John Rice

Little Jiffy, Mark Iv

IN this paper three changes and one new development for the method of exploratory factor analysis (a second generation Little Jiffy) developed by Kaiser (1970) are described. Following this short description a step-by-step computer algorithm of the revised method-dubbed Little Jiffy, Mark IV-is presented. Extensive empirical experience with &dquo;a second generation Little Jiffy&dquo; (Kaiser, 1970) indicates that the method, for large matrices, consistently mildly underfactors. A revision is called for. Thus, the writers adopt as the answer for the crucially important question of the &dquo;number of factors&dquo; Guttman’s (1954) classic weaker lower bound, the index of the covariance matrix (with zeros in the diagonal) under consideration. This answer is the same as that given by Kaiser’s (1956, 1960, 1970) extensively used &dquo;eigenvalues greater than one of R.&dquo;

Semiparametric Estimates of the Relation between Weather and Electricity Sales

Abstract A nonlinear relationship between electricity sales and temperature is estimated using a semiparametric regression procedure that easily allows linear transformations of the data. This accommodates introduction of covariates, timing adjustments due to the actual billing schedules, and serial correlation. The procedure is an extension of smoothing splines with the smoothness parameter estimated from minimization of the generalized cross-validation criterion introduced by Craven and Wahba (1979). Estimates are presented for residential sales for four electric utilities and are compared with models that represent the weather using only heating and cooling degree days or with piecewise linear splines.

Convergence rates for partially splined models

A partial spline model is a semi-parametric regression model. In this paper we analyze the convergence rates of estimates of the parametric and nonparametric components of the model under a particular assumption on the design. We show that the estimate of the parametric component of the model is generally biased and that this bias can be larger than the standard error. To force the bias to be neglible with respect to the standard error, it is necessary to undersmooth the nonparametric component.

Deconvolution of microfluorometric histograms with B splines

Abstract We consider the problem of estimating a probability density from observations from that density which are further contaminated by random errors. We propose a method of estimation using spline functions, discuss the numerical implementation of the method, and prove its consistency. The problem is motivated by the analysis of DNA content obtained by microfluorometry, and an example of such an analysis is included.

On the estimation of the parameters of a power spectrum

Three methods of estimating the parameters of a power spectrum are analyzed. The three methods are shown to give consistent and, under certain conditions, asymptotically equivalent results. However, one method, based on an approximate likelihood analysis, is seen to be superior to the other two in some respects.

Correlation functions of a function of a finite-state Markov process with application to channel kinetics

Abstract We show that the lagged moments of all orders of a function of a finite-state Markov process are determined by the first three moments. We discuss the application of this and subsidiary results to the analysis of data on channels in cell membranes.

Effect of probenecid on cerebrospinal fluid methotrexate kinetics

The effect of probenecid (PBC) on methotrexate (MTX) kinetics in the cerebrospinal fluid (CSF) and serum was studied in 4 patients on high‐dose MTX with leucovorin rescue to determine whether addition of PBC could prolong effective CSF MTX levels. Each patient received 2 courses of MTX, 1 with and 1 without PBC. PBC caused a 2.8 to 4.2‐fold increase in CSF MTX concentrations but failed to prolong the CSF half‐life (t½). PBC prolonged the initial MTX elimination tVi in the blood from 2.7 to 4.1 hr, but had little effect on subsequent t½is. No effect of MTX on PBC clearance was detected. Our data suggest that in man PBC in concentrations that were high enough to inhibit the renal clearance of MTX failed to alter the clearance of MTX from the CSF when both drugs were administered systemically.

Bandwidth choice for differentiation

We propose a class of procedures for choosing the bandwidth, or smoothing parameter, for linear nonparametric estimates of the rth derivative of a smooth function observed with error on a discrete set of points. These procedures are based on minimizing a nearly unbiased estimate of the integrated mean square error. Theoretical justification is provided in the special case of a tapered Fourier series estimate.

A note on single-channel autocorrelation functions

It is shown for time-reversible ion channel gating mechanisms that the sojourn time autocorrelation functions are necessarily nonnegative, decreasing, and convex. It is also shown, again for time-reversible mechanisms, that the lagged moments of all orders are determined by the first three moments. The application of these results to the statistical analysis of single-channel kinetics is briefly discussed.

A METHOD FOR MAXIMIZING THE RATIO OF TWO QUADRATIC FORMS.

A method for solving for the largest eigenvalue and associated eigenvector of the eigenequation (A - XB)s = 0 is presented. The method is contrasted with other procedures for the same problem.