12‐Month‐Old Infants' Perception of Attention Direction in Static Video Images

Twelve‐month‐old infants' ability to perceive gaze direction in static video images was investigated. The images showed a woman who performed attention‐directing actions by looking or pointing toward 1 of 4 objects positioned in front of her (2 on each side). When the model just pointed at the objects, she looked straight ahead, and when she just looked, her hands were hidden below the tabletop. An eye movement system (TOBII) was used to register the gaze of the participants. We found that the infants clearly discriminated the gaze directions to the objects. There was no tendency to mix up the 2 object positions, located 10° apart, on the same side of the model. The infants spent more time looking at the attended objects than the unattended ones and they shifted gaze more often from the face of the model to the attended object than to the unattended objects. Pointing did not significantly increase the infants' tendency to move gaze to the attended object, irrespective of whether the pointing gesture was accompanied by looking or not. In all conditions the infants spent most of the time looking at the model's face. This tendency was especially noticeable in the pointing‐only condition and the condition where the model just looked straight ahead.     

A neoclassical Kaldor model of real wage declines

A model linking macroeconomic equilibrium and income distribution in balanced growth equilibria is developed as a variant to the Kaldor model of factor shares. It departs from the original Kaldor model in assuming equal saving rates and a neoclassical production function. Macroeconomic equilibrium (national savings equal to investment) combines with competitive microeconomic behavior to determine the real wage and real interest rate. An increase in the ratio of national debt to labor reduces the real wage, explaining recent declines.     

On Loss Distributions from Installment-Repaid Loans

The banks have been accumulating huge data bases for many years and are increasingly turning to statistics to provide insight into customer behaviour, among other things. Credit risk is an important issue and certain stochastic models have been developed in recent years to describe and predict loan default. Two of the major models currently used in the industry are considered here, and various ways of extending their application to the case where a loan is repaid in installments are explored. The aspect of interest is the probability distribution of the total loss due to repayment default at some time. Thus, the loss distribution is determined by the distribution of times to default, here regarded as a discrete-time survival distribution. In particular, the probabilities of large losses are to be assessed for insurance purposes.     

Optimal Ordering Policies for Stochastic Inventory Problems with Observed Information Delays

Information delays exist in an inventory system when it takes time to collect, process, validate, and transmit inventory/demand data. A general framework is developed in this paper to describe information flows in an inventory system with information delays. We characterize the sufficient statistics for making optimal decisions. When the ordering cost is linear, the optimality of a state‐dependent base‐stock policy is established even when information flows are allowed to cross over time. Additional insights into the problem are obtained via a comparison between our models and the models with stochastic order lead times. We also show that inventory can substitute for information and vice versa.     

On sequentially rejective subset selection procedures

A technique for selection procedures, called sequential rejection, is investigated. It is shown that this technique is posssible to apply to certain selection goals of the "all or nothing" type, i.e. "selecting a subset containing all good populations" or "selecting a subset containing no bad population". The analogy with existing sequential techniques in the general theory of simultaneous statistical inference is pointed out.     

Some further aspects of the löwner-ordering antitonicity of the moore-penrose inverse

A survey is given of known proofs of the antitonicity of the inverse matrix function for positive definite matrices w.r.t. the Lowner partial ordering, and of the corresponding result for the Moore-Penrose inverse of nonnegative definite matrices [the theorem of Milliken and Akdeniz (1977)]. A short new proof of the latter result is obtained by employing an extremal representation of a nonnegative definite quadratic form. Another proof of this result involving Schur complements is also given, and is seen to be extendable to the case of symmetric (not necessarily nonnegative definite) matrices. A geometrical interpretation of Milliken and Akdeniz's theorem is presented. As an application, the relationship between the concepts of greater (maximum) concentration and smaller (minimum) dispersion is considered for a pair (class) of vector-valued statistics with possibly degenerate distributions.     

Statistical analysis for Kumaraswamy’s distribution based on record data

In this paper we review some results that have been derived on record values for some well known probability density functions and based on m records from Kumaraswamy’s distribution we obtain estimators for the two parameters and the future sth record value. These estimates are derived using the maximum likelihood and Bayesian approaches. In the Bayesian approach, the two parameters are assumed to be random variables and estimators for the parameters and for the future sth record value are obtained, when we have observed m past record values, using the well known squared error loss (SEL) function and a linear exponential (LINEX) loss function. The findings are illustrated with actual and computer generated data.     

Goodness-of-Fit Tests for Multivariate Distributions

We propose three new statistics, Z _p , C _p , and R _p for testing a p-variate (p ≥ 2) normal distribution and compare them with the prominent test statistics. We show that C _p is overall most powerful and is effective against skew, long-tailed as well as short-tailed symmetric alternatives. We show that Z _p and R _p are most powerful against skew and long-tailed alternatives, respectively. The Z _p and R _p statistics can also be used for testing an assumed p-variate nonnormal distribution.