Abstract: Based on a random sample from a univariate distribution with density $f$, this note exhibits a class of kernel estimators of the $p$th order derivative $f^{(p)}$ of $f, p \geqq 0$ fixed. These estimators improve some known estimators of $f^{(p)}$ by weakening the conditions, sharpening the rates of convergence, or both for the properties of strong consistency, asymptotic unbiasedness and mean square consistency, each uniform on the real line.

Abstract: In an electronic calculator essentially comprising a multidigit display, a keyboard and a data processor unit, a multidigit liquid crystal display is deposited together with integral key actuators of the keyboard of a flexible circuit film which carries electrical conductor leaves in a desired pattern. The conductor leaves to be in contact with terminals of the liquid crystal display are formed to extend in the direction of length of the liquid crystal display to thereby establish room for a battery compartment.

Abstract: SUMMARY The procedure, due to Aitchison & Aitken (1976), of analyzing multivariate binary data by kernel methods is extended to deal with missing data problems. The performance of the techniques is discussed for univariate, bivariate and for specific multivariate data. Comparisons are drawn with other approaches. Multivariate binary.

Abstract: Lower bounds on the radius of various confidence sets for density functions and their derivatives are determined. In each case investigated, the smallest radius obtainable and the radius actually obtained by using known estimates exhibit the same dependency on the fixed sample size $n$. The lower bounds are derived using methods in Meyer (1976). Although only a few combinations of pseudometric and density class are considered here, the techniques illustrated can be used elsewhere with little conceptual difficulty.

Abstract: : This paper proposes an approach to non-parametric statistical continuous data science which seems to be consistent with the conventional theories and methods of non-parametric inference but seems to point the way to universally applicable procedures (for continuous data) which are asymptotically as efficient as the best conventional goodness of fit and parameter estimation procedures available for each particular problem. The methods described are programmed and found successful in test cases. However, in the space available here only 'Chapter 1' of this work can be discussed. It outline the ideas: how the basic general applied problems of statistical inference can be formulated as problems of estimation of distribution functions on the unit interval (or the unit hyper-cube), how such problems are more fruitfully treated as density estimation problems, and how to solve density estimation problems one can use the method which is the essence of the highly successful maximum likelihood method of parameter estimation: using a suitable information-theoretic divergence distance between densities, find the smooth density which is closest to a raw estimator of the density.

Abstract: A class of density estimates using a superposition of kernels where the kernel parameter can depend on the nearest neighbor distances is studied by the use of simulated data. Their performance using several measures of error is superior to that of the usual Parzen estimators. A tentative solution is given to the problem of calibrating the kernel peakedness when faced with a finite sample set.

Abstract: The rate at which the mean integrated square error decreases as sample size increases is evaluated for general $L^1$ kernel estimates and for the Fourier integral estimate for a probability density. The rates are compared to that of the minimum M.I.S.E.; the Fourier integral estimate is found to be asymptotically optimal.