On the estimation of the parameters of the von mises distribution

The usual maximum likelihood estimators of the parameters of the von Mises distribution are shown to perform badly in small samples. In view of this and the fact that these estimators require a large amount of computation, alternative, simpler estimators are proposed. It is shown that these estimators are at least comparable to the traditional estimators and are, in many cases, superior to them. We also apply the procedure of jackknifing to the maximum likelihood estimator of the concentration parameter of the von Mises distribution and compare the properties of the jackknifed estimator with the other estimators considered in this paper.     

Bayesian forecasting with changing linear models

This investigation considers a general linear model which changes parameters exactly once during the observation period. Assuming all the parameters are unknown and a proper prior distribution, the Bayesian predictive distribution of the future observations is derived.

It is shown that the predictive distribution is a mixture of multivariate t distributions and that the mixing distribution is the marginal posterior mass function of the change point parameter.     

CONSTRUCTING MORE POWERFUL EXACT TESTS OF EQUIVALENCE FROM BINARY MATCHED PAIRS

In randomized clinical trials, it is often necessary to demonstrate that a new medical treatment does not substantially differ from a standard reference treatment. Formal testing of such ‘equivalence hypotheses’ is typically done by combining two one‐sided tests (TOST). A quite different strand of research has demonstrated that replacing nuisance parameters with a null estimate produces P‐values that are close to exact ( Lloyd 2008a ) and that maximizing over the residual dependence on the nuisance parameter produces P‐values that are exact and optimal within a class ( Röhmel & Mansmann 1999 ; Lloyd 2008a ). The three procedures – TOST, estimation and maximization of a nuisance parameter – can each be expressed as a transformation of an approximate P‐value. In this paper, we point out that TOST‐based P‐values will generally be conservative, even if based on exact and optimal one‐sided tests. This conservatism is avoided by applying the three transforms in a certain order – estimation followed by TOST followed by maximization. We compare this procedure with existing alternatives through a numerical study of binary matched pairs where the two treatments are compared by the difference of response rates. The resulting tests are uniformly more powerful than the considered competitors, although the difference in power can range from very small to moderate.     

Dynamic Probabilities of Restrictions in State Space Models: An Application to the Phillips Curve

Using the Savage–Dickey density ratio and an alternative approach that uses more relaxed assumptions, we develop methods to calculate the probability that a restriction holds at a point in time without assuming that the restriction holds at any other points in time. Both approaches use MCMC output only from the unrestricted model to compute the time-varying posterior probabilities for all models of interest. Using U.S. data, we find the probability that the long-run Phillips curve is vertical to be fairly high, but decreases over time. The probability that the NAIRU is not identified fluctuates over time, but increases after 1990.     

Estimation Under Inequality Constraints: Semiparametric Estimation of Conditional Duration Models

This article proposes a semiparametric estimator of the parameter in a conditional duration model when there are inequality constraints on some parameters and the error distribution may be unknown. We propose to estimate the parameter by a constrained version of an unrestricted semiparametrically efficient estimator. The main requirement for applying this method is that the initial unrestricted estimator converges in distribution. Apart from this, additional regularity conditions on the data generating process or the likelihood function, are not required. Hence the method is applicable to a broad range of models where the parameter space is constrained by inequality constraints, such as the conditional duration models. In a simulation study involving conditional duration models, the overall performance of the constrained estimator was better than its competitors, in terms of mean squared error. A data example is used to illustrate the method.     

Power and Sample Size for Approximate Chi-Square Tests

Approximate chi-square tests for hypotheses concerning multinomial probabilities are considered in many textbooks. In this article power calculations and sample size based on power are discussed and illustrated for the three most frequently used tests of this type. Available noncentrality parameters and existing tables permit a relatively easy solution of these kinds of problems.     

On Minimum Variance Unbiased Estimators

The problem of finding minimum variance unbiased estimators of various parameters for parametric distributions is an important one in statistics. This article gives analytical formulas for the minimum variance unbiased estimators of parametric functions, which are usually used in a classroom, for two types of densities. The first type is the one-parameter regular exponential family, and the second is a two-parameter family of a continuous random variable whose range depends on the unknown parameters.     

Nonparametric estimation in one-way random effects models

We present a rank based method for obtaining point and interval estimates of a scale version of the intraclass correlation coefficient in a one-way random effects model. When compared to the method of Arvesen and Schmitz (1970), the new method is not only applicable to a broader class of situations, but also much easier to implement. Results of a simulation study indicate that the new procedure compares favorably with the Arvesen-Schmitz procedure and the classical normal theory procedure especially If the random components have heavy tailed distributions.     

Change Point Detection in The Skew-Normal Model Parameters

Bayesian inference under the skew-normal family of distributions is discussed using an arbitrary proper prior for the skewness parameter. In particular, we review some results when a skew-normal prior distribution is considered. Considering this particular prior, we provide a stochastic representation of the posterior of the skewness parameter. Moreover, we obtain analytical expressions for the posterior mean and variance of the skewness parameter. The ultimate goal is to consider these results to one change point identification in the parameters of the location-scale skew-normal model. Some Latin American emerging market datasets are used to illustrate the methodology developed in this work.     

Transmuted two-parameter Lindley distribution

In this study, we propose a new distribution using the quadratic rank transmutation map named as transmuted two-parameter Lindley distribution (TTLD). This distribution is more flexible than the two-parameter Lindley distribution (TLD). The properties of the TTLD are examined, and estimation methods for the parameters of this distribution are discussed. The usefulness of the TTLD is demonstrated on some real data.