Statistical Analysis Of Cometary Data

In this study an attempt is made to assess statistically the validity of two theories as to the origin of comets. This subject still leads to great controversy amongst astronomers but recently two main schools of thought have developed.

These are that comets are of

(i) planetary origin,

(ii) interstellar origin.

Many theories have been expanded within each school of thought but at the present time one theory in each is generally accepted. This paper sets out to identify the statistical implications of each theory and evaluate each theory in terms of their implications.     

Is there an alternative to the european farm typology?

The 1978 European Community Typology for Agricultural Holdings is described in this paper and contrasted with a data based, polythetic-multivariate classification based on cluster analysis.

The requirement to reduce the size of the variable set employed in an optimisation-partition method of clustering suggested the value of principal components and factor analysis for the identification of major ‘source’ dimensions against which to measure farm differences and similarities.

The Euclidean cluster analysis incorporating the reduced dimensions quickly converged to a stable solution and was little influenced by the initial number or nature of ‘seeding’ partitions of the data.

The assignment of non-sampled observations from the population to cluster classes was completed using classification functions.

The final scheme, based on a sample of over 2,000 observations, was found to be both capable of interpretation and meaningful in terms of agricultural structure and practice and much superior in its explanatory power when compared with a version of the principal activity typology.     

A threshold based approach to merge data in financial risk management

According to the last proposals by the Basel Committee, banks are allowed to use statistical approaches for the computation of their capital charge covering financial risks such as credit risk, market risk and operational risk.

It is widely recognized that internal loss data alone do not suffice to provide accurate capital charge in financial risk management, especially for high-severity and low-frequency events. Financial institutions typically use external loss data to augment the available evidence and, therefore, provide more accurate risk estimates. Rigorous statistical treatments are required to make internal and external data comparable and to ensure that merging the two databases leads to unbiased estimates.

The goal of this paper is to propose a correct statistical treatment to make the external and internal data comparable and, therefore, mergeable. Such methodology augments internal losses with relevant, rather than redundant, external loss data.     

Implicit Estimation for the Stochastic Volatility Model

Efficient, accurate, and fast Markov Chain Monte Carlo estimation methods based on the Implicit approach are proposed. In this article, we introduced the notion of Implicit method for the estimation of parameters in Stochastic Volatility models.

Implicit estimation offers a substantial computational advantage for learning from observations without prior knowledge and thus provides a good alternative to classical inference in Bayesian method when priors are missing.

Both Implicit and Bayesian approach are illustrated using simulated data and are applied to analyze daily stock returns data on CAC40 index.     

On the Evolution and Asymptotic Analysis of Open Markov Populations: Application to Consumption Credit

In this paper, we study, by means of randomized sampling, the long-run stability of some open Markov population fed with time-dependent Poisson inputs. We show that state probabilities within transient states converge—even when the overall expected population dimension increases without bound—under general conditions on the transition matrix and input intensities.

Following the convergence results, we obtain ML estimators for a particular sequence of input intensities, where the sequence of new arrivals is modeled by a sigmoidal function. These estimators allow for the forecast, by confidence intervals, of the evolution of the relative population structure in the transient states.

Applying these results to the study of a consumption credit portfolio, we estimate the implicit default rate.     

Trends cycles and seasons: Econometric methods of signal extraction

Alternative methods of trend extraction and of seasonal adjustment are described that operate in the time domain and in the frequency domain.

The time-domain methods that are implemented in the TRAMO–SEATS and the STAMP programs are compared. An abbreviated time-domain method of seasonal adjustment that is implemented in the IDEOLOG program is also presented. Finite-sample versions of the Wiener–Kolmogorov filter are described that can be used to implement the methods in a common way.

The frequency-domain method, which is also implemented in the IDEOLOG program, employs an ideal frequency selective filter that depends on identifying the ordinates of the Fourier transform of a detrended data sequence that should lie in the pass band of the filter and those that should lie in its stop band. Filters of this nature can be used both for extracting a low-frequency cyclical component of the data and for extracting the seasonal component.     

Dynamic image analysis using Bayesian shape and texture models

In this paper, we discuss the implementation of fully Bayesian analysis of dynamic image sequences in the context of stochastic deformable templates for shape modelling, Markov/Gibbs random fields for modelling textures, and dynomation.

Throughout, Markov chain Monte Carlo algorithms are used to perform the Bayesian calculations.     

Throughput and delay analysis of an opportunistic tree algorithm

Tree algorithms are a well-known class of random access algorithms with a provable maximum stable throughput under the infinite population model (as opposed to ALOHA or the binary exponential backoff algorithm). In this article, we propose a tree algorithm for opportunistic spectrum usage in cognitive radio networks. A channel in such a network is shared among so-called primary and secondary users, where the secondary users are allowed to use the channel only if there is no primary user activity. The tree algorithm designed in this article can be used by the secondary users to share the channel capacity left by the primary users.

We analyze the maximum stable throughput and mean packet delay of the secondary users by developing a tree structured Quasi-Birth Death Markov chain under the assumption that the primary user activity can be modeled by means of a finite state Markov chain and that packets lengths follow a discrete phase-type distribution.

Numerical experiments provide insight on the effect of various system parameters and indicate that the proposed algorithm is able to make good use of the bandwidth left by the primary users.     

Using spatial models as priors in astronomical image analysis

Optical astronomers now normally collect digital images by means of charge-coupled device detectors, which are blurred by atmospheric motion and distorted by physical noise in the detection process. We examine Bayesian procedures to clean such images using explicit models from spatial statistics for the underlying structure, and compare these methods with those based on maximum entropy.

This is an undated version of Molina and Ripley (1989) containing brief details of later work. Sections 1–5, 7 and 8 follow that paper and describe the deconvolution of galaxies. Further examples have been published in Molina et al. (1992a) for an astronomical audience. Work on the deconvolution of planetary images from Molina et al. (1992b, c) is reported in Section 6 with examples included in Section 7.     

Improved Measures of the Spread of Data for Some Unknown Complex Distributions Using Saddlepoint Approximations

Measures of the spread of data for random sums arise frequently in many problems and have a wide range of applications in real life, such as in the insurance field (e.g., the total claim size in a portfolio). The exact distribution of random sums is extremely difficult to determine, and normal approximation usually performs very badly for this complex distributions. A better method of approximating a random-sum distribution involves the use of saddlepoint approximations.

Saddlepoint approximations are powerful tools for providing accurate expressions for distribution functions that are not known in closed form. This method not only yields an accurate approximation near the center of the distribution but also controls the relative error in the far tail of the distribution.

In this article, we discuss approximations to the unknown complex random-sum Poisson–Erlang random variable, which has a continuous distribution, and the random-sum Poisson-negative binomial random variable, which has a discrete distribution. We show that the saddlepoint approximation method is not only quick, dependable, stable, and accurate enough for general statistical inference but is also applicable without deep knowledge of probability theory. Numerical examples of application of the saddlepoint approximation method to continuous and discrete random-sum Poisson distributions are presented.     

Slowing time: Markov-modulated Brownian motions with a sticky boundary

We define a new family of stochastic processes called Markov modulated Brownian motions with a sticky boundary at zero. Intuitively, each process is a regulated Markov-modulated Brownian motion whose boundary behavior is modified to slow down at level zero.

To determine the stationary distribution of a sticky MMBM, we follow a Markov-regenerative approach similar to the one developed with great success in the context of quasi-birth-and-death processes and fluid queues. Our analysis also relies on recent work showing that Markov-modulated Brownian motions arise as limits of a parametrized family of fluid queues.     

Analysis of variance for circular data

Over the last 25 years, increasing attention has been given to the problem of analysing data arising from circular distributions. The most important circular distribution was introduced by Von Mises (1918) which takes the form:

[Formulas]

where Io(k) is a modified Bessel function, u0 is the mean direction and k is the concentration parameter of the distribution. Watson & Williams (1956) laid the foundation of analysis of variance type techniques for the two-dimensional case of circular data using the Von Mises distribution. Stephens (1962a,b; 1969, 1972). Upton (1974) and Stephens (1982) made further improvements to Watson & Williams’ work. In this paper the authors will discuss the pitfalls of the methods adopted by Stephens (1982) and present a unified analysis of variance type approach for circular data.     

Bayesian inference and data cloning in the calibration of population projection matrices

Discrete time models are used in Ecology for describing the dynamics of an age-structured population. They can be introduced from a deterministic or from a stochastic viewpoint. We analyze a stochastic model for the case in which the dynamics of the population is described by means of a projection matrix. In this statistical model, fertility rates and survival rates are unknown parameters which are estimated by using a Bayesian approach and also data cloning, which is a simulation-based method especially useful with complex hierarchical models.

Both methodologies are applied to real data from the population of Steller sea lions located in the Alaska coast since 1978–2004. The estimates obtained from these methods show a good behavior when they are compared to the nonmissing actual values.     

Detecting and identifying interventions with the Whittle spectral approach in a long memory panel data model

This article provides a procedure for the detection and identification of outliers in the spectral domain where the Whittle maximum likelihood estimator of the panel data model proposed by Chen [W.D. Chen, Testing for spurious regression in a panel data model with the individual number and time length growing, J. Appl. Stat. 33(88) (2006b), pp. 759–772] is implemented. We extend the approach of Chang and co-workers [I. Chang, G.C. Tiao, and C. Chen, Estimation of time series parameters in the presence of outliers, Technometrics 30 (2) (1988), pp. 193–204] to the spectral domain and through the Whittle approach we can quickly detect and identify the type of outliers. A fixed effects panel data model is used, in which the remainder disturbance is assumed to be a fractional autoregressive integrated moving-average (ARFIMA) process and the likelihood ratio criterion is obtained directly through the modified inverse Fourier transform. This saves much time, especially when the estimated model implements a huge data-set.

Through Monte Carlo experiments, the consistency of the estimator is examined by growing the individual number N and time length T, in which the long memory remainder disturbances are contaminated with two types of outliers: additive outlier and innovation outlier. From the power tests, we see that the estimators are quite successful and powerful.

In the empirical study, we apply the model on Taiwan's computer motherboard industry. Weekly data from 1 January 2000 to 31 October 2006 of nine familiar companies are used. The proposed model has a smaller mean square error and shows more distinctive aggressive properties than the raw data model does.     

Constant-partially accelerated life tests for Marshall–Olkin exponential series system with dependent masked data

This paper considers the constant-partially accelerated life tests for series system products, where dependent M-O bivariate exponential distribution is assumed for the components.

Based on progressive type-II censored and masked data, the maximum likelihood estimates for the parameters and acceleration factors are obtained by using the decomposition approach. In addition, this method can also be applied to the Bayes estimates, which are too complex to obtain as usual way. Finally, a Monte Carlo simulation study is carried out to verify the accuracy of the methods under different masking probabilities and censoring schemes.     

Estimating the parameter in the Pauling equation

Four procedures are suggested for estimating the parameter ‘a’ in the Pauling equation:

e-X/a+e ? Y/a = 1.

The procedures are: using the mean of individual solutions, least squares with Y the subject of the equation, least squares with X the subject of the equation and maximum likelihood using a statistical model. In order to compare these estimates, we use Efron's bootstrap technique (1979), since distributional results are not available. This example also illustrates the role of the bootstrap in statistical inference.     

Model-based study of families of exponential-type estimators in presence of non response

Among other types of non sampling errors, non response error (NRE) is an inherent component of any sample survey, which is supposed to be given much attention during the designing and execution stages. With increasing awareness of these estimators, therefore, there is an urge for the development of suitable techniques for controlling them.

This article proposes two families of estimators for population mean in the presence of non response and discuses various properties under model approach, namely polynomial regression model. The families include some existing estimators. Comparison of efficiencies along with the robustness of the estimators under misspecification of models has been empirically discussed.     

Departure from independence and stationarity in a handball match

This paper analyses direct and indirect forms of dependence in the probability of scoring in a handball match, taking into account the mutual influence of both playing teams. Non-identical distribution (i.d.) and non-stationarity, which are commonly observed in sport games, are studied through the specification of time-varying parameters.

The model accounts for the binary character of the dependent variable, and for unobserved heterogeneity. The parameter dynamics is specified by a first-order auto-regressive process.

Data from the Handball World Championships 2001–2005 show that the dynamics of handball violate both independence and i.d., in some cases having a non-stationary behaviour.