Showing papers in "Scandinavian Journal of Statistics in 2003"
TL;DR: A clustering procedure of functional data emphasizing the functional nature of the objects is proposed, which consists of fitting the functional data by B‐splines and partitioning the estimated model coefficients using a k‐means algorithm.
Abstract: Data in many different fields come to practitioners through a process naturally described as functional. Although data are gathered as finite vector and may contain measurement errors, the functional form have to be taken into account. We propose a clustering procedure of such data emphasizing the functional nature of the objects. The new clustering method consists of two stages: fitting the functional data by B-splines and partitioning the estimated model coefficients using a k-means algorithm. Strong consistency of the clustering method is proved and a real-world example from food industry is given.
347 citations
TL;DR: In this article, a simple extension of Pearl's d-separation criterion, called mseparation, is applied to acycfic directed mixed graphs, in which directed edges and bi-directed edges may occur.
Abstract: We consider acycfic directed mixed graphs, in which directed edges (x->y) and bi-directed edges (x 4-+ y) may occur. A simple extension of Pearl's d-separation criterion, called m-separation, is applied to these graphs. We introduce a local Markov property which is equivalent to the global property resulting from the m-separation criterion for arbitrary distributions.
256 citations
TL;DR: In this article, the authors consider the problem of testing for parameter changes in time series models based on a cusum test and develop a test for parameter change in a more general framework, such as the change of the parameters in a random coefficient autoregressive (1) model and that of the autocovariances of a linear process.
Abstract: In this paper, we consider the problem of testing for parameter changes in time series models based on a cusum test. Although the test procedure is well established for the mean and variance in time series models, a general parameter case has not been discussed in the lit- erature. Therefore, here we develop a cusum test for parameter change in a more general framework. As an example, we consider the change of the parameters in a random coeefficient autoregressive (1) model and that of the autocovariances of a linear process. Simulation results are reported for illustration.
208 citations
TL;DR: In this paper, the null hypothesis of no effect of ψ restricted to the Hilbert space generated by the random variable X is tested based on the norm of the empirical cross-covariance operator of (X, Y).
Abstract: The functional linear model with scalar response is a regression model where the predictor is a random function defined on some compact set of R and the response is scalar. The response is modelled as Y=ψ(X)+e, where ψ is some linear continuous operator defined on the space of square integrable functions and valued in R. The random input X is independent from the noise e. In this paper, we are interested in testing the null hypothesis of no effect, that is, the nullity of ψ restricted to the Hilbert space generated by the random variable X. We introduce two test statistics based on the norm of the empirical cross-covariance operator of (X, Y). The first test statistic relies on a X 2 approximation and we show the asymptotic normality of the second one under appropriate conditions on the covariance operator of X. The test procedures can be applied to check a given relationship between X and Y. The method is illustrated through a simulation study.
186 citations
TL;DR: In this article, a local partial likelihood technique is proposed to estimate the time-dependent coefficients in Cox's regression model, which is useful as a diagnostic tool and can be used in uncovering time-dependencies or departure from the proportional hazards model.
Abstract: This article develops a local partial likelihood technique to estimate the time-dependent coefficients in Cox's regression model. The basic idea is a simple extension of the local linear fitting technique used in the scatterplot smoothing. The coefficients are estimated locally based on the partial likelihood in a window around each time point. Multiple time-dependent covariates are incorporated in the local partial likelihood procedure. The procedure is useful as a diagnostic tool and can be used in uncovering time-dependencies or departure from the proportional hazards model. The programming involved in the local partial likelihood estimation is relatively simple and it can be modified with few efforts from the existing programs for the proportional hazards model. The asymptotic properties of the resulting estimator are established and compared with those from the local constant fitting. A consistent estimator of the asymptotic variance is also proposed. The approach is illustrated by a real data set from the study of gastric cancer patients and a simulation study is also presented.
162 citations
TL;DR: In this paper, the detailed distributional properties of integrated non-Gaussian Ornstein-Uhlenbeck (intOU) processes are studied and the tail behavior of the intOUprocess is analyzed.
Abstract: In this paper, we study the detailed distributional properties of integrated non- Gaussian Ornstein-Uhlenbeck (intOU) processes. Both exact and approximate results are given. We emphasize the study of the tail behaviour of the intOUprocess. Our results have many potential applications in financial economics, as OUprocesses are used as models of instantaneous variance in stochastic volatility (SV) models. In this case, an intOUprocess can be regarded as a model of integrated variance. Hence, the tail behaviour of the intOUprocess will determine the tail behaviour of returns generated by SV models.
139 citations
TL;DR: The estimation of the parameters of a mixture of Gaussian densities is considered, within the framework of maximum likelihood, and a solution to likelihood function degeneracy which consists in penalizing the likelihood function is adopted.
Abstract: The estimation of the parameters of a mixture of Gaussian densities is considered, within the framework of maximum likelihood Due to unboundedness of the likelihood function, the maximum likelihood estimator fails to exist We adopt a solution to likelihood function degeneracy which consists in penalizing the likelihood function The resulting penalized likelihood function is then bounded over the parameter space and the existence of the penalized maximum likelihood estimator is granted As original contribution we provide asymptotic properties, and in particular a consistency proof, for the penalized maximum likelihood estimator Numerical examples are provided in the finite data case, showing the performances of the penalized estimator compared to the standard one
104 citations
TL;DR: In this article, the authors explore the usefulness of the multivariate skew-normal distribution in the context of graphical models and show how the factorization of the likelihood function according to a graph can be rearranged in order to obtain a parameter based factorization.
Abstract: This paper explores the usefulness of the multivariate skew-normal distribution in the context of graphical models A slight extension of the family recently discussed by Azzalini & Dalla Valle (1996) and Azzalini & Capitanio (1999) is described, the main motivation being the additional property of closure under conditioning After considerations of the main probabilistic features, the focus of the paper is on the construction of conditional independence graphs for skew-normal variables Necessary and sufficient conditions for conditional independence are stated, and the admissible structures of a graph under restriction on univariate marginal distribution are studied Finally, parameter estimation is considered It is shown how the factorization of the likelihood function according to a graph can be rearranged in order to obtain a parameter based factorization
89 citations
TL;DR: In this paper, the authors develop general modification methods that turn any density estimator into one which is a bona fide density, and which is always better in performance under one set of conditions and arbitrarily close to the desired performance under a complementary set.
Abstract: . Several old and new density estimators may have good theoretical performance, but are hampered by not being bona fide densities; they may be negative in certain regions or may not integrate to 1. One can therefore not simulate from them, for example. This paper develops general modification methods that turn any density estimator into one which is a bona fide density, and which is always better in performance under one set of conditions and arbitrarily close in performance under a complementary set of conditions. This improvement-for-free procedure can, in particular, be applied for higher-order kernel estimators, classes of modern h4 bias kernel type estimators, superkernel estimators, the sinc kernel estimator, the k-NN estimator, orthogonal expansion estimators, and for various recently developed semi-parametric density estimators.
73 citations
TL;DR: In this paper, the authors considered a study where each subject may experience multiple occurrences of an event and the rate of the event occurrences is of primary interest, and proposed estimation procedures to estimate the regression parameter.
Abstract: This paper considers a study where each subject may experience multiple occurrences of an event and the rate of the event occurrences is of primary interest. Specifically, we are concerned with the situations where, for each subject, there are only records of the accumulated counts for the event occurrences at a finite number of time points over the study period. Sets of observation times may vary from subject to subject and differ between groups. We model the mean of the event occurrence number over time semiparametrically, and estimate the regression parameter. The proposed estimation procedures are illustrated with data from a bladder cancer study (Byar, 1980). Both asymptotics and simulation studies on the estimators are presented.
69 citations
TL;DR: A simple adjustment of the sample probabilities is proposed and it is shown that this gives faster convergence and the improved SIR version is better than MH for small sample sizes.
Abstract: . The sampling-importance resampling (SIR) algorithm aims at drawing a random sample from a target distribution π. First, a sample is drawn from a proposal distribution q, and then from this a smaller sample is drawn with sample probabilities proportional to the importance ratios π/q. We propose here a simple adjustment of the sample probabilities and show that this gives faster convergence. The results indicate that our version converges better also for small sample sizes. The SIR algorithms are compared with the Metropolis–Hastings (MH) algorithm with independent proposals. Although MH converges asymptotically faster, the results indicate that our improved SIR version is better than MH for small sample sizes. We also establish a connection between the SIR algorithms and importance sampling with normalized weights. We show that the use of adjusted SIR sample probabilities as importance weights reduces the bias of the importance sampling estimate.
TL;DR: In this paper, a semi-parametric median residual life regression model is proposed for small cell lung cancer patients with moderate censoring, which is based on Dirichlet process mixing.
Abstract: With survival data there is often interest not only in the survival time distribution but also in the residual survival time distribution. In fact, regression models to explain residual survival time might be desired. Building upon recent work of Kottas & Gelfand (J. Amer. Statist. Assoc. 96 (2001) 1458), we formulate a semiparametric median residual life regression model induced by a semiparametric accelerated failure time regression model. We utilize a Bayesian approach which allows full and exact inference. Classical work essentially ignores covariates and is either based upon parametric assumptions or is limited to asymptotic inference in non-parametric settings. No regression modelling of median residual life appears to exist. The Bayesian modelling is developed through Dirichlet process mixing. The models are fitted using Gibbs sampling. Re- sidual life inference is implemented extending the approach of Gelfand & Kottas (J. Comput. Graph. Statist. 11 (2002) 289). Finally, we present a fairly detailed analysis of a set of survival times with moderate censoring for patients with small cell lung cancer.
TL;DR: In this paper, a partial linear regression model with measurement errors in possibly all the variables is considered and a method of moments and deconvolution is used to construct a new class of parametric estimators together with a non-parametric kernel estimator.
Abstract: . In this paper, we consider a partial linear regression model with measurement errors in possibly all the variables. We use a method of moments and deconvolution to construct a new class of parametric estimators together with a non-parametric kernel estimator. Strong convergence, optimal rate of weak convergence and asymptotic normality of the estimators are investigated.
TL;DR: In this article, the authors proposed a local likelihood estimator for generalized additive models that is closely related to the local scoring estimator fitted by local polynomial regression, and they derived the statistical properties of the estimator and showed that it achieves the same asymptotic convergence rate as a one-dimensional LRP estimator.
Abstract: Generalized additive models are a popular class of multivariate nonparametric regression models, due in large part to the ease of use of the local scoring estimation algorithm. However, the theoretical properties of the local scoring estimator are poorly understood. In this article, we propose a local likelihood estimator for generalized additive models that is closely related to the local scoring estimator fitted by local polynomial regression. We derive the statistical properties of the estimator and show that it achieves the same asymptotic convergence rate as a one-dimensional local polynomial regression estimator. We also propose a wild bootstrap estimator for calculating pointwise confidence intervals for the additive component functions. The practical behavior of the proposed estimator is illustrated through simulation experiments and an example.
TL;DR: The Diaconis-Sturmfels algorithm is a method for sampling from conditional distributions, based on the algebraic theory of toric ideals, which is applied to categorical data analysis through the notion of Markov basis as mentioned in this paper.
Abstract: The Diaconis-Sturmfels algorithm is a method for sampling from conditional distributions, based on the algebraic theory of toric ideals. This algorithm is applied to categorical data analysis through the notion of Markov basis. An application of this algorithm is a non-parametric Monte Carlo approach to the goodness of fit tests for contingency tables. In this paper, we characterize or compute the Markov bases for some log-linear models for two-way contingency tables using techniques from Computational Commutative Algebra, namely Grobner bases. This applies to a large set of cases including independence, quasi-independence, symmetry, quasi-symmetry. Three examples of quasi-symmetry and quasi-independence from Fingleton (Models of category counts, Cambridge University Press, Cambridge, 1984) and Agresti (An Introduction to categorical data analysis, Wiley, New York, 1996) illustrate the practical applicability and the relevance of this algebraic methodology.
TL;DR: In this article, the authors study the effect on the coverage accuracy of the prediction interval of substi- tuting the true covariance parameters by estimators, and the effect of bootstrap calibration of coverage properties of the resulting 'plugin' interval.
Abstract: Kriging is a method for spatial prediction that, given observations of a spatial process, gives the optimal linear predictor of the process at a new specified point. The kriging predictor may be used to define a prediction interval for the value of interest. The coverage of the prediction interval will, however, equal the nominal desired coverage only if it is constructed using the correct underlying covariance structure of the process. If this is unknown, it must be estimated from the data. We study the effect on the coverage accuracy of the prediction interval of substi- tuting the true covariance parameters by estimators, and the effect of bootstrap calibration of coverage properties of the resulting 'plugin' interval. We demonstrate that plugin and bootstrap calibrated intervals are asymptotically accurate in some generality and that bootstrap calibration appears to have a significant effect in improving the rate of convergence of coverage error.
TL;DR: In this paper, a unified procedure is developed for estimation of constrained parametric or non-parametric regression models with unspecified error distributions, and the convergence rate of the maximum estimator based on the sieve empirical likelihood is given.
Abstract: The empirical likelihood cannot be used directly sometimes when an infinite dimensional parameter of interest is involved. To overcome this difficulty, the sieve empirical likelihoods are introduced in this paper. Based on the sieve empirical likelihoods, a unified procedure is developed for estimation of constrained parametric or non-parametric regression models with unspecified error distributions. It shows some interesting connections with certain extensions of the generalized least squares approach. A general asymptotic theory is provided. In the parametric regression setting it is shown that under certain regularity conditions the proposed estimators are asymptotically efficient even if the restriction functions are discontinuous. In the non-parametric regression setting the convergence rate of the maximum estimator based on the sieve empirical likelihood is given. In both settings, it is shown that the estimator is adaptive for the inhomogeneity of conditional error distributions with respect to predictor, especially for heteroscedasticity.
TL;DR: This paper presents a general formulation of an algorithm, the adaptive independent chain (AIC), that was introduced in a special context in Gasemyr et al. and shows that under certain conditions, the algorithm produces an exact sample from Π in a finite number of iterations, and hence that it converges to II.
Abstract: In this paper, we present a general formulation of an algorithm, the adaptive independent chain (AIC), that was introduced in a special context in Gasemyr et al. [Methodol. Comput. Appl. Probab. 3 (2001)]. The algorithm aims at producing samples from a specific target distribution Π, and is an adaptive, non-Markovian version of the Metropolis-Hastings independent chain. A certain parametric class of possible proposal distributions is fixed, and the parameters of the proposal distribution are updated periodically on the basis of the recent history of the chain, thereby obtaining proposals that get ever closer to Π. We show that under certain conditions, the algorithm produces an exact sample from Π in a finite number of iterations, and hence that it converges to II. We also present another adaptive algorithm, the componentwise adaptive independent chain (CAIC), which may be an alternative in particular in high dimensions. The CAIC may be regarded as an adaptive approximation to the Gibbs sampler updating parametric approximations to the conditionals of II.
TL;DR: This work considers the combination of path sampling and perfect simulation in the context of both likelihood inference and non‐parametric Bayesian inference for pairwise interaction point processes.
Abstract: We consider the combination of path sampling and perfect simulation in the context of both likelihood inference and non-parametric Bayesian inference for pairwise interaction point processes Several empirical results based on simulations and analysis of a data set are presented, and the merits of using perfect simulation are discussed
TL;DR: In this paper, the authors characterized the asymptotic behavior of the likelihood ratio test statistic (LRTS) for testing homogeneity (i.e. no mixture) against gamma mixture alternatives.
Abstract: This paper characterizes the asymptotic behaviour of the likelihood ratio test statistic (LRTS) for testing homogeneity (i.e. no mixture) against gamma mixture alternatives. Under the null hypothesis, the LRTS is shown to be asymptotically equivalent to the square of Davies's Gaussian process test statistic and diverges at a log log n rate to infinity in probability. Based on the asymptotic analysis, we propose and demonstrate a computationally efficient method to simulate the null distributions of the LRTS for small to moderate sample sizes.
TL;DR: In this paper, a sieve approximation with variable length Markov chains of increasing order was used for the estimation of minimal state spaces and probability laws in the class of stationary processes defined on finite categorical spaces.
Abstract: .
We develop new results about a sieve methodology for the estimation of minimal state spaces and probability laws in the class of stationary processes defined on finite categorical spaces. Using a sieve approximation with variable length Markov chains of increasing order, we show that an adapted version of the Context algorithm yields asymptotically correct estimates for the minimal state space and for the underlying probability distribution. As a side product, the method of sieves yields a nice graphical tree representation for the potentially infinite dimensional minimal state space of the data generating process, which is very useful for exploration of the memory.
TL;DR: The authors developed conditional frequentist tests that allow the reporting of data-dependent error probabilities, error probabilities that have a strict frequentist interpretation and that reflect the actual amount of evidence in the data.
Abstract: Testing of a composite null hypothesis versus a composite alternative is considered when both have a related invariance structure The goal is to develop conditional frequentist tests that allow the reporting of data-dependent error probabilities, error probabilities that have a strict frequentist interpretation and that reflect the actual amount of evidence in the data The resulting tests are also seen to be Bayesian tests, in the strong sense that the reported frequentist error probabilities are also the posterior probabilities of the hypotheses under default choices of the prior distribution The new procedures are illustrated in a variety of applications to model selection and multivariate hypothesis testing
TL;DR: In this paper, Cramer-von Mises type goodness of fit tests for interval censored data case 2 are proposed based on a resampling method called the leveraged bootstrap, and their asymptotic consistency is shown.
Abstract: Cramer-von Mises type goodness of fit tests for interval censored data case 2 are proposed based on a resampling method called the leveraged bootstrap, and their asymptotic consistency is shown. The proposed tests are computationally efficient, and in fact can be applied to other types of censored data, including right censored data, doubly censored data and (mixture of) case k interval censored data. Some simulation results and an example from AIDS research are presented.
TL;DR: In this article, the authors correct two proofs concerning Markov properties for graphs representing marginal independence relations, and show that these properties are correct for the case of graphs with marginal independence.
Abstract: . We correct two proofs concerning Markov properties for graphs representing marginal independence relations.
TL;DR: In this paper, the authors consider a two-dimensional diffusion process X V where V is ergodic and X has drift and diffusion co-fluence completely determined by V, and their concern is estimation of θ from discrete-time observations of X.
Abstract: The objective of this paper is parametric inference for stochastic volatility models. We consider a two-dimensional diffusion process X V where V is ergodic and X has drift and diffusion coefcient completely determined by V . The drift and the diffusion coefcient for V depend on an unknown parameter θ , and our concern is estimation of θ from discrete-time observations of X. The volatility process V remains unobserved. We consider approximate maximum likelihood estimation: for the k’th order approximation we pretend that the observations form a k’th order Markov chain, nd the corresponding approximate loglikelihood function, and maximize it with respect to θ . The approximate log-likelihood function is not known analytically but can easily be calculated by simulation. For each k the method yields consistent and asymptotically normal estimators. Simulations from the model where V is a Cox-Ingersoll-Ross model are used for illustration.
TL;DR: In this article, the edge of a two-dimensional bounded set is estimated based on the Haar series and extreme values of the point process using a finite random set of points drawn from the interior.
Abstract: . We present a new method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on Haar series and extreme values of the point process. We give conditions for various kind of convergence and we obtain remarkably different possible limit distributions. We propose a method of reducing the negative bias, illustrated by a simulation.
TL;DR: An important problem in statistical practice is the selection of a suitable statistical model, and a data-driven adaptive procedure is called a model metaselection, based on the analysis of recursive prediction residuals obtained from each strategy with increasing sample sizes.
Abstract: An important problem in statistical practice is the selection of a suitable statistical model. Several model selection strategies are available in the literature, having different asymptotic and small sample properties, depending on the characteristics of the data generating mechanism. These characteristics are difficult to check in practice and there is a need for a data-driven adaptive procedure to identify an appropriate model selection strategy for the data at hand. We call such an identification a model metaselection, and we base it on the analysis of recursive prediction residuals obtained from each strategy with increasing sample sizes. Graphical tools are proposed in order to study these recursive residuals. Their use is illustrated on real and simulated data sets. When necessary, an automatic metaselection can be performed by simply accumulating predictive losses. Asymptotic and small sample results are presented.
TL;DR: A class of log‐linear models, referred to as labelled graphical models (LGMs), is introduced for multinomial distributions that generalize graphical models by employing partial conditional independence restrictions which are valid only in subsets of an outcome space.
Abstract: A class of log-linear models, referred to as labelled graphical models (LGMs), is introduced for multinomial distributions. These models generalize graphical models (GMs) by employing partial conditional independence restrictions which are valid only in subsets of an outcome space. Theoretical results concerning model identifiability, decomposability and estimation are derived. A decision theoretical framework and a search algorithm for the identification of plausible models are described. Real data sets are used to illustrate that LGMs may provide a simpler interpretation of a dependence structure than GMs.
TL;DR: In this article, the authors proposed two new approaches to estimate the confidence interval for intraclass correlation to assess inter-rater reliability when the number of raters is small and the rater effect is not negligible.
Abstract: Calculation of a confidence interval for intraclass correlation to assess inter-rater reliability is problematic when the number of raters is small and the rater effect is not negligible. Intervals produced by existing methods are uninformative: the lower bound is often close to zero, even in cases where the reliability is good and the sample size is large. In this paper, we show that this problem is unavoidable without extra assumptions and we propose two new approaches. The first approach assumes that the raters are sufficiently trained and is related to a sensitivity analysis. The second approach is based on a model with fixed rater effect. Using either approach, we obtain conservative and informative confidence intervals even from samples with only two raters. We illustrate our point with data on the development of neuromotor functions in children and adolescents.
TL;DR: In this article, the Strauss disc processes with inhibition distance r and disc radius R are considered and formulas for the mean and variance of the vacancy (non-covered area) are derived.
Abstract: . Hard-core Strauss disc processes with inhibition distance r and disc radius R are considered. The points in the Strauss point process are thought of as trees and the discs as crowns. Formulas for the mean and the variance of the vacancy (non-covered area) are derived. This is done both for the case of a fixed number of points and for the case of a random number of points. For tractability, the region is assumed to be a torus or, in one dimension, a circle in which case the discs are segments. In the one-dimensional case, the formulas are exact for all r. This case, although less important in practice than the two-dimensional case, has provided a lot of inspiration. In the two-dimensional case, the formulas are only approximate but rather accurate for r < R. Markov Chain Monte Carlo simulations confirm that they work well. For R ≤ r < 2R, no formulas are presented. A forestry estimation problem, which has motivated the research, is briefly considered as well as another application in spatial statistics.