Estimating the discount rate policy reaction function of the monetary authority

This paper estimates a policy rule that explains the sign and the magnitude of the Federal Reserve's (Fed's) discount rate changes. It sets out a two-sided Type II Tobit model and develops a procedure for its estimation, considering the discrete and censored nature of the changes. The results suggest that the Fed has conducted discount rate policy counter-cyclically to influence output and to curb inflation, and that the Fed's response to policy indicators varies over monetary regimes. Furthermore, consistency is found between the model prediction of the discount rate change and a classification based on whether the change is technical or non-technical. Copyright © 1999 John Wiley & Sons, Ltd.     

Goodness-of-fit tests for discrete models based on the integrated distribution function

This paper presents a new widely applicable omnibus test for discrete distributions which is based on the difference between the integrated distribution function Ψ(t)=∫_t ^∞ (1−F(x))dx and its empirical counterpart. A bootstrap version of the test for common lattice models has accurate error rates even for small samples and exhibits high power with respect to competitive procedures over a large range of alternatives. Received: July 1998     

The Identification of a Mixture of First‐Order Binary Markov Chains*

Let S be the number of components in a finite discrete mixing distribution. We prove that the number of waves of panel being greater than or equal to 2S is a sufficient condition for global identification of a dynamic binary choice model in which all the parameters are heterogeneous. This model results in a mixture of S binary first‐order Markov Chains.     

An inflated multivariate integer count hurdle model: an application to bid and ask quote dynamics

In this paper we develop a model for the conditional inflated multivariate density of integer count variables with domain ?ⁿ, n ∈ ?. Our modelling framework is based on a copula approach and can be used for a broad set of applications where the primary characteristics of the data are: (i) discrete domain; (ii) the tendency to cluster at certain outcome values; and (iii) contemporaneous dependence. These kinds of properties can be found for high‐ or ultra‐high‐frequency data describing the trading process on financial markets. We present a straightforward sampling method for such an inflated multivariate density through the application of an independence Metropolis–Hastings sampling algorithm. We demonstrate the power of our approach by modelling the conditional bivariate density of bid and ask quote changes in a high‐frequency setup. We show how to derive the implied conditional discrete density of the bid–ask spread, taking quote clusterings (at multiples of 5 ticks) into account. Copyright © 2009 John Wiley & Sons, Ltd.     

Discrete discrepancy in factorial designs

Discrepancy measure can be utilized as a uniformity measure for comparing factorial designs. A so-called discrete discrepancy has been used to evaluate the uniformity of factorials. In this paper we give linkages among uniformity measured by the discrete discrepancy, generalized minimum aberration, minimum moment aberration and uniformity measured by the centered L₂-discrepancy/the wrap-around L₂-discrepancy. These close linkages provide a significant justification for the discrete discrepancy used to measure uniformity of factorial designs.     

Activity signature functions for high-frequency data analysis

We define a new concept termed activity signature function, which is constructed from discrete observations of a continuous-time process, and derive its asymptotic properties as the sampling frequency increases. We show that the function is a useful device for estimating the activity level of the underlying process and in particular for deciding whether the process contains a continuous martingale. An application to $ /DM exchange rate over 1986–1999 indicates that a jump-diffusion model is more plausible than a pure-jump model. A second application to internet traffic at NASA servers shows that an infinite variation pure-jump model is appropriate for its modeling.     

Asymptotic normality of M-estimators in a semiparametric model with longitudinal data

Suppose that the longitudinal observations (Y _ij , X _ij , t _ij ) for i = 1, . . . ,n; j = 1, . . . ,m _i are modeled by the semiparamtric model where β ₀ is a k × 1 vector of unknown parameters, g(·) is an unknown estimated function and e _ij are unobserved disturbances. This article consider M-type regressions which include mean, median and quantile regressions. The M-estimator of the slope parameter β ₀ is obtained through piecewise local polynomial approximation of the nonparametric component. The local M-estimator of g(·) is also obtained by replacing β ₀ in model with its M-estimator and using local linear approximation. The asymptotic distribution of the estimator of β ₀ is derived. The asymptotic distributions of the local M-estimators of g(·) at both interior and boundary points are also established. Various applications of our main results are given. The research is supported in part by National Natural Science Foundation of China (Grant No. 10671089).     

Tests for location-scale families based on the empirical characteristic function

A class of procedures is presented for using random samples to test the fit of location-scale families—distributions F(·;θ₁,θ₂) such that Z=(X−θ₁)/θ₂ has distribution Working with empirically standardized data, the test statistic is a measure of distance between the empirical characteristic function, and the c.f. of Z under the null hypothesis, ϕ₀(t). The closed-form test statistic is derived by integrating over the product of a weight function times Using as weight function for each location-scale family the squared modulus of ϕ₀ itself presents a unified test procedure. Included as special cases are well-known tests for normal and Cauchy laws. Small-sample powers are compared with those of Anderson-Darling tests for each of seven univariate location-scale families.     

The life-length of banknotes*

Abstract With the aid of the Bank's banknote sorting system the issue and subsequent withdrawal of f 25–banknotes on three varieties of paper have been recorded for two-and-a-half years. The aim was to measure the durability of the three paper varieties in circulation. The results of this second trial with f 25–banknotes confirm the statistical model developed previously for the first trial with f 100–banknotes. GRESHAM's Law is equally not applicable, neither to f 25–banknotes nor to f 100–banknotes. A two-parameter gamma distribution fits the cumulative fraction of banknotes withdrawn reasonably well.     

The association between two random elements: A complete characterization and odds ratio models

For random elements X and Y (e.g. vectors) a complete characterization of their association is given in terms of an odds ratio function. The main result establishes for any odds ratio function and any pre-specified marginals the unique existence of a corresponding joint distribution (the joint density is obtained as a limit of an iterative procedure of marginal fittings). Restricting only the odds ratio function but not the marginals leads to semi-parmetric association models for which statistical inference is available for samples drawn conditionally on either X or Y. Log-bilinear association models for random vectors X and Y are introduced which generalize standard (regression) models by removing restrictions on the marginals. In particular, the logistic regression model is recognized as a log-bilinear association model. And the joint distribution of X and Y is shown to be multivariate normal if and only if both marginals are normal and the association is log-bilinear.Acknowledgements The author thanks both referees for their helpful comments which improved the first draft of the paper.     

Slow convergence of the number of near-maxima for Burr XII distributions

A near-maximum is an observation which falls within a distance a of the maximum observation in an independent and identically distributed sample of size n. Subject to some conditions on the tail thickness of the population distribution, the number K _n (a) of near-maxima is known to converge in probability to one or infinity, or in distribution to a shifted geometric law. In this paper we show that for all Burr XII distributions K _n (a) converges almost surely to unity, but this convergence property may not become clear under certain cases even for very large n. We explore the reason of such slow convergence by studying a distributional continuity between Burr XII and Weibull distributions. We have also given a theoretical explanation of slow convergence of K _n (a) for the Burr XII distributions by showing that the rate of convergence in terms of P{K _n (a) > 1} tending to zero changes very little with the sample size n. Illustrations of the limiting behaviour K _n (a) for the Burr XII and the Weibull distributions are given by simulations and real data. The study also raises an important issue that although the Burr XII provides overall better fit to a given data set than the Weibull distribution, cautions should be taken for the extrapolation of the upper tail behaviour in the case of slow convergence.      

Parametric bootstrap tests for continuous and discrete distributions

Statistical procedures based on the estimated empirical process are well known for testing goodness of fit to parametric distribution families. These methods usually are not distribution free, so that the asymptotic critical values of test statistics depend on unknown parameters. This difficulty may be overcome by the utilization of parametric bootstrap procedures. The aim of this paper is to prove a weak approximation theorem for the bootstrapped estimated empirical process under very general conditions, which allow both the most important continuous and discrete distribution families, along with most parameter estimation methods. The emphasis is on families of discrete distributions, and simulation results for families of negative binomial distributions are also presented.     

Pairwise Multiple Comparisons under Violation of the Independence Assumption

Several multiple comparison procedures (MCPs)were compared for their rates of Type I error and fortheir ability to detect true pairwise differencesamong means when independence of observationsassumption were not satisfied. Monte Carlo resultsshowed that, if independence is not met, none of theprocedures maintain controlled at the chosennominal level, neither using error rate per comparisonor the error rate experimentwise. However, once thedependence of the data was corrected the Type I errorrate was maintained at the same level as when thecorrelation was zero in all the procedures, except forthe Fisher's (1935) least significant differenceprocedure (LSD) and Hayter's (1986) two-stagemodified LSD procedure (FH). At the sametime, conform the correlation increased by a smallamount the power rates also, specially, when the powerwas examined using per-pair power.     

Linearity of regression for non-adjacent order statistics

Let X ₁,X ₂,…,X _n be a random sample from a continuous distribution with the corresponding order statistics X _1:n≤X _2:n≤…≤X _n:n. All the distributions for which E(X _{k+r: n}|X _k:n)=a X _k:n+b are identified, which solves the problem stated in Ferguson (1967). Received February 1998     

A new approach to inter-rater agreement through stochastic orderings: the discrete case

We wish to study inter-rater agreement comparing groups of observers who express their ratings on a discrete or ordinal scale. The starting point is that of defining what we mean by “agreement”. Given d observers, let the scores they assign to a given statistical unit be expressed as a d-vector in the real space. We define a deterministic ordering among these vectors, which expresses the degree of the raters’ agreement. The overall scoring of the raters on the sample space will be a d-dimensional random vector. We then define an associated partial ordering among the random vectors of the ratings, illustrate a number of its properties, and look at order-preserving functions (agreement measures). In this paper we also show how to test the hypothesis of greater agreement against the unrestricted hypothesis, and the hypothesis of equal agreement against the hypothesis that an agreement ordering holds. The test is applied to real data on two medical observers rating clinical guidelines.     

The Fallacy of Misplaced Leadership*

abstract The leadership literature typically talks about the discrete individuality of its subject and particularly the personal qualities and capabilities of a few key people occupying top positions in a hierarchy. Current leadership research now has begun to generate new knowledge about leadership practice in relations of interpersonal exchange. Nevertheless, there is an urgent need for the ramifications of this insight to be more sufficiently developed. The current discussion explores how a perspective of process studies challenges the dominance of the field by individual social actors and discrete schemes of relations. Its aims are twofold. First, it will show how both of these latter epistemologies are lacking and suggest that current leadership research and development activities must rise to the ontological challenge of processes rather than things. Second, it looks at some methodological implications of this way of thinking as a productive incitement to future management studies.     

On the Lp error of the Grenander-type estimator in the Cox model

We consider the Cox regression model and study the asymptotic global behavior of the Grenander-type estimator for a monotone baseline hazard function. This model is not included in the general setting of Durot (2007). However, we show that a similar central limit theorem holds for L_p-error of the Grenander-type estimator. As an illustration of application of our main result, we propose a test procedure for a Weibull baseline distribution, based on the L_p-distance between the Grenander estimator and a parametric estimator of the baseline hazard. Simulation studies are performed to investigate the performance of this test.     

The dynamics of within-group and between-group interaction

The article strengthens and provides a dynamic extension of the theory on collective rent seeking and private provision of a public good. Each individual agent within each group chooses in continuous or discrete time a continuous or discrete effort level. The combined effort within each group provides within-group public goods which are used as an input in the between-group n-group competition for an external prize. Intergroup mobility and intergroup warfare are allowed for. Each group and each individual agent within each group get a fraction of the prize based on a linear combination of equity and relative effort. A model/algorithm is developed generating analytical results and simulations illustrating how the interaction within and between groups proceeds through time.     

On a bayesian criterion for choosing predictive sub-models in linear regression

Summary We treat the model selection problem in regression as a decision problem in which the decisions are the alternative predictive distributions based on the different sub-models and the parameter space is the set of possible future values of the regressand. The loss function balances out the conflicting needs for a predictive distribution with mean close to the true value ofy but without too great a variation. The treatment is Bayesian and the criterion derived is a Bayesian generalization of Mallows (1973)C _p , the Bivar criterion (Young 1982) and AIC (Akaike 1974). An application using a graphical sensitivity analysis is presented.     

Diagnostic analysis for a vector autoregressive model under Student′s t‐distributions

In this paper, we use the local influence method to study a vector autoregressive model under Student^′s t‐distributions. We present the maximum likelihood estimators and the information matrix. We establish the normal curvature diagnostics for the vector autoregressive model under three usual perturbation schemes for identifying possible influential observations. The effectiveness of the proposed diagnostics is examined by a simulation study, followed by our data analysis using the model to fit the weekly log returns of Chevron stock and the Standard & Poor's 500 Index as an application.