Lord Aldington's Disservice to Wealth Creation

The habitual opposition to the growth of service industries from traditionalists and manufacturing interests is rehearsed in the Aldington Report on Overseas Trade John McEnery (right), former Under-Secretary at the Department of Trade and Industry, and author of IEA Research Monograph Manufacturing Two Nations, condemns outmoded patterns of thought and recalls on the Upper House to abandon its manufacturing myopia     

Approximation for the cumulative and inverse gamma distribution

The gamma distribution function can be expressed in terms of the Normal distribution and density functions with sufficient accuracy for most practical purposes.
The distribution function for the density x^Λ-1e^-x/μ/μ^ΛΓ(A) on 0 -R(Λ){(1 + 1/1 2Λ) φ(z) + 11 -z/4Λ^1/2+2(z²+ 2)/45Λ] φ(z) /3 Λ^1/2} where φ(z)≅1/[1 +_e^{-2z(√2/π+z2 /28)}] and φ(z) = e^{-z2 /2}/√2π are the Normal distribution and density functions, y is the appropriate root of y-y²/6+y³/36-y⁴/270= In (x/Λμ), z= Λ^1/2 y, and R( Λ) is the remainder term in Stirling's approximation for In Γ(Λ).     

An improved empirical Bayes test for positive exponential families

We exhibit an empirical Bayes test δ^* _n for a decision problem using a linear error loss in a class of positive exponential families. This empirical Bayes test δ^* _n possesses the asymptotic optimality, and its associated regret converges to zero with rate n ⁻¹(ln n )⁶ This rate of convergence improves the previous results in the literature in the sense that a faster rate of convergence is achieved under much weaker conditions. Examples are presented to illustrate the performance of the empirical Bayes test δ^* _n     

Fourier inversion and the Hausdorff distance

This paper continues research done by F.H. Ruymgaart and the author. For a function f on R ^d we consider its Fourier transform F f and the functions f_M (M>0) derived from F f by the formula f_M(x) =( F( ε_M · F f ))(− x );, where the ε_M are suitable integrable functions tending to 1 pointwise as M →∞. It was shown earlier that, relative to a metric d _H , analogous to the Hausdorff distance between closed sets, one has d _H (f_M, f) = O( M ^−½) for all f in a certain class. We now show that, for such f , the estimate O( M ^−½) is optimal if and only if f has a discontinuity point.     

The asymptotic distribution of the sum of weighted squared residuals in binary choice models

It is claimed by some authors that the distribution of the sum of weighted squared residuals, used as a goodness of fit measure in binary choice models, behaves for large n as a x²_n– k–1 distribution. This claim seems to be based on a false analogy with the well–known Pearson x² statistic for frequency tables with a fixed number of cells and cell sizes tending to infinity. We derive the asymptotic (normal) distribution and show that the approximation by the x² distribution in general will not be valid. A new x² test is proposed based on the asymptotic normality of the measure.     

PSEUDO-R2 MEASURES FOR SOME COMMON LIMITED DEPENDENT VARIABLE MODELS

Abstract. A large number of different Pseudo- R ² measures for some common limited dependent variable models are surveyed. Measures include those based solely on the maximized likelihoods with and without the restriction that slope coefficients are zero, those which require further calculations based on parameter estimates of the coefficients and variances and those that are based solely on whether the qualitative predictions of the model are correct or not. The theme of the survey is that while there is no obvious criterion for choosing which Pseudo- R ² to use, if the estimation is in the context of an underlying latent dependent variable model, a case can be made for basing the choice on the strength of the numerical relationship to the OLS- R ² in the latent dependent variable. As such an OLS- R ² can be known in a Monte Carlo simulation, we summarize Monte Carlo results for some important latent dependent variable models (binary probit, ordinal probit and Tobit) and find that a Pseudo- R ² measure due to McKelvey and Zavoina scores consistently well under our criterion. We also very briefly discuss Pseudo- R ² measures for count data, for duration models and for prediction-realization tables.     

A smoothed maximum score estimator for the binary choice panel data model with an application to labour force participation

In a binary choice panel data model with individual effects and two time periods, Manski proposed the maximum score estimator based on a discontinuous objective function and proved its consistency under weak distributional assumptions. The rate of convergence is low ( N ^1/3) and its limit distribution cannot easily be used for statistical inference. In this paper we apply the idea of Horowitz to smooth Manski's objective function. The resulting smoothed maximum score estimator is consistent and asymptotically normal with a rate of convergence that can be made arbitrarily close to N ^1/2, depending on the strength of the smoothness assumptions imposed. The estimator can be applied to panels with more than two time periods and to unbalanced panels. We apply the estimator to analyze labour force participation of married Dutch females.     

Scheduling identical jobs on uniform parallel machines

We address the problem of scheduling n identical jobs on m uniform parallel machines to optimize scheduling criteria that are nondecreasing in the job completion times. It is well known that this can be formulated as a linear assignment problem, and subsequently solved in O ( n ³) time. We give a more concise formulation for minsum criteria, and show that general minmax criteria can be minimized in O ( n ²) time. We present faster algorithms, requiring only O ( n + m log m ) time for minimizing makespan and total completion time, O ( n log n ) time for minimizing total weighted completion time, maximum lateness, total tardiness and the weighted number of tardy jobs, and O ( n log² n ) time for maximum weighted tardiness. In the case of release dates, we propose an O ( n log n ) algorithm for minimizing makespan, and an O ( mn ^2m+1) time dynamic programming algorithm for minimizing total completion time.     

The effect of rounding off in samples

Dit artikel bevat een elementaire behandeling van afrondingseffecten in steekproeven.
Zoals men verwacht, neemt de variantie van het steekproefgermddelde door af ronding der waarnemingen toe met een factor 1 + b ²/12σ _x ², waarbij b het afrondings- interval en σ _x ² de stamvariantie is, in analogie met de bekende correcties van Sheppard. Verder wordt het effect van afronding op de variantie van de steek-proefvariantie onderzocht. Er wordt op gewezen, dat de afrondingsfout ε in één steekproef gecorreleerd is met de afwijking van de nauwkeurige — d.w.z. niet afgeronde — stochastische variabele x van zijn gemiddelde μ, hoewel deze correlatie gemiddeld nul is. Het gevolg is, dat de variantie van de steekproefvariantie toeneemt. Bij "gewone" waarschijnlijkheidsverdelingen, die continue naar nul gaan bij x →, is deze toename gelijk aan
1/ n (1/3 b ²σ _x ²+ 1/180 b ⁴)
waarbij n de grootte van de steekproef is. Bij normale verdelingen is het effect ongeveer twee maal zo groot als de toename volgens de Sheppard's correctie van de afgeronde variantie.     

First-Order Integer-Valued Autoregressive (INAR (1)) Process: Distributional and Regression Properties

Some properties of a first-order integer-valued autoregressive process (INAR)) are investigated. The approach begins with discussing the self-decomposability and unimodality of the 1-dimensional marginals of the process {X_n} generated according to the scheme X_n=α° X _n-i +e_n, where α° X _n-1 denotes a sum of X_{n - 1}, independent 0 - 1 random variables Y^(n-1), independent of X _n-1 with Pr -( y ^{(n - 1)}= 1) = 1 - Pr ( y ^(n-i)= 0) =α. The distribution of the innovation process ( e _n) is obtained when the marginal distribution of the process ( X _n) is geometric. Regression behavior of the INAR(1) process shows that the linear regression property in the backward direction is true only for the Poisson INAR(1) process.     

De omvang van de steekproef bij een enkelvoudig steekproefsysteem

Summary  (Sample size for a single sampling scheme).
The operating characteristic of a sampling scheme may be specified by the producers 1 in 20 risk point ( p ₁), at which the probability of rejecting a batch is 0.05, and the consumers 1 in 20 risk point ( p ₂) at which the probability of accepting a batch of that quality is also 0.05.
A nomogram is given (fig. 2) to determine for single sampling schemes and for given values of p₁ and p ₂ the necessary sample size ( n ) and the allowable number of defectives in the sample ( c ).
The nomogram may reversedly be used to determine the producers and consumers 1 in 20 risk points for a given single sampling scheme.
The curves in this nomogram were computed from a table of percentage points of the χ² distribution. For v > 30 Wilson and Hilferty's approximation to the χ² distribution was used.     

On the generalized Poisson distribution

We use Euler's difference lemma to prove that, for θ > 0 and 0 ≤λ < 1, the function P _n defined on the non-negative integers by
P _n (θ, λ) = [θ(θ + n λ) ^{n −1}/ n !]e^{− n λ−θ}
defines a probability distribution, known as the Generalized Poisson Distribution.     

On X2- tests for contingency tables of negative multinomial types

Om te toets of die twee kenmerke waarvolgens die frekwensies in 'n gebeurlikseidstabel opgestel is onafhanklik is, word gewoonlik 'n X² toets gebruik. In die opstelling van so 'n toets word die totale frekwensie as vas beskou. In hierdie artikel word aangetoon hoe 'n X²-toets nog gebruik kan word wanneer die steekproefneming voortgesit word totdat 'n vooraf vasgestelde frekwensie in een selbereik word. Die totale frekwensie is dan 'n stogastiese veranderlike. Die eienskappe van die randverdelings van 'n negatiewe multinomiaalverdeling word gebruik om die parameters wat in die X²-verdeling optree te skat.     

Asymptotic properties of estimators for the volume fractions of jointly stationary random sets

In the present paper, we show how a consistent estimator can be derived for the asymptotic covariance matrix of stationary 0–1-valued vector fields in R ^d , whose supports are jointly stationary random closed sets. As an example, which is of particular interest for statistical applications, we consider jointly stationary random closed sets associated with the Boolean model in R ^d such that the components indicate the frequency of coverage by the single grains of the Boolean model. For this model, a representation formula for the entries of the covariance matrix is obtained.     

A different solution of a problem posed by Theil and Schweitzer

De vraag naar de nauwkeurigste (d.i. kleinste tweede moment) schatter van de restvariantie a² bij lineaire regressieanalyse met isomore onafhankelijke normaal verdeelde residuen wordt opnieuw beantwoord, maar longs vrijwel geheel andere weg dan door THEIL en SCHWEITZER [3] bewandeld. Het blijkt bovendien dat deling van de residuele som van kwadraten door het bijbehorende aantal vrijheids-graden + 2 niet alleen in de klasse der kwadratische funk ties der waarnemingen maar zelfs in de klasse van alle veelvouden van zuivere schattingen van σ² de nauwkeurigste is. Gebruik wordt gemaakt van de in een appendix bewezen stelling, dat de traditionele schatter van σ², waarbij de residuele som van kwadraten door het bijbehorend aantal vrijheidsgraden wordt gedeeld, de nauwkeurigste is onder alle zuivere schatters.     

Why do Employment Rates Differ Across the Regions of Britain?

Both unemployment and non-employment in Great Britain fell steadily after 1993. The ratio of jobs to the working age population — the employment rate — rose. But the increasing regional dispersion of employment rates remains a puzzle. By 2000–01, this dispersion was close to its 1974 and 1985 peak levels, though it has narrowed since 2001. This paper by John Muellbauer & Gavin Cameron ¹ examines this puzzle in the context of different measures of the employment rate and examines what we know and what we do not know about what drives relative employment rates across the British regions. It summarises the findings from an econometric study and examines the outlook for relative employment across the British regions.     

Exceptional Convergence of the Sample Variance

The case is investigated when Hoeffding's one sample U–statistic theorem for the sample variance S² is not applicable. It is shown that this occurs only when the parent distribution is the two–point distribution with jumps of equal magnitude. For this exceptional case the standardised S² is shown to converge in distribution to (1 – V )√2, where V has chi–square distribution with one degree of freedom.     

A note on the upper bound for the distance in total variation between the binomal and the Poisson distribution

Abstract  The total variation distance between the binomial B ( n, p ) distribution and the Poisson P ( np ) distribution is smaller than 2 ^1/2 p (1- p )^-1/2 according to V ERVAAT [4], [5]. We shall sharpen this inequality by using a result due to K EMPERMAN [1], C SISZÁR [2] and K ULLBACK [3].     

Characteristic properties of order statistics based on random sample size from an exponential distribution

Suppose X₁, X₂, X_m is a random sample of size m from a population with probability density function f (x), x > 0), and let X_{1, m}< × 2, m <… < X_{m, m} be the corresponding order statistics.
We assume m is an integer-valued random variable with P( m = k ) = p (1- p )^k-1, k = 1,2,… and 0 < p < 1. Two characterizations of the exponential distribution are given based on the distributional properties of X_{l, m}.     

Labour Relations Deteriorate in Nationalised Industry

It has long been argued that the relations between employees and employers would improve once industry was nationalised. John McEnery, until recently a senior civil setvant, argues that it is the nature of nationalisation to make labour relations worse than in private industry.