1,721,091 research outputs found
SIMULAZIONI CONDIZIONATE PER FAMIGLIE DI REGRESSIONE E SCALA
No full textA regression-scale model is of the form y=X\beta+\sigma\epsilon, where X is a fixed nxp design matrix, \beta\in\Real^p an unknown regression coefficient, \sigma>0 a scale parameter, and \epsilon represents an n-dimensional vector of errors whose density is known. Inference is usually made conditionally on the sample configuration a=(y-X\hat\beta)/\hat\sigma, where (\hat\beta,\hat\sigma) are the maximum likelihood estimates. Higher-order asymptotics provide very accurate approximations to exact conditional procedure thus avoiding multidimensional numerical integration. This paper presents how by means of the Metropolis-Hastings algorithm, a powerful Markov Chain Monte Carlo technique, conditional properties of these methods can be assessed. MCMC are necessary, as the conditional distributions involved are only known up to the normalizing constant
Approximate Conditional Inference in Logistic and Loglinear Models
No full textRecently developed small-sample asymptotics provide nearly exact inference for parametric statistical models. One approach is via approximate conditional and marginal inference, respectively, in multiparameter exponential families and regression-scale models. Although the theory is well developed, these methods are under-used in practical work. This article presents a set of S-Plus routines for approximate conditional inference in logistic and loglinear regression models. It represents the first step of a project to create a library for small-sample inference which will include methods for some of the
most widely used statistical models. Details of how the methods have been implemented are discussed. An example illustrates the code
hoa: An R package bundle for higher order likelihood inference
No full textThe likelihood function represents the basic ingredient of many commonly used statistical methods for estimation, testing and the calculation of confidence intervals. In practice, much application of likelihood inference relies on first order asymptotic results such as the central limit theorem. The approximations can, however, be rather poor if the sample size is small or, generally, when the average information available per parameter is limited. Thanks to the great progress made over the past twenty-five years or so in the theory of likelihood inference, very accurate approximations to the distribution of statistics such as the likelihood ratio have been developed. These not only provide modifications to well-established approaches, which result in more accurate inferences, but also give insight on when to rely upon first order methods. We refer to these developments as higher order asymptotics. One intriguing feature of the theory of higher order likelihood asymptotics is that relatively simple and familiar quantities play an essential role. The higher order approximations discussed in this paper are for the significance function, which we will use to set confidence limits or to calculate the p-value associated with a particular hypothesis of interest. We start with a concise overview of the approximations used in the remainder of the paper. Our first example is an elementary one-parameter model where one can perform the calculations easily, chosen to illustrate the potential accuracy of the procedures. Two more elaborate examples, an application of binary logistic regression and a nonlinear growth curve model, follow. All examples are carried out using the R code of the hoa package bundle
Fisher's Legacy: (Pseudo) Likelihood and Some Recent Challenges
No full textIl presente lavoro intende fornire una panoramica sugli sviluppi più recenti ed innovativi nella teoria dell’inferenza basata sulla funzione di verosimiglianza. I metodi saranno illustrati utilizzando due esempi. Il primo si ispira a risultati recenti in fisica nucleare; il secondo riguarda due sperimentazioni in ambito forestale
A Computer Algebra Package for Approximate Conditional Inference in Multiparameter Exponential Families
No full textThis paper presents a set of REDUCE procedures making a number of existing higher-order asymptotic results available for both theoretical and practical research. Attention has been restricted to the context of approximate conditional inference for multiparameter full rank exponential families. Most of the procedures support algebraic computation as well as numerical calculation for a given data set. Examples are given for both kinds of applications. All numerical results involve discrete data following log-linear models
Valutazione dell'intercambiabilità ed affidabilità della strumentazione EMDEX(TM) utilizzata nello studio SETIL
No full textIl progetto SETIL riguarda uno studio epidemiologico multicentrico italiano sull'eziologia dei tumori del sistema linfoemopoietico e dei neuroblastomi nel bambino attualmente in corso di svolgimento. Uno dei punti chiave dello studio è valutare se e come l'esposizione a campi magnetici a bassissima frequenza (ELF-MF) modifichi il rischio delle patologie oggetto di studio. Il protocollo prevede l'impiego di due diversi strumenti per la misurazione dei campi magnetici ELF. Misure a breve termine (o spot) dovrebbero essere eseguite con strumenti EMDEX II , mentre per le misure prolungate si dovrebbero utilizzare dosimetri del tipo EMDEX Lite , meno precisi (e costosi) dei primi. Sul campo si è, tuttavia, verificata la necessità di adottare il primo dosimetro disponibile, non differenziando, dunque, tra misure spot e misure prolungate, onde evitare tempi di attesa eccessivamente lunghi. La domanda che si pone è se i due strumenti siano intercambiabili, ovvero forniscano, in condizioni sperimentali comparabili, valori equivalenti al fine dell'analisi epidemiologica. Un secondo quesito d'interesse riguarda l'affidabilità dei valori rilevati, ovvero se questi effettivamente rispecchino l'intensità del campo magnetico misurato. // L'obiettivo del presente lavoro è rispondere ai due quesiti posti circa l'intercambiabilità della strumentazione adottata e l'affidabilità delle misure fornite. A questi fini si sono utilizzati i dati ottenuti in due sessioni di taratura degli strumenti utilizzati per la misurazione dei campi magnetici residenziali dei casi e controlli reclutati, effettuate presso il Dipartimento di Ivrea dell'Agenzia Regionale per la Protezione Ambientale (A.R.P.A.) del Piemonte. Si riportano, inoltre, alcune considerazioni circa le implicazioni dei risultati ottenuti sul funzionamento della strumentazione EMDEX per lo studio SETIL
CONDITIONAL SIMULATION FOR REGRESSION-SCALE MODELS
No full textA regression-scale model is of the form y = Xeta + sigmaepsilon, where X is a fixed nxp design matrix, etainReal^p an unknown regression coefficient, sigma>0 a scale parameter, and epsilon represents an n-dimensional vector of errors whose density is known. Inference is usually made conditionally on the sample configuration a = (y - Xhateta)/hatsigma, where (hateta, hatsigma) are the maximum likelihood estimates. Higher-order asymptotics provide very accurate approximations to exact conditional procedures thus avoiding multidimensional numerical integration. This paper presents how by means of the Metropolis-Hastings algorithm, a powerful Markov chain Monte Carlo technique which allows to simulate from distributions that are only known up to the normalizing constant, conditional properties of these methods can be assessed
Higher-Order Asymptotics in Practice
No full textThe S-PLUS library HOA implements several of the most promising higher-order solutions for three widely used model classes: logistic and logliner models, linear nonnormal and nonlinear heteroscedastic regression models. This contribution discusses how it is possible to implement efficiently small-sample asymptotics in a numerical
computing environment
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