The uniform convergence of the nadaraya-watson regression function estimate

If (X₁,Y₁), …, (X_n,Y_n) is a sequence of independent identically distributed R_d × R-valued random vectors then Nadaraya (1964) and Watson (1964) proposed to estimate the regression function m(x) = ? {Y₁|X₁ = x{ by where K is a known density and {h_n} is a sequence of positive numbers satisfying certain properties. In this paper a variety of conditions are given for the strong convergence to 0 of ess_Xsup|m_n (X)-m(X)| (here X is independent of the data and distributed as X₁). The theorems are valid for all distributions of X₁ and for all sequences {h_n} satisfying h_n → 0 and nh/log n→0.     

The Easterlin hypothesis in the recent experience of higher-income OECD countries: A panel-data approach

The Easterlin hypothesis emphasizes the effect of relative cohort size on fertility. Models based on the Easterlin hypothesis have performed well in explaining time series fertility data, although these results have been for long historical time series and have typically been restricted to single country studies. These models are not adequate to determine if the hypothesis still holds and if the success of the Easterlin hypothesis is an artifact of the time period chosen. We use panel data analysis and temporal causality tests to see of the Easterlin hypothesis holds for higher-income OECD countries. The results support the Easterlin hypothesis.All correspondence to Yongil Jeon. An earlier version, The Easterlin hypothesis in OECD countries, was presented at the annual conference of the European society for population economics, Bilbao, Spain, June 2002. We are grateful to two anonymous referees for their helpful comments. The usual caveat applies. Responsible editor: Junsen Zhang.     

A model of the inflationary process in six major O.E.C.D. economies: Empirical results and policy implications

In contrast to most recent empirical work on inflation which has concentrated on the size and stability of coefficients in the wage equation, this paper provides a reexamination of the price equation. Evidence is presented on the structural determinants of inflation in six large industrial nations. It is demonstrated that price equations which include capital costs and excess demand among the regressors perform exceedingly well according to the usual statistical criteria. The results of this study indicate that the inflationary process possesses a high degree of uniformity among the larger industrial countries. This pertains not only with respect to the specific independent variables in price equations, but also with respect to the high degree of uniformity of the estimated coefficients. Additionally, the findings indicate that lower productivity growth and higher capital costs have contributed significantly to the inflationary process since 1974. Furthermore, since higher capital costs are one consequence of tighter monetary policies, the adoption of such policies in response to the two oil price shocks of the 1970s may have offset their intended deflationary effects on prices through the linkage of wage costs and aggregate demand.     

Disappointing and deviant youth and the rage of the elders

A generalized adult hostility toward youth derives from the complexities of the parent/child relationship, often mirrored in the helper/client and therapist/patient dyads. Parents derive considerable or little narcissistic gain from the accomplishments of their offspring, and conversely, are disappointed or even mortified by their failures. This is particularly true of narcissistically vulnerable parents—helpers and therapists as well—and accounts for widespread attitudes of competition, disparagement, and outright hostility toward young people. In the extreme, the pathological situations of emotional exploitation, incest, and physical abuse occur, but lesser forms of exploitation, such as personally gratifying advocacy, political gain, cultism, and enhancement of professional status, point to similar, but seemingly less destructive, forms of narcissistic gain. Youth may respond by conforming, defying, disappointing, and deviating. Adults may be either pleased, or enraged.     

On the non-Markovian structure of discrete order statistics

In this note we show that the Markov Property holds for order statistics while sampling from a discrete parent population if and only if the population has at most two distinct units. This disproves the claim of Gupta and Gupta (1981) that for geometric parent, the order statistics form a Markov chain.     

Admissible estimators in finite population sampling employing various types of prior information

We consider some estimators of the total and variance of a finite population from Bayesian and pseudo-Bayesian perspectives. Recently, Meeden and Ghosh (1982a, 1982b) have provided quite simple but powerful tools for proving admissibility of estimators and estimator-design pairs is finite population sampling problems. We consider what these techniques yield in the way of admissibility results for the estimators discussed.     

A basic lemma and the analysis of block and Kronecker product designs

In this paper the analysis of the class of block designs whose C matrix can be expressed in terms of the Kronecker product of some elementary matrices is considered. The analysis utilizes a basic result concerning the spectral decomposition of the Kronecker product of symmetric matrices in terms of the spectral decomposition of the component matrices involved in the Kronecker product. The property (A) of Kurkjian and Zelen (1963) is generalised and the analysis of generalised property (A) designs is given. It is proved that a design is balanced factorially if and only if it is a generalised property (A) design. A method of analysis of Kronecker product block designs whose component designs are equi-replicate and proper is also suggested.     

The superharmonic condition for simultaneous estimation of means in exponential familles

The mean vector associated with several independent variates from the exponential subclass of Hudson (1978) is estimated under weighted squared error loss. In particular, the formal Bayes and “Stein-like” estimators of the mean vector are given. Conditions are also given under which these estimators dominate any of the “natural estimators”. Our conditions for dominance are motivated by a result of Stein (1981), who treated the N_p (θ, I) case with p ≥ 3. Stein showed that formal Bayes estimators dominate the usual estimator if the marginal density of the data is superharmonic. Our present exponential class generalization entails an elliptic differential inequality in some natural variables. Actually, we assume that each component of the data vector has a probability density function which satisfies a certain differential equation. While the densities of Hudson (1978) are particular solutions of this equation, other solutions are not of the exponential class if certain parameters are unknown. Our approach allows for the possibility of extending the parametric Stein-theory to useful nonexponential cases, but the problem of nuisance parameters is not treated here.     

Tracing developmental trends in Ira Gordon's programs for children and families

Ira Gordon's work in the area of child and family services is traced for six of his programs according to two main trends: (1) perceptions of families through the years and the changing roles of parents in the education of their children; and (2) curriculum changes in activities brought into homes. Gordon's programs, some being initiated as early as 1966, focused upon parents, infants, toddlers, and school-age children and utilized home visitations as a major intervention strategy. Evidence of successes reported for these programs has shown the impact of early intervention upon children as well as their families, school, and community.