Constructing tests for exponentiality has been an active and fruitful research area, with numerous applications in engineering, biology and other sciences concerned with life-time data. In the present paper, we construct and investigate powerful tests for exponentiality based on two well known quantities: the Atkinson index and the Moran statistic. We provide an extensive study of the performance of the tests and compare them with those already available in the literature.
This paper studies properties of the likelihood ratio (LR) tests associated with the limited information maximum likelihood (LIML) estimators in a structural form estimation when the number of instrumental variables is large. Two types of asymptotic theories are developed to approximate the distribution of the likelihood ratio (LR) statistic under the null hypothesis H0:β=β0: a (large sample) asymptotic expansion and a large-Kn asymptotic theory. Size comparisons of two modified LR tests based on these two asymptotics are made with Moreira's conditional likelihood ratio (CLR) test and the large K t-test.
The so-called Hodrick-Prescott filter was first introduced in actuarial science to estimate trends from claims data and now is widely used in economics and finance to estimate and predict e.g. business cycles and trends in financial data series. This filter depends on the noise-to-signal ratio α that acts as a smoothing parameter. We propose a new consistent estimator of this smoothing parameter and construct corresponding non-asymptotic confidence intervals with a precise confidence level.
The problem of evaluating the goodness of the predictive distributions developed by the Bayesian model averaging approach is investigated. Considering the maximization of the posterior mean of the expected log-likelihood of the predictive distributions (Ando (2007a)), we develop the Bayesian predictive information criterion (BPIC). According to the numerical examples, we show that the posterior mean of the log-likelihood has a positive bias comparing with the posterior mean of the expected log-likelihood, and that the bias estimate of BPIC is close to the true bias. One of the advantages of BPIC is that we can optimize the size of Occam's razor. Monte Carlo simulation results show that the proposed method performs well.
The Akaike information criterion (AIC) has been successfully used in the literature in model selection when there are a small number of parameters p and a large number of observations N. The cases when p is large and close to N or when p>N have not been considered in the literature. In fact, when p is large and close to N, the available AIC does not perform well at all. We consider these cases in the context of finding the number of components of the mean vector that may be different from zero in one-sample multivariate analysis. In fact, we consider this problem in more generality by considering it as a growth curve model introduced in Rao (1959) and Potthoff and Roy (1964). Using simulation, it has been shown that the proposed AIC procedures perform well.
Trend extraction from time series is often performed by using the filter proposed by Leser (1961), also known as the Hodrick-Prescott filter. Practical problems arise, however, if the time series contains structural breaks (as produced by German unification for German time series, for instance), or if some data are missing. This note proposes a method for coping with these problems.
For estimating the median θ of a spherically symmetric univariate distribution under squared error loss, when θ is known to be restricted to an interval [−m,m], m known, we derive sufficient conditions for estimators δ to dominate the maximum likelihood estimator δmle. Namely: (i) we identify a large class of models where for sufficiently small m, all Bayesian estimators with respect to symmetric about 0 priors supported on [−m,m] dominate δmle, and (ii) we provide for Bayesian estimators δπ sufficient dominance conditions of the form m ≤ cπ, which are applicable to various models and priors π. In terms of the models, applications include Cauchy and Student distributions, densities which are logconvex on (θ,∞) including scale mixtures of Laplace distributions, and logconcave on (θ, ∞) densities with logconvex on (θ,∞) first derivatives such as normal, logistic, Laplace and hyperbolic secant, among others. In terms of priors π which lead to dominating δπ's in (ii), applications include the uniform density, as well as symmetric densities about 0, which are also absolutely continuous, nondecreasing and logconcave on (0,m).
This paper discusses the asymptotic properties of the posterior density under Whittle measure. The Bernstein-von Mises theorem is shown for short- and long-memory stationary processes. Applications to Bayesian inference for time series are provided.
For r× r tables with ordered categories, Tomizawa (1995) considered the collapsed symmetry model. This model indicates the structure of symmetry for the r−1 ways of collapsing the r× r table into a 2× 2 table by choosing cut points after the u-th row and after the u-th column for u=1,...,r−1. This paper proposes a collapsed symmetry (C) model for multi-way tables with ordered categories. The proposed model is an extension of the complete symmetry model and a special case of the marginal homogeneity (M) model. Also for multi-way tables, this paper proposes the collapsed quasi-symmetry (CQS) model which is an extension of the C model, and gives a theorem that the C model holds if and only if both the CQS and M models hold. An example is given.
The problem of estimating linear functions of ordered scale parameters of two Gamma distributions is considered under entropy loss. A necessary and sufficient condition for the maximum likelihood estimator (MLE) to dominate the crude unbiased estimator (UE) is given on two non-negative coefficients. Furthermore, improvement on the UE of the reciprocal of each scale parameter is also obtained under entropy loss. Some numerical results are given to illustrate how much improvement is obtained over the UE.