Stein's identity,Fisher information,and projection pursuit: A triangulation

Two separate structure discovery properties of Fisher's LDF are derived in a mixture multivariate normal setting. One of the properties is related to Fisher information and is proved by using Stein's identity. The other property is on lack of unimodality. The properties are used to give three selection rules for choice of informative projections of high-dimensional data, not necessarily multivariate normal. Their usefulness in the two group-classification problem is studied theoretically and by means of examples. Extensions and various issues about practical implementation are discussed.     

Nonparametric functionals of spectral distributions and their applications to time series analysis

There is a close analogy between empirical distributions of i.i.d. random variables and normalized spectral distributions of wide-sense stationary processes. Herein we make use of this analogy to develop nonparametric comparisons of two spectral distributions and nonparametric tests of stationarity versus change-point alternatives via spectral analysis of a time series.     

Time series,point processes,and hybrids

Techniques developed for the study of time series, point processes, and marked point processes can suggest corresponding techniques for each other, and common techniques can be recognized. In this paper connections are drawn based on conceptual foundations, basic parameters, analyses, displays, algorithms, problems, models. The definitions and techniques are brought out by specific scientific problems. The emphasis is on the single-realization stationary case and on the use of second- and third-order moments to help understand the realization. The tool of stacking, at a particular period, is employed in several of the examples.     

Variance of the difference between two estimated responses

Minimization of the maximum and average variance of the difference between estimated responses are taken as design criteria for univariate polynomial regression models. An optimal design under the first criterion is derived for the second-order model and a class of designs nearly optimal under the second criterion is obtained for the general polynomial models.     

Balanced arrays of strength 4 and balanced fractional 3m factorial designs

A connection between a balanced fractional 2^m factorial design of resolution 2l + 1 and a balanced array of strength 2l with index set {μ₀, μ₁,…, μ_2l} was established by Yamamoto, Shirakura and Kuwada (1975). The main purpose of this paper is to give a connection between a balanced fractional 3^m factorial design of resolution V and a balanced array of strength 4, size N, m constraints, 3 levels and index set {λ_l0l1l2}.     

Optimum invariant tests on discriminant coefficients or means of multinormal population with additional information

Some optimum invariant tests are derived for certain hypotheses on discriminant coefficients or means when some extra observations are available on some components of a random vector X, which is distributed as N(μ,Σ), where μ and Σ are unknown.     

Four mols of order 10 with a hole of order 2

A transversal design with hole T[6;10]?T[6;2] is constructed from a separable group divisible design GD[5,1,8;48].     

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.     

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.