomial model used and therefore will have a wide range of applications. It is certainly useful for the proportional odds model, introduced by McCullagh. This proportional odds model is used in some simulation studies to investigate the performance of the new statistic.
Optimality and Robustness to the Unavailability of Blocks in Block Designs
Authors: Bhaumik Dulal K. , Whittinghill Dexter C. 
Published: December 2018

SUMMARY
This paper investigates the optimality of designs derived from binary, variance-balanced incomplete block designs (BIBDs) by removing t equal-sized blocks which are not necessarily disjoint. It is shown that the optimal design is derived by removing blocks which have disjoint sets of treatments, and the worst design is derived by removing identical blocks. For BIBDs and t = 2 all resulting designs are ordered. The implication for competing BIBDs which have the same parameters v, b and k but different support sizes (numbers of distinct blocks) is addressed. Optimality and robustness are measured through the non-zero eigenvalues of the C-matrix of the design missing observations using the universal optimality criteria of Bondar.
A Bivariate Signed Rank Test for the Two-Sample Location Problem
Authors: Peters Dawn , Randles Ronald H. 
Published: December 2018

SUMMARY
A signed rank affine invariant test for the difference in location between two elliptically symmetric populations is proposed. Asymptotic properties of the test are developed under the null hypothesis and under contiguous alternatives. The proposed statistic is compared with three of its competitors using Monte Carlo studies and Pitman asymptotic relative efficiencies. It is seen that the signed rank statistic introduced is especially powerful when the underlying distribution is light tailed. For heavy-tailed distributions a bivariate test due to Mardia is preferred. However, the proposed statistic performs better than Hotelling's T 2-statistic for both light- and heavy-tailed populations, performing almost as well as Hotelling's T 2-statistic under bivariate normality.
Some Tools for Functional Data Analysis
Authors: Ramsay J. O. , Dalzell C. J. 
Published: December 2018

SUMMARY
Multivariate data analysis permits the study of observations which are finite sets of numbers, but modern data collection situations can involve data, or the processes giving rise to them, which are functions. Functional data analysis involves infinite dimensional processes and/or data. The paper shows how the theory of L-splines can support generalizations of linear modelling and principal components analysis to samples drawn from random functions. Spline smoothing rests on a partition of a function space into two orthogonal subspaces, one of which contains the obvious or structural components of variation among a set of observed functions, and the other of which contains residual components. This partitioning is achieved through the use of a linear differential operator, and we show how the theory of polynomial splines can be applied more generally with an arbitrary operator and associated boundary constraints. These data analysis tools are illustrated by a study of variation in temperature–precipitation patterns among some Canadian weather-stations.
Percentage Points of Likelihood Ratio Tests for Threshold Autoregression
Authors: Chan K. S. 
Published: December 2018

SUMMARY
Likelihood ratio tests for threshold autoregression have been considered by Chan, and Chan and Tong. However, except for the simplest case, percentage points of the (asymptotic) null distribution of the test statistic have not been tabulated. The purpose of this paper is to tabulate the approximate upper percentage points for the general case. This is done via the Poisson clumping heuristic developed by Aldous. Monte Carlo experiments show that the approximation is quite good. As an illustration, the test is then applied to two data sets.
Comparison between the Conditional Likelihood Ratio and the Usual Likelihood Ratio Tests
Authors: Mukerjee Rahul 
Published: December 2018

SUMMARY
This paper compares, under contiguous alternatives, the conditional likelihood ratio test of Cox and Reid with the usual likelihood ratio test on the basis of second-order power. It is seen that although the power of the former is identical, up to the second order, with that of the likelihood ratio test with known nuisance parameter, it does not hold with the latter. This provides a justification for the use of the conditional likelihood ratio test, rather than the usual likelihood ratio test, in the presence of a nuisance parameter.
Gittins Indices and Oil Exploration
Authors: Benkherouf L. , Glazebrook K. D. , Owen R. W. 
Published: December 2018

SUMMARY
An earlier study by Benkherouf and Bather considered the question of when the results of oil exploration in a single area were sufficiently discouraging to render it optimal to stop drilling altogether. This stopping problem is now considerably elaborated by the inclusion of a choice between several areas in which to explore. Our oil exploration problem is modelled as a Bayesian sequential decision problem with a Markovian structure. Optimal drilling strategies are determined by Gittins indices. These indices also play an important part in the evaluation of heuristics.
Prediction for Seemingly Unrelated Regressions
Authors: Percy David F. 
Published: December 2018

SUMMARY
The seemingly unrelated regressions model is described and analysed from a Bayesian perspective. The predictive density for this model cannot, in general, be evaluated analytically. Two approximations are proposed and investigated. These are Gibbs sampling and a first-order approximation based on a Bayes estimate of the precision matrix. These approximations are then compared on simulated data and both appear to give good results. Extensions to allow for missing data are also discussed.
Modelling Probabilistic Agent Opinion
Authors: West Mike , Crosse Jo 
Published: December 2018

SUMMARY
A single agent (an individual, expert or model) provides a decision maker with probabilistic information partially or completely describing the agent's opinion about a collection of uncertain quantities or events. This paper discusses ways in which the decision maker may model the agent's opinion to provide rules for updating his own probability for a related event or random quantity of particular interest. Concepts discussed include the relevance of the agent's information and experience, the accord between the agent and decision maker in terms of common or conflicting information and calibration of probability assessments. New theory develops and extends that of Genest and Schervish, requiring only a partial specification of the decision maker's prior over the agent's opinion. Several illustrative examples are developed.
Linear Filters and Non-Linear Systems
Authors: Broomhead D. S. , Huke J. P. , Muldoon M. R. 
Published: December 2018

SUMMARY
It has been asserted in the literature that the low pass filtering of time series data may lead to erroneous results when calculating attractor dimensions. Here we prove that finite order, non-recursive filters do not have this effect. In fact, a generic, finite order, non-recursive filter leaves invariant all the quantities that can be estimated by using embedding techniques such as the method of delays.
Empirical Functionals and Efficient Smoothing Parameter Selection
Authors: Hall Peter , Johnstone Iain 
Published: December 2018

SUMMARY
A striking feature of curve estimation is that the smoothing parameter ĥ 0, which minimizes the squared error of a kernel or smoothing spline estimator, is very difficult to estimate. This is manifest both in slow rates of convergence and in high variability of standard methods such as cross-validation. We quantify this difficulty by describing nonparametric information bounds and exhibit asymptotically efficient estimators of ĥ 0 that attain the bounds. The efficient estimators are substantially less variable than cross-validation (and other current procedures) and simulations suggest that they may offer improvements at moderate sample sizes, at least in terms of minimizing the squared error. The key is a stochastic decomposition of the empirical functional ĥ 0 in terms of a smooth quadratic functional of the unknown curve. Examples include the estimation of densities, regression functions and continuous signals in Gaussian white noise.
Collapsibility of Relative Risk in Contingency Tables with a Response Variable
Authors: Geng Zhi 
Published: December 2018

SUMMARY
We consider the collapsibility of relative risks in contingency tables with a polytomous response variable. Simple collapsibility of relative risks means that they are consistent over all levels of a collapsed variable and also coincide with the corresponding marginal relative risk. Strong collapsibility of relative risks means that they retain simple collapsibility no matter how the variable is partially collapsed. We present necessary and sufficient conditions for simple and strong collapsibilities of relative risks.
Asymptotically Efficient Allocation Rules for Two Bernoulli Populations
Authors: Li Zhaohai , Zhang Cun-Hui 
Published: December 2018

SUMMARY
Given two Bernoulli populations with unknown means, we consider the problem of sampling x 1, x 2, ... sequentially from these populations such as to maximize the expected value of the sum S n = x 1 + x 2 + ... + x n as n → ∞. We obtain an asymptotically efficient rule. Simulation studies show that it performs well for moderate values of n.
A Logic of Probability, with Application to the Foundations of Statistics
Authors: Vovk V. G. 
Published: December 2018

SUMMARY
A simple example shows that the classical theory of probability implies more than one can deduce via Kolmogorov's calculus of probability. Developing Dawid's ideas I propose a new calculus of probability which is free from this drawback. This calculus naturally leads to a new interpretation of probability. I argue that attempts to create a general empirical theory of probability should be abandoned and we should content ourselves with the logic of probability establishing relations between probabilistic theories and observations. My approach to the logic of probability is based on a variant of Ville's principle of the excluded gambling strategy. In addition to the classical theory of probability this approach is applied to the probabilistic theories provided by the problem of testing validity of probability forecasts and by statistical models.
Approximating Posterior Distributions by Mixtures
Authors: West Mike 
Published: December 2018

SUMMARY
Kernel density estimation techniques are used to smooth simulated samples from importance sampling function approximations to posterior distributions, resulting in revised approximations that are mixtures of standard parametric forms, usually multivariate normal or T-distributions. Adaptive refinement of such mixture approximations involves repeating this process to home-in successively on the posterior. In fairly low dimensional problems, this provides a general and automatic method of approximating posteriors by mixtures, so that marginal densities and other summaries may be easily computed. This is discussed and illustrated, with comment on variations and extensions suited to sequential Bayesian updating of Monte Carlo approximations, an area in which existing and alternative numerical methods are difficult to apply.
The Assumptions on Which Causal Inferences Rest
Authors: Stone Richard 
Published: December 2018

SUMMARY
Statisticians commonly make causal inferences from the results of randomized experiments, but usually question causal inferences from observational studies on the grounds that untestable assumptions are required. This paper explains the basis for this situation and examines, within quite a general framework, various assumptions that appear in the literature. It is demonstrated how the role of each assumption is intimately related to the sort of causal inference being considered. Contrary to general belief, it is shown that neither ‘no confounding’ nor ‘randomization’ are sufficient assumptions for testing the fundamental causal hypothesis of ‘no causation’. They become sufficient, however, if supplemented by a ‘modelling’ assumption for how unobserved covariates affect potential responses. Without supplementary assumptions, no confounding and randomization allow testing of weaker but more important hypotheses, such as ‘no mean effect’. This follows from the sufficiency of an assumption of ‘ignorable treatment assignment’ for testing the hypothesis of ‘no distribution effect‘. It is argued that these ideas will have some operational relevance if we can quantify our beliefs about how closely assumptions hold. to illustrate, a novel form of sensitivity analysis is contrasted with an analysis presented by Rosenbaum and Rubin.
Bayesian Interval Estimates Which are Also Confidence Intervals
Authors: Severini Thomas A. 
Published: December 2018

SUMMARY
Let Y 1, . . ., Yn denote independent observations each distributed according to a distribution depending on a scalar parameter θ suppose that we are interested in constructing an interval estimate for θ. One approach is to use Bayesian inference. For a given prior density, we can construct an interval such that the posterior probability that θ lies in the interval is some specified value. In this paper, a method is given for constructing a Bayesian interval estimate such that the coverage probability of the interval is approximately equal to the posterior probability of the interval.
Canonical Correlation Analysis When the Data are Curves
Authors: Leurgans S. E. , Moyeed R. A. , Silverman B. W. 
Published: December 2018

SUMMARY
It is not immediately straightforward to extend canonical correlation analysis to the context of functional data analysis, where the data are themselves curves or functions. The obvious approach breaks down, and it is necessary to use a method involving smoothing in some way. Such a method is introduced and discussed with reference to a data set on human gait. The breakdown of the unsmoothed method is illustrated in a practical context and is demonstrated theoretically. A consistency theorem for the smoothed method is proved.
Adversarial Life Testing
Authors: Lindley Dennis V. , Singpurwalla Nozer D. 
Published: December 2018

SUMMARY
The life testing of items that exhibit a distribution of times to failure is undertaken for making decisions such as design qualification and reliability demonstration. In such contexts, procedures based on the Bayesian paradigm have assumed a common prior distribution of item reliability by both the consumer and the manufacturer. In this paper we consider the adversarial situation wherein both parties agree on a statistical model for lifetimes but use different prior distributions. We require that the consumer's criteria for acceptance and rejection be known to the manufacturer. We illustrate our approach via the case of exponentially distributed life lengths and relate it to the approach specified in standard MIL STD 781C.