Augustine C. M. Wong

York University · Department of Mathematics and Statistics

Complex data pose unique challenges for data processing [...]

This paper reviews the potential use of fuzzy c-means clustering (FCM) and explores modifications to the distance function and centroid initialization methods to enhance image segmentation. The application of interest in the paper is the segmentation of breast tumours in mammograms. Breast cancer is the second leading cause of cancer deaths in Cana...

The two-parameter gamma distribution is one of the most commonly used distributions in analyzing environmental, meteorological, medical, and survival data. It has a two-dimensional minimal sufficient statistic, and the two parameters can be taken to be the mean and shape parameters. This makes it closely comparable to the normal model, but it diffe...

In recent years, the Poisson lognormal mixed model has been frequently used in modeling count data because it can accommodate both the over-dispersion of the data and the existence of within-subject correlation. Since the likelihood function of this model is expressed in terms of an intractable integral, estimating the parameters and obtaining infe...

The scope of the contributions to this Special Issue will include new and original research motivated by real-world problems. The articles will focus on approximate inference, methods, and statistical applications in a wide range of areas, including finance, economics, environmetrics, biological, psychonometrics, social sciences, physical sciences,...

A higher-order likelihood-based asymptotic method to obtain inference for the difference between two KS Sharpe ratios when gross returns of an investment are assumed to be lognormally distributed is proposed. Theoretically, our proposed method has O n − 3 / 2 distributional accuracy, whereas conventional methods for inference have O n − 1 / 2 distr...

The infinite weighted sum of random variables originates from the linear process, random walk, and series representation of Brownian motion and stochastic integral in goodness-of-fit test. In general, this infinite weighted sum of random variables is approximated by the truncated one-term approximation. However, it is very time consuming to numeric...

Without the ability to use research tools and procedures that yield consistent measurements, researchers would be unable to draw conclusions, formulate theories, or make claims about generalizability of their results. In statistics, the coefficient of variation is commonly used as the index of reliability of measurements. Thus, comparing coefficien...

The linear model often serves as a starting point for applying statistics in psychology. Often, formal training beyond the linear model is limited, creating a potential pedagogical gap because of the pervasiveness of data non-normality. We reviewed 61 recently published undergraduate and graduate textbooks on introductory statistics and the linear...

A frequently encountered statistical problem is to determine if the variability among k populations is heterogeneous. If the populations are measured using different scales, comparing variances may not be appropriate. In this case, comparing coefficient of variation (CV) can be used because CV is unitless. In this paper, a non-parametric test is in...

Four CaCO3 added LLDPE polymer systems were compounded in a 24 mm diameter, co-rotating, closely intermeshed twin-screw extruder. The compounds differed from each other by the weight percent of CaCO3 added. A laser beam system installed at the die exit of a capillary rheometer was used to determine the diameter of the swollen extrudate. Extrudate s...

The present work reports the empirical findings of the effects of mean particle size and weight percentage of CaCO3 on selected rheological characteristics of filled LDPE. The experimental results indicated that the two parameters studied had noticeable influence on the selected rheological properties of LDPE. Studies on the slip velocity and criti...

The Sharpe ratio is a widely used risk-adjusted performance measurement in economics and finance. Most of the known statistical inferential methods devoted to the Sharpe ratio are based on the assumption that the data are normally distributed. In this article, without making any distributional assumption on the data, we develop the adjusted empiric...

This paper proposes composite likelihood based tests to perform model comparisons. The models are compared based on their expected composite Kullback–Leibler distances to the true underlying model. The asymptotic distributions of the test statistics are derived under both fixed alternatives and local alternatives. With an additional variance estima...

Data transformations have been promoted as a popular and easy-to-implement remedy to address the assumption of normally distributed errors (in the population) in linear regression. However, the application of data transformations introduces non-ignorable complexities which should be fully appreciated before their implementation. This paper adds to...

In many areas of applied statistics, confidence intervals for the mean of the population is of interest. Confidence intervals are typically constructed assuming normality although non-normally distributed data are a common occurrence in practice. Given a large enough sample size, confidence intervals for the mean can be constructed by applying the...

In many areas of applied statistics, confidence intervals for the mean of the population are of interest. Confidence intervals are typically constructed assuming normality although non-normally distributed data are a common occurrence in practice. Given a large enough sample size, confidence intervals for the mean can be constructed by applying the...

We consider the use of default priors in the Bayes methodology for seeking information concerning the true value of a parameter. By default prior, we mean the mathematical prior as initiated by Bayes [Philos. Trans. R. Soc. Lond. 53 (1763) 370-418] and pursued by Laplace [Théorie Analytique des Probabilités (1812) Courcier], Jeffreys [Theory of Pro...

Stress-strength reliability problems arise frequently in applied statistics and related fields. Often they involve two independent and possibly small samples of measurements on strength and breakdown pressures (stress). The goal of the researcher is to use the measurements to obtain inference on reliability, which is the probability that stress wil...

The cumulant generating function of the statistic (Formula presented.) defined in Chang et al. (Stat Probab Lett 82:1755–1760, 2012) for testing homogeneity of the scale-like parameters of several inverse Gaussian distributions is derived in this paper. Then two saddlepoint-based methods are proposed to obtain the asymptotic distribution function o...

We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method is more accurate than standard methods as it possesses a third-order distri-butional accuracy. Simulations studies are provided to show t...

In this paper, a small-sample asymptotic method is proposed for higher order inference in the stress–strength reliability model, R=P(YX), where X and Y are distributed independently as Burr-type X distributions. In a departure from the current literature, we allow the scale parameters of the two distributions to differ, and the likelihood-based thi...

This paper derives a saddlepoint based approximation for the cumulative distribution function of the Bartlett–Box M-statistic that tests the equality of covariance matrices for several samples from graphical Gaussian models Markov with respect to a decomposable graph . The proposed saddlepoint-based method has third-order accuracy (). Simulation re...

Recent years have seen a heightened interest in estimating effect size—a common measure of effect magnitude in biomedical research—because of its direct clinical relevance. In this article, three interval estimates of effect size for randomized comparative parallel-group studies with unequal variances are discussed. Two real-life examples illustrat...

This article develops a procedure to obtain highly accurate confidence interval estimates for the stress-strength reliability R = P(X > Y) where X and Y are data from independent normal distributions of unknown means and variances. Our method is based on third-order likelihood analysis and is compared to the conventional first-order likelihood rati...

In this paper, a new approximation of the marginal posterior distribution function is obtained. Moreover, for the location-scale model, by applying the shrinkage argument, a new approximation of the conditional distribution function of the signed likelihood ratio statistic given an ancillary statistic is derived from the approximated marginal poste...

An improved likelihood-based method is proposed to test for the significance of the first-order moving average model. Compared with commonly used tests which depend on the asymptotic properties of the maximum likelihood estimate and the likelihood ratio statistic, the proposed method has remarkable accuracy. Application of the method to a data set...

In this paper, we consider the problem of inference on the correlation coefficient from a bivariate normal distribution with known variances. The problem is theoretically interesting because the model belongs to the curved exponential family and the standard inferential methods cannot be directly applied. It is also of practical interest because th...

The Sharpe ratio is the prominent risk-adjusted performance measure used by practitioners. Statistical testing of this ratio using its asymptotic distribution has lagged behind its use. In this paper, highly accurate likelihood analysis is applied for inference on the Sharpe ratio. Both the one- and two-sample problems are considered. The methodolo...

In applied work, the two-parameter exponential distribution gives useful representations of many physical situations. Confidence interval for the scale parameter and predictive interval for a future independent observation have been studied by many, including Petropoulos (2011) and Lawless (1977), respectively. However, interval estimates for the t...

A simple connection between the Bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant of the p∗ formula–an approximate conditional density for the maximum likelihood estimate given an exact or an approximate ancillary statistic–was established in Barndorff-Nielsen and Cox (1984). In this paper, the exp...

Hidden periodicity is a featured phenomenon in many area of the real world, for example, in astronomy and climatology. Under white noise assumption, the problem of searching for hidden periodicity has been studied extensively in the literature. However, under mixed spectra, especially when compound periodicities are involved, most of the existing m...

Kim and Hayter (20087. Kim , J. , Hayter , A. J. ( 2008 ). Testing the equality of the non centrality parameters of the two non central t-distributions with identical degrees of freedom . Communications in Statistics: Simulation and Computation 37 : 1709 – 1717 . [Taylor & Francis Online], [Web of Science ®]View all references) showed that testin...

This paper deals with the interval estimation of P(Y<X)P(Y<X) when X and Y are two independent generalized Pareto random variables with a common scale parameters. An asymptotic confidence interval for P(Y<X)P(Y<X) is constructed based on the modified signed log-likelihood ratio statistic. Monte Carlo simulations are performed to illustrate the accu...

In order to model climate data time series that often contain periodic variations, trends, and sudden changes in mean (mean shifts, mostly artificial), this study proposes a hybrid-domain (HD) algorithm, which incorporates a time domain test and a newly developed frequency domain test through an iterative procedure that is analogue to the well know...

Inference for the difference of two independent normal means has been widely studied in staitstical literature. In this paper, we consider the case that the variances are unknown but with a known relationship between them. This situation arises frequently in practice, for example, when two instruments report averaged responses of the same object ba...

An improved likelihood-based method based on Fraser et al. (1999) is proposed in this paper to test the significance of the second lag of the stationary AR(2) model. Compared with the test proposed by Fan and Yao (2003) and the signed log-likelihood ratio test, the proposed method has remarkable accuracy. Simulation studies are performed to illustr...

In introductory statistics texts, the power of the test of a one-sample mean when the variance is known is widely discussed. However, when the variance is unknown, the power of the Student's t-test is seldom mentioned. In this note, a general methodology for obtaining inference concerning a scalar parameter of interest of any exponential family mod...

The visualization and image analysis techniques developed by the authors for the study of quantifying the dynamic quality of mixing of a single-screw extruder were employed to investigate the mixing performance of screws of different configurations. The mixing quality was quantified by calculating the variances of the light intensity of the bitmap...

In this paper, a likelihood-based analysis is developed and applied to obtain interval estimates for the stress-strength reliability R=P(XY) using lower record data from the one parameter generalized exponential distribution. The proposed method has a third order of accuracy. Monte Carlo simulations are used to illustrate the supreme accuracy of th...

Statistics has many inference procedures for examining a model with data to obtain information concerning the value of a parameter of interest. If these give different results for the same model and data, one can reasonably want a satisfactory explanation. Over the last eighty years, three very simple examples have appeared intermittently in the li...

Wong (200812. Wong , A. ( 2008 ). Approximating the F distribution via a general version of the modified signed log-likelihood ratio statistic . Computational Statistics & Data Analysis 53 : 3902 – 3912 . [CrossRef]View all references) proposed a third-order likelihood-based method to approximate the p-value function of any scalar parameter of the...

The two-parameter gamma model is widely used in reliability, environmental, medical and other areas of statistics. It has a two-dimensional sufficient statistic, and a two-dimensional parameter which can be taken to describe shape and mean. This makes it closely comparable to the normal model, but it differs substantially in that the exact distribu...

A sample (X1 …, Xn) is drawn from a population of size N. Karlin (1974) conjectured that for any function ϕ in a certain class of real-valued functions on the sample space, ϕ is at least as large for sampling with replacement as for any other random replacement sampling plan. This conjecture is proved under the assumption that ≫On tire un échantill...

Testing for first-order autocorrelation in small samples using the standard asymptotic test can be seriously misleading. Recent methods in likelihood asymptotics are used to derive more accurate p-value approximations for testing the autocorrelation parameter in a regression model. The methods are based on conditional evaluations and are thus speci...

A simple normal approximation for the cumulative distribution function of the F distribution is obtained via a general version of the modified signed log-likelihood ratio statistic. This approximation exhibits remarkable accuracy even when the degrees of freedom are small. Using the same methodology, but with a simpler set up, simple and accurate n...

The theoretical advancements in higher-order likelihood-based inference methods have been tremendous over the past two decades. The application of these methods in the applied literature however has been far from widespread. A critical barrier to adoption has likely been the computational difficulties associated with the implementation of these met...

Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual evaluation of such $p$-values is by simulations, and such simulations do verify that the global distribution of the $...

In this paper, a likelihood based analysis is developed and applied to obtain confidence intervals and p values for the stress-strength reliability R = P(X < Y) with right truncated exponentially distributed data. The proposed method is based on theory given in Fraser et al. (Biometrika 86:249–264, 1999) which involves implicit but appropriate cond...

Inference concerning the correlation coefficient of two random variables from the bivariate normal distribution has been investigated by many authors. In particular, Fisher [1915. Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika 10, 507-521] and Hotelling [1953. New lig...

Statistical inference methods for the Weibull parameters and their functions usually depend on extensive tables, and hence are rather inconvenient for the practical applications. In this paper, we propose a general method for constructing confidence intervals for the Weibull parameters and their functions, which eliminates the need for the extensiv...

A standard approach to the analysis of skewed response data with concomitant information is to use a log-transformation to normalize the distribution of the response variable and then conduct a log- regression analysis. However, the mean response at original scale is often of interest. El-Shaarawi and Viveros developed an interval estimation of the...

The Weibull distribution is widely used in lifetime data analysis. For example, in studies on the time to the occurrence of tumors in human populations or in laboratory animals, the time of occurrence of tumors is generally assumed to be distributed as a Weibull distribution. Moreover, in engineering, the voltage levels at which failure occurred in...

Likelihood is widely used in statistical applications, both for the full parameter by obvious direct calculation and for component interest parameters by recent asymptotic theory. Often, however, we want more detailed information concerning an inference procedure, information such as say the distribution function of a measure of departure which wou...

In the recent literature on option valuation, Fourier analysis has been successfully applied to determine numerically the prices of options. However, most of these numerical methods can both be slow and inaccurate. Rogers and Zane (Ann. Appl. Probab. 9 (1999) 493-503) first propose the application of the saddlepoint approximation method to compute...

The linear and nonlinear seemingly unrelated regression problem with general error distribution is analyzed using recent likelihood theory that arguably provides the definitive distribution for assessing a scalar parameter; this involves implicit but well defined conditioning and marginalization for determining intrinsic measures of departure. High...

Recent third-order likelihood analysis theory is applied to obtain improved confldence intervals for scalar component interest parameters of the Weibull model. This theory involves implicit but appropriate conditioning and marginalization. Both the censored and complete Weibull models are examined where primary interest is focussed on assessing the...

Inference concerning the ratio of two means based two independent two-parameter gamma models with common shape parameter was examined in Booth et al. (19994. Booth , J. G. , Hobert , J. P. and Ohman , P. A. (1999). On the probable error of the ratio of two gamma means. Biometrika, 86: 439–452. View all references) and a computationally intensive...

An improved interval estimation for the two-parameter Birnbaum–Saunders distribution is discussed. The proposed method is based on the recently developed higher-order likelihood-based asymptotic procedure. The probability coverages of confidence intervals are based on the proposed method and those procedures discussed in Ng et al. (Comput. Statist....

Recent likelihood theory gives complete inference for scalar parameters in continu- ous statistical models; the methodology involves conditioning at an initial stage, and marginalization at a subsequent stage. Using three simple examples we outline this general route from model with data to likelihood and p-value function for assessing an arbitrary...

The Valencia International Meetings on Bayesian Statistics, held every four years, provide the main forum for researchers in the area of Bayesian Statistics to come together to present and discuss frontier developments in the field. The resulting Proceedings provide a definitive, up-to-date overview encompassing a wide range of theoretical and appl...

To construct a confidence interval for the mean of a log-normal distribution in small samples, we propose likelihood-based approaches - the signed log-likelihood ratio and modified signed log-likelihood ratio methods. Extensive Monte Carlo simulation results show the advantages of the modified signed log-likelihood ratio method over the signed log-...

The estimation of signal frequency count in the presence of background noise has had much discussion in the recent physics literature, and Mandelkern [1] brings the central issues to the statistical community, leading in turn to extensive discussion by statisticians. The primary focus however in [1] and the accompanying discussion is on the constru...

Bartlett's test for homogeneity of variances is rather nonrobust. However, when it is applicable, it is more powerful than various other tests. Dyer and Keating (198016. Dyer , D. D. and Keating , J. P. 1980. On the determination of critical values for Bartlett's test. J. Amer. Statist. Assoc., 75: 313–319. [Taylor & Francis Online], [Web of Scie...

For an interest parameter ψ(θ) the Bayesian method eliminates the nuisance parameter λ(θ) by integrating with respect to a conditional prior for λ given ψ. This conditional prior may be difficult to specify in both the subjective and objective Bayesian contexts. We propose the use of results from likelihood theory that give highly accurate third or...

Existing methods for comparing the means of two independent skewed log-normal distributions do not perform well in a range of small-sample settings such as a small-sample bioavailability study. In this article, we propose two likelihood-based approaches-the signed log-likelihood ratio statistic and modified signed log-likelihood ratio statistic-for...

In applied statistics, the coefficient of variation is widely calculated and interpreted even when the sample size of the data set is very small. However, confidence intervals for the coefficient of variation are rarely reported. One of the reasons is the exact confidence interval for the coefficient of variation, which is given in Lehmann (Testing...

We study a factor analysis model with two normally distributed observations and one factor. Two approximate conditional inference procedures for the factor loading are developed. The first proposal is a very simple procedure but it is not very accurate. The second proposal gives extremely accurate results even for very small sample size. Moreover,...

In this paper, the authors propose saddlepoint approximation methods for fast and accurate computation of value-at-risk in large complex portfolios. The method is applicable to portfolios whose value may be estimated by means ofdelta±gamma'' approximation based on a large number of underlying risk factors whose random vector of returns has a known...

this paper see http://www.math.yorku.ca/Who/Faculty/AWong/research.html. First we express the log density as a Taylor series to fourth degree about some convenient point. As our typical interest lies in probabilities calculated relative to an observed data point we take the expansion point to be (y

We develop simple approximations for the p-values to use with regression models having linear or nonlinear parameter structure and normal or nonnormal error distribution; computer iteration then gives confidence intervals. Both frequentist and Bayesian versions are given. The approximations are derived from recent developments in likelihood analysi...

INTRODUCTION Recent methods of third order asymptotics can produce significance probabilities that have remarkable accuracy, but for implementation require the sample space dimension to be equal to that for the full parameter. From a practical viewpoint this effectively restricts the approximations to location, transformation and exponential models...

Fraser (1968) and Lawless (1982, Appendix G) discussed exact conditional intervals for the parameters and quantiles of the location-scale model when complete data are used. Moreover, Lawless (1982) extended the exact method to failure-censored (Type II censored) data. Nevertheless, the exact intervals are difficult to obtain in practice and are una...

We show the second order relative accuracy, on bounded sets, of the studentized bootstrap, exponentially tilted bootstrap and nonparametric likelihood tilted bootstrap, for means and smooth functions of means. We also consider the relative errors for larger deviations. Our method exploits certain connections between Edgeworth and saddlepoint approx...

The use of the Pareto distribution as a model for various socio-economic phenomena dates back to the late nineteenth century. Recently, it has also been recognized as a useful model for the analysis of lifetime data. In this paper, we apply the approximate studentization method to obtain inference for the scale parameter of the Pareto distribution,...

This article compares the accuracy of tail probabilities obtained by various approximate inference procedures for the shape parameter of the gamma distribution which has one or more nuisance parameters. The approximate inference procedures being studied are the asymptotic normality of the maximum likelihood estimator, the asymptotic normality of th...

A simple and accurate method is discussed for approximating the noncentral chi‐squared distribution; it is based on recent developments in third order asymptotic methods. The method is easy to apply and uses only a standard normal distribution function evaluation.

With a parametric model, a measure of departure for an interest parameter is often easily constructed but frequently depends in distribution on nuisance parameters; the elimination of such nuisance parameter effects is a central problem of statistical inference. Fraser & Wong (1993) proposed a nuisance-averaging or approximate Studentization method...

Sometimes we cannot specify a statistical model in a parametric form completely. For example, we might assume that a random variable has a distribution that is roughly normal in the centre of the distribution but with tails that are arbitrary. We might then be interested in inference for the mean of the distribution, using methods that are insensit...

The problem of predicting a future observation based on an observed sample is discussed. As a device for eliminating the parameter from the conditional distribution of a future observation given the observed sample, we suggest averaging with respect to an exact or approximate confidence distribution function. It is shown that in many standard probl...