On theE-optimality of certain asymmetrical designs under mixed effects model

TheE-optimality of the following designs within the class of all proper and connected designs with givenb, k andv under mixed effects model are established.

1. A group divisible design with λ₂ = λ₁ + 1.
2. A group divisible design with λ₁ = λ₂ + 1 and group size 2.
3. A linked block design.
4. The dual of design (i)
5. The dual of design (ii).

All these designs are known to satisfy the same optimality property under fixed effects model whenk<v, while the design (i) is known to beE-optimal even whenk>v. From the results proved here, theE-optimality of designs (ii, (iii), (iv) and (v) under fixed effects model in the situation whenk >v also follows.     

Self-reflexive networks: Theory · topology · applications

We present a new type of Artificial Neural Networks: the Self-Reflexive Networks. We utter the theoretical presuppositions; their dynamics is analogous to the one ascribed to autopoietic systems: self-referentiality, unsupervised learning and unintentionally cooperative and contractual activities of their own units. We also hypothesize a new concept of perception. We present the basic equations of Self-Reflexive Networks, new concepts as the one of dynamic target, of Re-entry with dedicated and fixed connections, of Meta-Units. Therefore, we experiment a specific type of Self-Reflexive Networks, the Monodedicated, within the interpretation of a toy-DB and we have hinted at other already made experimentations, experimentations in process and planned experimentations. From the applicative work that we present a few specifics and novelties of this type of Neural Networks emerge:

1. the capability of answering to complex, strange, wrong or not precise questions, through the same algorithms through which the learning phase took place.
2. the capability of spontaneously transforming their own learning inaccuracy in analogic capability and original self-organization capability.
3. the capability of spontaneously integrate the models that it experienced in different moments in an achronical hyper-model.
4. the capability of behaving as it had explored a decisions graph of large dimensions, both deeply and in extension. With the consequence of behaving as an Addressing Memory forself-dynamic Contents.
5. the capability of always learning, rapidly and anyway, besides the complexity of the learning patterns.
6. the capability of answering simultaneously from different points of view, behaving, in this case, as a network that builds more similarity models for each vector-stimulus that it receives.
7. the capability of adjusting in a biunivocal way, each question to the consulting DB and each DB to the question that are submitted. The consequence of this fact is the continuous creation of new answering models.
8. the capability of building during the learning phase, a weights matrix that provides a subconceptual representation of the bi-directional relations between each couple of input variables.
9. the capability, through the Metaunits, to integrate in a unitary typology, nodes with different saturation speed and, therefore, with different memory: in fact, while the SR units are short memory nodes, since each new stumulus zeros the previous stimulus, the Metaunits memorize the SR different stimulus during time, functioning as an average length memory. This fact should confirm that the avarage length memory is of a different level from the immediate memory and that it is based only uponrelation among perceptive stimulus which are distributed in parallel and in sequence. In this context the weights matrix constitute the SR long term memory. And in this sense it will be opportune to think at a methodic through which the Metaunits can influence during time, the same weights matrix. In any case, in the SR there areservice nodes orfilter nodes andlearning nodes as if they were weights (the Metaunits).

     

Su di una politica di bonus

Si prende in considerazione una politica di Bonus attuata da una Compagnia di assicurazione e si studia l'andamento della perdita attesa della Compagnia al variare dell'entità del Bonus nei casi in cui:

1. la funzioneL(s), che esprime il livello minimo dell'entità dei sinistri non occultabili all'istantes, sia lineare ins;
2. la funzioneL(s) renda massima la previsione del guadagno di ogni singolo assicurato.

     

Una nota su operazioni associative,trasformate integrali e problemi di caratterizzazione in statistica

In questa nota si studia una equazione funzionale che ha interessanti applicazioni al Calcolo delle Probabilità. Si illustrano due possibilità applicative:

1. la scelta del nucleo delle trasformate integrali;
2. la caratterizzazione di opportune classi di variabili casuali.

     

Inference robustness of ARIMA models under non-normality —Special application to stock price data

Wold's decomposition theorem [Wold] states that every weakly stationary stochastic process can be written as a linear combination of orthogonal shocks. For practical reasons, however, it is desirable to employ models which use parameters parsimoniously.Box andJenkins [1970] show how parsimony can be achieved by representing the linear process in terms of a small number of autoregressive and moving average terms (ARIMA-models). The Gaussian hypothesis assumes that the shocks follow a normal distribution with fixed mean and variance. In this case the process is characterized by first and second order moments. The normality assumption seems reasonable for many kinds of series. However, it was pointed out byKendall [1953],Mandelbrot [1963, 1967],Fama [1965],Mandelbrot andTaylor [1967] that particularly for stock price data the distribution of the shocks appears leptokurtic: In this paper we investigate the sensitivity of ARIMA models to non-normality of the distribution of the shocks. We suppose that the distribution function of the shocks is a member of the symmetric exponential power family, which includes the normal as well as leptokurtic and platikurtic distributions. A Bayesian approach is adopted and the inference robustness of ARIMA models with respect to

1. the estimation of parameters
2. the forecasts of future observations is discussed.

     

Conditions for the optimality of exponential smoothing forecast procedures

Exponential smoothing procedures, in particular those recommended byBrown [1962] are used extensively in many areas of economics, business and engineering. It is shown in this paper that:

1. Brown's forecasting procedures are optimal in terms of achieving minimum mean square error forecasts only if the underlying stochastic process is included in a limited subclass of ARIMA (p, d, q) processes. Hence, it is shown what assumptions are made when using these procedures.
2. The implication of point (i) is that the users ofBrown's procedures tacitly assume that the stochastic processes which occur in the real world are from the particular restricted subclass of ARIMA (p, d, q) processes. No reason can be found why these particular models should occur more frequently than others.
3. It is further shown that even if a stochastic process which would lead toBrown's model occurred, the actual methods used for making the forecasts are clumsy and much simpler procedures can be employed.

     

Verso un unico tipo di concavità

La classica disuguaglianza che definisce la concavità di una funzione: $$f(\alpha x + \bar \alpha y) \geqq \alpha f(x) + \bar \alpha f(y){\mathbf{ }}\bar \alpha = 1 - \alpha$$ può essere generalizzata in due modi:

1. ammettendo pesi diversi nei due membri;
2. ammettendo medie diverse dall'aritmetica.

In questo lavoro si mostra come queste due estensioni contengano vari tipi di concavità generalizzata proposti in letteratura: quasi concavità, pseudoconcavità, concavità forte, “concavificabilità”. Le due estensioni citate si possono per di più riunire in un'unica che prevede sia pesi eventualmente diversi nei due membri sia medie non necessariamente artimetiche. Presentiamo anche alcune semplici proprietà di queste funzioni concave generalizzate.     

Sul ruolo dei riassunti esaustivi ai fini della previsione in contesto Bayesiano (2a parte)

Proseguendo nella ricerca, la cui prima parte è stata pubblicata nel precedente numero di questa Rivista, trattiamo delle successioni di riassunti esaustivi a fini preditivi (r.e.f.p.) ed affrontiamo i seguenti problemi:

1. assegnata una distribuzione predittiva per cui esiste un r.e.f.p. è possibile individuare un modello ipotetico con essa compatibile?
2. in caso affermativo, qual è il collegamento tra tale r.e.f.p. e gli eventuali r.e. in senso classico relativi al modello ipotetico individuato?

Infine analizzeremo, in modo piuttosto informale e perciò ulteriormente sviluppabile, il problema dell'espressione analitica di un r.e.f.p.     

What managers need to know about knowledge-based pay

KBP is an innovative compensation approach wiyh some important advantages for both workers and management. It is growing in use, but there is still not much information available to guide managers who want to use it. Our research suggests that each KBP implementation is idiosyncratic. At CARCO, each of the several plants using KBP designed its own KBP plan. They had very little information upon which they could draw. Likewise, at CONCO the plant manager and other key executives set out the philosophy and structure of KBP with very little guidance, except some discussion with one manager who had some experience with it. At this time, each application of KBP must be individually worked out with respect to such issues as the method of evaluation for pay advancement, the levels at which pay increases ought to be granted, and ways to provide opportunities for skill advancement. There are other areas that we need to know more about:

• •⊎ Under what conditions should an organizationwide or job-circle KBP approach be implemented?
• •⊎ How does the relationship between the range of skills and the range of pay affect performance and satisfaction?
• •⊎ When job circles are used, what guides should be used for grouping jobs into KBP classes?
• •⊎ How does the size of an organization and the range of task variety relate to KBP plans?
• •⊎ How do organizational and pay system differences affect practices such as rotation and participation?

KBP is an interesting and potentially useful approach to compensation. We have suggested some approaches to these issues in this article, but we all need to know more about it.     

On generalized transforms of distribution functions

In this note we discuss the following problem. LetX andY to be two real valued independent r.v.'s with d.f.'sF and ?. Consider the d.f.F*? of the r.v.X oY, being o a binary operation among real numbers. We deal with the following equation: $$\mathcal{G}^1 (F * \phi ,s) = \mathcal{G}^2 (F,s)\square \mathcal{G}^3 (\phi ,s)\forall s \in S$$ where \(\mathcal{G}^1 ,\mathcal{G}^2 ,\mathcal{G}^3 \) are real or complex functionals, т another binary operation ands a parameter. We give a solution, that under stronger assumptions (Aczél 1966), is the only one, of the problem. Such a solution is obtained in two steps. First of all we give a solution in the very special case in whichX andY are degenerate r.v.'s. Secondly we extend the result to the general case under the following additional assumption: $$\begin{gathered} \mathcal{G}^1 (\alpha F + (1 - \alpha )\phi ,s) = H[\mathcal{G}^i (F,s),\mathcal{G}^i (\phi ,s);\alpha ] \hfill \\ \forall \alpha \in [0,1]i = 1,2,3 \hfill \\ \end{gathered} $$ .     

Technology transfer from universities to small and medium-sized enterprises — an empirical survey from the standpoint of such enterprises

This paper describes an investigation during which 225 small and medium-sized enterprises were asked about their experience of cooperation with universities in dealing with technical and scientific problems. About a quarter replied that they had had such experience in the last ten years. These were asked the following questions:

• &#x02022;- Were they satisfied with the cooperation?
• &#x02022;- What were the arguments against cooperation?
• &#x02022;- What especially important factors facilitated cooperation?

The results show that companies, in practice, ascribe the highest significance to factors quite different from those which are emphasized in theoretical literature.     

Central limit theorem for linear eigenvalue statistics of the Wigner and the sample covariance random matrices

We consider n × n real symmetric random matrices n ^?1/2 W with independent (modulo symmetry condition) entries and the (null) sample covariance matrices n ^?1 A ^T A with independent entries of m × n matrix A. Assuming first that the 4th cumulant (excess) κ ₄ of entries of W and A is zero and that their 4th moments satisfy a Lindeberg type condition, we prove that linear statistics of eigenvalues of the above matrices satisfy the central limit theorem (CLT) as n → ∞, m → ∞, ${m/n\rightarrow c\in[0,\infty)}$ with the same variance as for Gaussian matrices if the test functions of statistics are smooth enough (essentially of the class ${\mathbb{C}^5}$ ). This is done by using a simple “interpolation trick”. Then, by using a more elaborated techniques, we prove the CLT in the case of non-zero excess of entries for essentially ${\mathbb{C}^4}$ test function. Here the variance contains additional term proportional to κ ₄. The proofs of all limit theorems follow essentially the same scheme.     

A note on compact differentiability and theδ-method

Letη _n ,n ∈ ?, be arbitrary functions defined on a probability space (ω,A,P) with values in a normed vector spaceB ₁ ,μ ∈ B ₁ andξ ₀ a separable random element inB ₁ such thatξ _n :=√n(η _n ?μ) converges weakly toξ ₀ in the sense of Hoffmann-Jørgensen. Then with (B ₂, ∥·∥₂) being another normed vector space andφ:B ₁→B ₂ compactly differentiable atμ with derivateD _μ, the random variable $\parallel \sqrt n (\phi (n_n ) - \phi (\mu )) - D_\mu (\sqrt n (n_n - \mu ))\parallel 2*$ converges to 0P-stochastically where “*” denotes the measurable cover. We show that the classicalδ — method extends to the non-measurable case where in the proof we shall not make use of any representation theorems but only of a slight refinement of the usual characterisation of compact differentiability, due to the fact that we will not assume {ξ _n :n ∈ ?} being tight.     

The sales job and preparation for management

“The types of work that lead of the top jobs have ovious variations by industry with a few aberrations. There is, nonetheless, a consistent pattern: less law experience than generally supposed, not much engineering or research and among younger executives a lot of sales.”

1 Editors of Fortune Magazine, The Executive Life, Garden City, N.Y.: Doubleday, 1956, p. 31.

Is there something about sales that produces better mangers?     

An extremal property of the generalized arcsine distribution

The main result of the paper is the following characterization of the generalized arcsine density p _γ (t) = t ^γ?1(1 ? t) ^γ?1/B(γ, γ)   with ${t \in (0, 1)}$ and ${\gamma \in(0,\frac12) \cup (\frac12,1)}$ : a r.v. ξ supported on [0, 1] has the generalized arcsine density p _γ (t) if and only if ${ {\mathbb E} |\xi- x|^{1-2 \gamma}}$ has the same value for almost all ${x \in (0,1)}$ . Moreover, the measure with density p _γ (t) is a unique minimizer (in the space of all probability measures μ supported on (0, 1)) of the double expectation ${ (\gamma-\frac12 ) {\mathbb E} |\xi-\xi^{\prime}|^{1-2 \gamma}}$ , where ξ and ξ′ are independent random variables distributed according to the measure μ. These results extend recent results characterizing the standard arcsine density (the case ${\gamma=\frac12}$ ).     

Grundgleichungen der Stereologie II

The densities of volume, surface and of integral of mean curvature and theEulerian characteristic per unit volume of a class of very general special structures are related to quantities which can be measured in specimens obtained by transmission microscopy. A correction for the overlap (Holmes effect) is developped which applies to systems of convex bodies with limited density of volume and the particles of which are randomly distributed if the thin sections have a thickness that is large in comparison with the mean caliper diameter of the particles.     

Bookshelf

• Handbook of Organizational Culture & Climate
• The Compensation Handbook, Fourth Edition
• Innovations in International and Cross‐Cultural Management
• The Leadership Investment
• Best Practices in Leadership Development Handbook
• Measuring Team Performance
• The Inner Work of Leaders
• The Radical Team Handbook
• Suppressed, Forced Out, and Fired: How Successful Women Lose Their Jobs
• Psychological Contracts In Employment

     

Stochastic orderings of convolution residuals

In this paper we study convolution residuals, that is, if $X_1,X_2,\ldots ,X_n$ are independent random variables, we study the distributions, and the properties, of the sums $\sum _{i=1}^lX_i-t$ given that $\sum _{i=1}^kX_i>t$ , where $t\in \mathbb R $ , and $1\le k\le l\le n$ . Various stochastic orders, among convolution residuals based on observations from either one or two samples, are derived. As a consequence computable bounds on the survival functions and on the expected values of convolution residuals are obtained. Some applications in reliability theory and queueing theory are described.     

Random weighting estimation of stable exponent

This paper presents a new random weighting method to estimation of the stable exponent. Assume that $X_1, X_2, \ldots ,X_n$ is a sequence of independent and identically distributed random variables with $\alpha $ -stable distribution G, where $\alpha \in (0,2]$ is the stable exponent. Denote the empirical distribution function of G by $G_n$ and the random weighting estimation of $G_n$ by $H_n$ . An empirical distribution function $\widetilde{F}_n$ with U-statistic structure is defined based on the sum-preserving property of stable random variables. By minimizing the Cramer-von-Mises distance between $H_n$ and ${\widetilde{F}}_n$ , the random weighting estimation of $\alpha $ is constructed in the sense of the minimum distance. The strong consistency and asymptotic normality of the random weighting estimation are also rigorously proved. Experimental results demonstrate that the proposed random weighting method can effectively estimate the stable exponent, resulting in higher estimation accuracy than the Zolotarev, Press, Fan and maximum likelihood methods.