ASYMPTOTIC EXPANSIONS APPLIED TO F-TEST CRITERIA

Using asymptotic expansions of the Kummer hypergeometric function, the sequential. F-test criterion is evaluated asymptotically in terms of the sample size. The continuation region inequalities for the test are inverted and expressed in terms of known test criteria. A rapidly converging algorithm for carrying out the sequential procedure is provided. This makes the F-test easier for the practitioner to use. Almost sure finite termination of the sequential. F-test is asserted by appealing to the continuation inequalities and a heuristic asymptotic expansion of the test criterion. Average stopping times of the sequential procedure for a variety of population means and population number configurations are tabulated. The computer symbolic manipulation program MAPLE was used to derive some formulae.     

When Infants Lose Exclusive Maternal Attention: Is It Jealousy?

To characterize infant reactions to jealousy evocation, 94 6‐month‐olds and their mothers were videotaped in an episode where the mothers directed positive attention toward a lifelike doll, and in 2 contrasting interactions: face‐to‐face play and a still‐face perturbation. Cross‐context comparisons of affects and behaviors revealed that jealousy evocation responses were distinguished by diminished joy and heightened anger and intensity of negative emotionality, comparable to levels displayed during the still‐face episode; heightened sadness, with durations exceeding those displayed during still‐face exposure; and an approach response consisting of interest, looks at mother, and diminished distancing, which was more pronounced than that demonstrated during play. Infants' heightened anger and sadness during jealousy evocation correlated with heightened maternal sensitivity and dyadic vocal turn‐taking, respectively, during play; and infants' diminished joy and interest during jealousy evocation were associated with heightened maternal withdrawal and intrusiveness, respectively, during play. Both fear and mother‐directed gaze were greater in girls. The discussion argues for interpreting the infant's mixed and agitated reaction to jealousy evocation as evidence of jealousy.     

Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines

Abstract.  We consider marginal semiparametric partially linear models for longitudinal/clustered data and propose an estimation procedure based on a spline approximation of the non-parametric part of the model and an extension of the parametric marginal generalized estimating equations (GEE). Our estimates of both parametric part and non-parametric part of the model have properties parallel to those of parametric GEE, that is, the estimates are efficient if the covariance structure is correctly specified and they are still consistent and asymptotically normal even if the covariance structure is misspecified. By showing that our estimate achieves the semiparametric information bound, we actually establish the efficiency of estimating the parametric part of the model in a stronger sense than what is typically considered for GEE. The semiparametric efficiency of our estimate is obtained by assuming only conditional moment restrictions instead of the strict multivariate Gaussian error assumption.     

Genetic algorithms for numerical optimization

Genetic algorithms (GAs) are stochastic adaptive algorithms whose search method is based on simulation of natural genetic inheritance and Darwinian striving for survival. They can be used to find approximate solutions to numerical optimization problems in cases where finding the exact optimum is prohibitively expensive, or where no algorithm is known. However, such applications can encounter problems that sometimes delay, if not prevent, finding the optimal solutions with desired precision. In this paper we describe applications of GAs to numerical optimization, present three novel ways to handle such problems, and give some experimental results.     

Bayesian prediction for progressively censored data from the Burr model

Received: August 14, 2000; revised version: April 23, 2001     

Characterizations of geometric distribution and discrete IFR (DFR) distributions using order statistics

Let X be a discrete random variable the set of possible values (finite or infinite) of which can be arranged as an increasing sequence of real numbers a₁<a₂<a₃<…. In particular, a_i could be equal to i for all i. Let X_1n≦X_2n≦?≦X_nn denote the order statistics in a random sample of size n drawn from the distribution of X, where n is a fixed integer ≧2. Then, we show that for some arbitrary fixed k(2≦k≦n), independence of the event {X_kn=X_1n} and X_1n is equivalent to X being either degenerate or geometric. We also show that the montonicity in i of P{X_kn = X_1n | X_1n = a_i} is equivalent to X having the IFR (DFR) property. Let a_i = i and $\text{G(i) = P(X≧i), i = 1, 2, …}$. We prove that the independence of {X_2n ? X_1n ∈B} and X_1n for all i is equivalent to X being geometric, where B = {m} (B = {m,m+1,…}), provided G(i) = q^i?1, 1≦i≦m+2 (1≦i≦m+1), where 0<q<1.     

The experience of carrying out the technical responsibility system in the birth control of Peng County, Sichuan Province]

Following the establishment of the system of fixed responsibility in production in Peng County, Sichuan Province, the County's Family Planning Office and Public Health Bureau in 1980 broadened the system of technical responsibility in birth control by defining tasks and goals. The commune public health office should guide birth control technology, lower the incidence of unplanned pregnancies and the number of abortions. The number of fertile women using IUDs should be over 80%, and its failure rate should be less then 10%; the failure rate of male ligature should be less than 3%. Commune members should give 1 jiao to the public health office for expenses incurred in birth control technology. If all the goals are reached, then there would be economic rewards outside the total public support system. That is, 1 jiao is awarded for each IUD inserted, 2 jiao for male ligatures and 3 jiao for female ligatures. Infractions such as poor attitude, irresponsibility, or delaying surgery are fined from 1-20 yuan. The following situations resulted from having implemented the system of technical responsibilty for birth control: 1) medical personnel had the authority to initiate action concerning birth control technology; 2) the quality of surgery was raised, while the incidence of errors was lowered; 3) the costs of surgery were lowered; and 4) because abortions are not awarded with economic incentives, medical personnel tended to perform more preventive surgery rather than corrective surgery.