Statistics for Spatial Data.

Technological change and deregulation have caused a major restructuring of the telecommunications equipment industry over the last two decades. We estimate the parameters of a production function for the equipment industry and then use those estimates to analyze the evolution of plant-level productivity over this period. The restructuring involved significant entry and exit and large changes in the sizes of incumbents. Since firms choices on whether to liquidate and the on the quantities of inputs demanded should they continue depend on their productivity, we develop an estimation algorithm that takes into account the relationship between productivity on the one hand, and both input demand and survival on the other. The algorithm is guided by a dynamic equilibrium model that generates the exit and input demand equations needed to correct for the simultaneity and selection problems. A fully parametric estimation algorithm based on these decision rules would be both computationally burdensome and require a host of auxiliary assumptions. So we develop a semiparametric technique which is both consistent with a quite general version of the theoretical framework and easy to use. The algorithm produces markedly different estimates of both production function parameters and of productivity movements than traditional estimation procedures. We find an increase in the rate of industry productivity growth after deregulation. This in spite of the fact that there was no increase in the average of the plants' rates of productivity growth, and there was actually a fall in our index of the efficiency of the allocation of variable factors conditional on the existing distribution of fixed factors. Deregulation was, however, followed by a reallocation of capital towards more productive establishments (by a down sizing, often shutdown, of unproductive plants and by a disproportionate growth of productive establishments) which more than offset the other factors' negative impacts on aggregate productivity.

The Dynamics Of Productivity In The Telecommunications Equipment Industry

Nonparametric regression is a set of techniques for estimating a regression curve without making strong assumptions about the shape of the true regression function. These techniques are therefore useful for building and checking parametric models, as well as for data description. Kernel and nearest-neighbor regression estimators are local versions of univariate location estimators, and so they can readily be introduced to beginning students and consulting clients who are familiar with such summaries as the sample mean and median.

/pdf/an-introduction-to-kernel-and-nearest-neighbor-nonparametric-2l6wb0z48n.pdf

An Introduction to Kernel and Nearest-Neighbor Nonparametric Regression

Technological change and deregulation have caused a major restructuring of the telecommunications equipment industry over the last two decades. Our empirical focus is on estimating the parameters of a production function for the equipment industry, and then using those estimates to analyze the evolution of plant-level productivity. The restructuring involved significant entry and exit and large changes in the sizes of incumbents. Firms' choices on whether to liquidate, and on input quantities should they continue, depended on their productivity. This generates a selection and a simultaneity problem when estimating production functions. Our theoretical focus is on providing an estimation algorithm which takes explicit account of these issues. We find that our algorithm produces markedly different and more plausible estimates of production function coefficients than do traditional estimation procedures. Using our estimates we find increases in the rate of aggregate productivity growth after deregulation. Since we have plant-level data we can introduce indices which delve deeper into how this productivity growth occurred. These indices indicate that productivity increases were primarily a result of a reallocation of capital towards more productive establishments.

/pdf/the-dynamics-of-productivity-in-the-telecommunications-4x42o22gre.pdf

The Dynamics of Productivity in the Telecommunications Equipment Industry

At the least sophisticated level of economic theory lies the belief that certain pairs of economic variables should not diverge from each other by too great an extent, at least in the long-run. Thus, such variables may drift apart in the short-run or according to seasonal factors, but if they continue to be too far apart in the long-run, then economic forces, such as a market mechanism or government intervention, will begin to bring them together again. Examples of such variables are interest rates on assets of different maturities, prices of a commodity in different parts ofthe country, income and expenditure by local government and the value of sales and production costs of an industry. Other possible examples would be prices and wages, imports and exports, market prices of substitute commodities, money supply and prices and spot and future prices of a commodity. In some cases an economic theory involving equilibrium concepts might suggest close relations in the long-run, possibly with the addition of yet further variables. However, in each case the correctness of the beliefs about long-term relatedness is an empirical question. The idea underlying cointegration allows specification of models that capture part of such beliefs, at least for a particular type of variable that is frequently found to occur in macroeconomics. Since a concept such as the long-run is a dynamic one, the natural area for these ideas is that of time-series theory and analysis. It is thus necessary to start by introducing some relevant time series models. Consider a single series Xf, measured at equal intervals of time. Time series theory starts by considering the generating mechanism for the series. This mechanism should be able to generate att of the statistical properties of the series, or at very least the conditional mean, variance and temporal autocorrelations, that is the 'linear properties' of the series, conditional on past data. Some series appear to be 'stationary', which essentially implies that the linear properties exist and are timeinvariant. Here we are concerned with the weaker but more technical

/pdf/developments-in-the-study-of-cointegrated-economic-variables-3ngb3it5q7.pdf

Developments in the study of cointegrated economic variables

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.

Semiparametric Estimates of the Relation between Weather and Electricity Sales

This paper is concerned with the problem of choosing a bandwidth parameter for nonparametric regression. We analyze a tapered Fourier series estimate and discuss the relationship of this estimate to a kernel estimate. We first consider a method based on an unbiased estimate of mean square error, and show that the bandwidth thus chosen is asymptotically optimal. Other methods are examined as well and are shown to be asymptotically equivalent. A small simulation shows, however, that for small or moderate sample size, the methods perform quite differently.

/pdf/bandwidth-choice-for-nonparametric-regression-2dmpd5nxid.pdf

Bandwidth Choice for Nonparametric Regression

This paper considers nonparametric estimation in a varying coefficient model with repeated measurements (Y ij , X ij , t ij ), for i = 1 n and j = 1 n i , where X ij = (X ij .,,X ijk ) T and (Y ij , X ij , t ij ) denote the jth outcome, covariate and time design points, respectively, of the ith subject. The model considered here is Y ij = X ij T β(t ij )+ e i (t ij ), where β(t)=(β 0 (t)., β k (t)) T , for k≥ 0, are smooth nonparametric functions of interest and e i (t) is a zero-mean stochastic process. The measurements are assumed to be independent for different subjects but can be correlated at different time points within each subject. Two nonparametric estimators of β(t), namely a smoothing spline and a locally weighted polynomial, are derived for such repeatedly measured data. A crossvalidation criterion is proposed for the selection of the corresponding smoothing parameters. Asymptotic properties, such as consistency, rates of convergence and asymptotic mean squared errors, are established for kernel estimators, a special case of the local polynomials. These asymptotic results give useful insights into the reliability of our general estimation methods. An example of predicting the growth of children born to HIV infected mothers based on gender, HIV status and maternal vitamin A levels shows that this model and the corresponding nonparametric estimators are useful in epidemiological studies.

Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data

We introduce a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors, generalizing smoothing splines to such samples by associating them with a corresponding mixed-effects model. The models are also useful for imputation of missing data and exploratory analysis of variance. We prove that the best linear unbiased predictors (BLUPs) from the extended mixed-effects model correspond to solutions of a generalized penalized regression where smoothing parameters are directly related to variance components, and we show that these solutions are natural cubic splines. The model parameters are estimated using a highly efficient implementation of the EM algorithm for restricted maximum likelihood (REML) estimation based on a preliminary eigenvector decomposition. Variability of computed estimates can be assessed with asymptotic techniques or with a novel hierarchical bootstrap resampling scheme for nested mixed-effects models. Our methods are applied to me...

Smoothing spline models for the analysis of nested and crossed samples of curves

We propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients. The method is applicable when the individual curves are sampled at variable and irregularly spaced points. This produces a low-rank, low-frequency approximation to the covariance structure, which can be estimated naturally by the EM algorithm. Smooth curves for individual trajectories are constructed as best linear unbiased predictor (BLUP) estimates, combining data from that individual and the entire collection. This framework leads naturally to methods for examining the effects of covariates on the shapes of the curves. We use model selection techniques--Akaike information criterion (AIC), Bayesian information criterion (BIC), and cross-validation--to select the number of breakpoints for the spline approximation. We believe that the methodology we propose provides a simple, flexible, and computationally efficient means of functional data analysis.

/pdf/nonparametric-mixed-effects-models-for-unequally-sampled-117zxgxqg0.pdf

John Rice

Papers

Semiparametric Estimates of the Relation between Weather and Electricity Sales

Bandwidth Choice for Nonparametric Regression

Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data

Smoothing spline models for the analysis of nested and crossed samples of curves

Nonparametric mixed effects models for unequally sampled noisy curves.