The measurement of capital utilisation rates

A strategy using spline function interpolation is developed f o r estimating capital utilisation rates . Cobb-Douglas, CES and translog functional forms are used in estimation. Tests for functional forms are conducted leading t o t h e s e l e c t i o n of the Cobb-Douglas form. Quarterly series of estimated utilisation rates and excess capacity measures are presented.     

Moments of some J-shaped distributions

This paper concerns a family of univariate distributions suggested by Topp & Leone in 1955. Topp & Leone provided no motivation for this new family and by way of properties they derived only the first four integer-order moments, i.e. E(Xn) for n=1, r 2, r 3, r 4 . In this paper we provide a motivation for the family of distributions and derive explicit algebraic expressions for: (1) hazard rate function; (2) E(Xn) when n ± 1 is any integer; (3) E(Xn) for n=1, r 2, r … r , r 10 , and (4) E[{X-E(X)} n] , n=2, r 3, r 4 . We also give an expression for the characteristic function and discuss issues on estimation and simulation. The main calculations of this paper use properties of the Gauss hypergeometric function.     

Large sample inference in random coefficient regression models

Random coefficient regression models have been used t odescribe repeated measures on members of a sample of n in dividuals . Previous researchers have proposed methods of estimating the mean parameters of such models. Their methods require that eachindividual be observed under the same settings of independent variablesor , lesss stringently , that the number of observations ,r , on each individual be the same. Under the latter restriction ,estimators of mean regression parameters exist which are consist ent as both r^→∞and n^→∞ and efficient as r^→∞, and large sample ( r large ) tests of mean parameters are available . These results are easily extended to the case where not a11 individuals are observed an equal number of times provided limit are taken as min(r) → ∞. Existing methods of inference , however, are not justified by the current literature when n is large and r is small, as is the case i n many bio-medical applications . The primary con tribution of the current paper is a derivation of the asymptotic properties of modifications of existing estimators as n alone tends to infinity, r fixed. From these properties it is shown that existing methods of inference, which are currently justified only when min(r) is large, are also justifiable when n is large and min(r) is small. A secondary contribution is the definition of a positive definite estimator of the covariance matrix for the random coefficients in these models. Use of this estimator avoids computational problems that can otherwise arise.     

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.     

Testing for Heteroscedasticity and/or Autocorrelation in Longitudinal Mixed Effect Nonlinear Models with AR(1) Errors

The effect of influental observation son the parameter estimates of ordinary least squares regression models has received considerable a t t e n t i o n fn the last decade. However, very little attention has been given to the problem of influential observation sinthea naysis of variace . The purpose of this paper is to show by way of examples that in fluential observations can alter the conclusions of tests of hypotheses in the analysis of variance . Regression diagno stics for identifying both extreme points and out liers can be used toreveal potential data and design problems.     

Local asymptotic normality of intermediate and central order statistics

Consider n independent random variables Z_i,…, Z_n on R with common distribution function F, whose upper tail belongs to a parametric family F(t) = F_θ(t),t ≥ x₀, where θ ∈ ? ? R ^d. A necessary and sufficient condition for the family F_θ, θ ∈ ?, is established such that the k-th largest order statistic Z_n?k+1:n alone constitutes the central sequence yielding local asymptotic normality ( LAN ) of the loglikelihood ratio of the vector (Z_n?i+1:n)¹ _i=kof the k largest order statistics. This is achieved for k = k(n)→_n→∞∞ with k/n→_n→∞ 0.

In the case of vectors of central order statistics ( Z_r:n, Z_r+1:n,…, Z_s:n ), with r/n and s/n both converging to q ∈ ( 0,1 ), it turns out that under fairly general conditions any order statistic Z_m:n with r ≤ m ≤s builds the central sequence in a pertaining LAN expansion.These results lead to asymptotically optimal tests and estimators of the underlying parameter, which depend on single order statistics only     

A comparison of approximations to the distribution of average kendall tau

The average Kendall tau test for the null hypothesis of compLete randomness in n judges' rankings of r objects was introduced by Ehrenberg (1952). The superior efficiency of this test. as measured by approximate Bahadur slope has been established by Alva, Cabilio, and Feigin (1982).

The purpose of this paper is first to provide further justification for the use of this test, and second to compare the accuracy of the asymptotic distribution to other app roxtmations to the null distribution for small values of r and n. In the process we generate tables for this exact dis tribution for r=3 and n=3(1)19, r=4 and n=3(1)9, r=5 and n=3(1)5.     

First German register based census in 2011

Summary The last censuses in Germany were accomplished in 1987 (former federal states) and 1981 (new federal states), respectively. Germany was the only country which did not participate in the EU-wide census in 2000. A traditional census was not feasible on political scale due to high costs and low acceptance by the population. Complete, precise and actual statistical registers as a condition for a register based census, are non-existent in Germany. Official statisticians developed a model for a register based census with interviewer-based surveys kept to a minimum. As the basic conditions were not favourable the model became very complex and many methods and procedures had to be developed for the special case of German registers. Core model elements were tested in a census test, such as quality of registers (e. g. municipal population registers, registers of the federal labour agency) and practicability of procedures (e. g. merging of registers, household generation). The test result was that a register based census is possible but much development work still has to be done, as the registers do not have an acceptable quality yet. Additional interviewer based surveys will be necessary for correction of errors of the register and survey of additional variables. This is also true if measures to improve municipal population registers, e. g. a feedback procedure and a nationwide tax number are taken into account. So these measures will not substitute the additional interviewer based surveys. Provided that the essential investments in development and preparation will be performed, Germany could participate in the 2011 EU-census-round with a register based census at a fraction of the cost of a traditional census. Finally, the census 2011 will show the real quality of the registers, how the model will work throughout the country and which measures have to be taken before the following census.

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Zusammenfassung In Deutschland wurde die letzte Volksz?hlung 1987 (Alte Bundesl?nder) bzw. 1981 (Neue Bundesl?nder) durchgeführt. An dem EU-weiten Zensus um das Jahr 2000 beteiligte sich Deutschland als einziger EU-Staat nicht, da ein herk?mmlicher Zensus aus Kosten- und Akzeptanzgründen politisch nicht durchsetzbar war. Die Voraussetzungen für einen Registerzensus, d. h. Statistikregister, die alle ben?tigten Merkmale mit hinreichender Genauigkeit und Aktualit?t enthalten, waren und sind nicht vorhanden. Amtliche Statistiker entwickelten ein Modell für einen registergestützten Zensus mit einem m?glichst geringen Anteil an prim?rstatistischen Erhebungen. Aufgrund der für einen Zensus auf Basis von Registern ungünstigen Rahmenbedingungen wurde dieses Modell relativ komplex und in vielen Bereichen statistisches Neuland betreten. Wesentliche Elemente des Modells wurden in einem sog. Zensustest überprüft. Getestet wurden insbesondere die Qualit?t und Aktualit?t vorhandener Register, wie Melderegister und Dateien der Bundesagentur für Arbeit, sowie die Eignung und Wirksamkeit der Verfahren, wie Zusammenführungen der Daten aus verschiedenen Quellen und Haushaltegenerierung. Die Tests best?tigten die Machbarkeit des Zensusmodells, zeigten aber gleichzeitig, dass noch umfangreiche Entwicklungsarbeiten erforderlich sind und dass die Register noch keine Qualit?t aufweisen, die einen Verzicht auf prim?rstatistische Erhebungen zur Korrektur und Erg?nzung der Registerergebnisse zulassen. Dies gilt auch unter Berücksichtigung der in den n?chsten Jahren vorgesehenen Ma?nahmen zur Verbesserung der Qualit?t der Melderegister, wie die Einführung eines elektronischen Rückmeldeverfahrens oder die Erg?nzung der Melderegister um eine bundeseinheitliche Steuernummer für jede Person. Soweit in den n?chsten Jahren die erforderlichen Investitionen in Entwicklung und Vorbereitung eines registergestützten Zensus get?tigt werden, k?nnte in Deutschland im Rahmen der n?chsten EU-Zensusrunde ein solcher Zensus im Jahre 2011 zu einem Bruchteil der Kosten eines herk?mmlichen Zensus durchgeführt werden. Erst mit diesem Zensus k?nnte dann letztlich festgestellt werden, welche Qualit?t die Register zu diesem Zeitpunkt aufweisen, wie sich das Modell eines registergestützten Zensus (fl?chendeckend) in der Praxis bew?hrt und welche Ma?nahmen für darauf folgende Zensen in Angriff genommen werden müssen.

     

Testing hypotheses in truncated samples by means of divergence statistics

In this paper we consider the problem of testing hypotheses in parametric models, when only the first r (of n) ordered observations are known.Using divergence measures, a procedure to test statistical hypotheses is proposed, Replacing the parameters by suitable estimators in the expresion of the divergence measure, the test statistics are obtained.Asymptotic distributions for these statistics are given in several cases when maximum likelihood estimators for truncated samples are considered.Applications of these results in testing statistical hypotheses, on the basis of truncated data, are presented.The small sample behavior of the proposed test statistics is analyzed in particular cases.A comparative study of power values is carried out by computer simulation.     

Multiple clusters on the line

Given N events occurring over time, define an n:t cluster as n consecutive events all contained within an interval of length t. In this paper we derive the expectation, variance and approximate distribution of the number of n:t clusters. The results have applications in epidemiological studies of rare diseases.     

Reliability estimation based on ranked set sampling

In this paper we consider the problem of estimating the reliability of an exponential component based on a Ranked Set Sample (RSS) of size n. Given the first r observations of that sample, 1≤r≤n, we construct an unbiased estimator for this reliability and we show that these n unbiased estimators are the only ones in a certain class of estimators. The variances of some of these estimators are compared. By viewing the observations of the RSS of size n as the lifetimes of n independent k-out-of-n systems, 1≤k≤n, we are able to utilize known properties of these systems in conjunction with the powerful tools of majorization and Schur functions to derive our results.     

Test of independence between tow sets of variates

In this paper asymptotic expansions of the null as well as non-null distributions of the likelihood ratio criterion for testing independence between two sets of variates are obtained. These appear to be better than the ones available in the literature . In factin the null case for p = 1 and p = 2 , t h e expansion reduces to the exact di stribution. In the non-null case, the expansion is given i n terms of non-central beta distributions and for the case when the population canonical correlation coefficients are small.     

Non-standard methods in evolutionary computation

The paper presents non-standard methods in evolutionary computation and discusses their applicability to various optimization problems. These methods maintain populations of individuals with nonlinear chromosomal structure and use genetic operators enhanced by the problem specific knowledge.     

Development of r,T hybrid sampling plans for exponential lifetime distributions

SUMMARY In the original hybrid reliability acceptance sampling plan RASP developed by Epstein for the exponential lifetime distribution, the sample size n and the number of failures r to be observed are determined given the truncation time T . However, these plans cannot be used when test items are expensive and or limited in number. Therefore, one wishes to have a plan in which n is given. In this paper, we develop hybrid RASPs in which r and T are determined, given n. These plans are tabulated for various combinations of parameter values, so that one may easily determine an appropriate plan.     

On the use of cross-validation to assess performance in multivariate prediction

We describe a Monte Carlo investigation of a number of variants of cross-validation for the assessment of performance of predictive models, including different values of k in leave-k-out cross-validation, and implementation either in a one-deep or a two-deep fashion. We assume an underlying linear model that is being fitted using either ridge regression or partial least squares, and vary a number of design factors such as sample size n relative to number of variables p, and error variance. The investigation encompasses both the non-singular (i.e. n > p) and the singular (i.e. n p) cases. The latter is now common in areas such as chemometrics but has as yet received little rigorous investigation. Results of the experiments enable us to reach some definite conclusions and to make some practical recommendations.     

Jury size and jury verdicts

The analysis of jury size and jury verdicts in criminal m a t t e r s now has along , though interrupted , history . Work In this subject in the 18th and 19th centuries by Condorcet arid Laplace is discussed and the Poisson model of the 1830's is highighted . The latter is modified t o analyze the America1 jury experience of the 20th century. Recent U. S. Supreme Court decis on sin the 1970's on jury size and jury decisiol - making have created a resurgence of interest especially on a comparison of six member and twelve member juries . Some comparisons of size in terms of probabilities of errors invericts are presented.     

The ubiquitous angle

Summary.  Previously we used the geometry of n -dimensional space to derive the paired samples t -test and its p -value. In the present paper we describe the 'ubiquitous' application of these results to single degree of freedom linear model hypothesis tests. As examples, we derive the p - and t -values for the independent samples t -test, for testing a contrast in an analysis of variance and for testing the slope in a simple linear regression analysis. An angle θ in n -dimensional space is again pivotal in the development of the ideas. The relationships between p , t , θ , F and the correlation coefficient are also described by using a 'statistical triangle'.     

FDR control of detected regions by multiscale matched filtering

Feature extraction from observed noisy samples is a common important problem in statistics and engineering. This paper presents a novel general statistical approach to the region detection problem in long data sequences. The proposed technique is a multiscale kernel regression in conjunction with statistical multiple testing for region detection while controlling the false discovery rate (FDR) and maximizing the signal-to-noise ratio via matched filtering. This is achieved by considering a one-dimensional region detection problem as its equivalent zero-dimensional peak detection problem. The detection method does not require a priori knowledge of the shape of the nonzero regions. However, if the shape of the nonzero regions is known a priori, e.g., rectangular pulse, the signal regions can also be reconstructed from the detected peaks, seen as their topological point representatives. Simulations show that the method can effectively perform signal detection and reconstruction in the simulated data under high noise conditions, while controlling the FDR of detected regions and their reconstructed length.     

A confidence interval for the scale parameter based on sukhtmes two-sample statistic

Sukhatme (1957) introduced a statistic which may be used to test the equality of variances in two independent samples from continuous distributions, centered at zero. It has become evident that this statistic cound be used to construct, analytically, a confidence interval for the scale parameter relating the two random variables(of.Laubscher (1968) and Noether (1967, pp. 66-69 and 1972)). In view of this additional use of the statistic, and since no tables of critical values exist, we provide such a table which makes the application of the statistic a practical proposition. In addition, a normal approximation is suggested for the use outside the range of Table III and the accuracy of this approximation is investigated. The Sukhatme test applied to sample values reduced by t n e i r medians i s studied in a small simulation exercise. It appears that this test when used in conjunction with the critical values of Sukhatme's statistic, is a very conservative one and that it is probably fairly robust with respect to the underlying population distribution.