Parameter Estimation for a Discretely Observed Integrated Diffusion Process

Abstract.  We consider the estimation of unknown parameters in the drift and diffusion coefficients of a one-dimensional ergodic diffusion X when the observation is a discrete sampling of the integral of X at times i Δ , i  =  1 ,…, n . Assuming that the sampling interval tends to 0 while the total length time interval tends to infinity, we first prove limit theorems for functionals associated with our observations. We apply these results to obtain a contrast function. The associated minimum contrast estimators are shown to be consistent and asymptotically Gaussian with different rates for drift and diffusion coefficient parameters.     

REMARKS ON OPTIMAL INFERENCE FOR MARKOV BRANCHING PROCESSES: A SEQUENTIAL APPROACH

Use of a suitable stopping rule yields exact uniformly most powerful tests and minimum variance unbiased estimators of various parameters of a Markov branching model with or without immigration. The population model discussed includes the pure birth, simple epidemic, immigration-death, M/M/ 1 queue, linear birth-death and a branching diffusion process, among others, as special cases.     

Statistical Properties of Threshold Models

This article focuses the attention on the Self Exciting Threshold Autoregressive Moving Average model (SETARMA) proposed in Tong (1983 Tong , H. ( 1983 ). Threshold Models in Nonlinear Time Series Analysis . London : Springer-Verlag .[Crossref] , [Google Scholar]). The stochastic structure of the model is discussed and different specifications are presented. Starting from one of them, we give sufficient conditions for the weak stationarity of the model that are discussed and critically compared to other results given in literature. In particular, after showing that the SETARMA model belongs to the class of the Random Coefficients Autoregressive models, widely discussed in Nicholls and Quinn (1982 Nicholls , D. F. , Quinn , B. G. (1982). Random Coefficients Autoregressive Models. An Introduction . New York : Springer-Verlag.[Crossref] , [Google Scholar]), we give some issues on the weak stationarity of its stochastic structure that are more general than those given in the existing literature and appear not affected by the moving average component.     

Influential observation in complex normal data for problems in allometry

Abstract

The aim of this paper is to investigate how some results related to the complex normal distribution are relevant in size and shape analysis. Our main focus is on the derivation of influential measures. In particular, Cook and Kullback–Leibler distances are combined with their respective asymptotic results as well as to an alternative process of defining cut-off points. Some numerical examples illustrate how these measures are used in practice. We perform an application to simulated and actual data. Results provide evidence that the methodology based on Kullback–Leibler distance outperforms one in terms of the Cook classic distance.     

Maximum likelihood estimation,from doubly censored samples,of the mean of a normal distribution with known coeffucient of variation

Let x be a random variable having the normal distribution with mean μ and variance c²μ², where c is a known constant. The maximum likelihood estimation of μ when the lowest r₁ and the highest r₂ sample values censored have been given the asymptotic variance of the maximum likelihood estimator is obtained.     

Influential observations in the analysis of variance

The effect of influentia lob servations on t h e parameter estimates of ordinary l e a s t squares regression models has received considerable attentio n fn the last decade. However, very little attention has been given t o the problem of in fluent ia lobserva- tions in the analysis of variance . The purpose of t h i s paper is t o show by way of examples that influential observations can alter the conclusions of tests of hypotheses in the analysis of variance . Regression diagnostics for identif y in g both extreme points and outliers can be used to reveal potential data and design problems.     

LIKELIHOOD APPROXIMATIONS AND DISCRETE MODELS FOR TIED SURVIVAL DATA

ABSTRACT

Ties among event times are often recorded in survival studies. For example, in a two week laboratory study where event times are measured in days, ties are very likely to occur. The proportional hazards model might be used in this setting using an approximated partial likelihood function. This approximation works well when the number of ties is small. On the other hand, discrete regression models are suggested when the data are heavily tied. However, in many situations it is not clear which approach should be used in practice. In this work, empirical guidelines based on Monte Carlo simulations are provided. These recommendations are based on a measure of the amount of tied data present and the mean square error. An example illustrates the proposed criterion.     

The Implications of Using Messy Data to Estimate Production-Frontier-Based Technical Efficiency Measures

An empirical study of efficiency at the plant level, requiring production and financial data, was done using frontier function specifications. It is not evident from the implementation of the production-frontier models that different methodologies will consistently flag the same observations as being efficient or inefficient. As a result, outlier diagnostics for individual observations and for subsets of observations are used to achieve a relative index of influentiality within the spectrum of efficiency. These outlier diagnostic tests consistently flag the same subset of efficient and inefficient observations as the frontier models and additionally clarify ranking discrepancies among the frontier model specifications.     

The Modeling and Seasonal Adjustment of Weekly Observations

Several important economic time series are recorded on a particular day every week. Seasonal adjustment of such series is difficult because the number of weeks varies between 52 and 53 and the position of the recording day changes from year to year. In addition certain festivals, most notably Easter, take place at different times according to the year. This article presents a solution to problems of this kind by setting up a structural time series model that allows the seasonal pattern to evolve over time and enables trend extraction and seasonal adjustment to be carried out by means of state-space filtering and smoothing algorithms. The method is illustrated with a Bank of England series on the money supply.