Interpolation,outliers mid inverse autocorrelations

The paper addresses the problem of estimating missing observations in an infinite realization of a linear, possibly nonstationary, stochastic processes when the model is known. The general case of any possible distribution of missing observations in the time series is considered, and analytical expressions for the optimal estimators and their associated mean squared errors are obtained. These expressions involve solely the elements of the inverse or dual autocorrelation function of the series.

This optimal estimator -the conditional expectation of the missing observations given the available ones- is equal to the estimator that results from filling the missing values in the series with arbitrary numbers, treating these numbers as additive outliers, and removing with intervention analysis the outlier effects from the invented numbers.     

Weighted logistic regression and robust analysis of diverse toxicology data

Simpson, Carroll, Zhou and Guth (1996) developed an ordinal response regression approach to meta-analysis of data from diverse toxicology studies, applying the methodology to a database of acute inhalation studies of tetra-chloroethylene. We present an alternative analysis of the same data, with two major differences: (1) interval censored scores are assigned worst-case values, e.g., a score known to be in the interval [0,1] is set equal to 1; and (2) the response is reduced to a binary response (adverse, nonadverse). We explore the stability of the analysis by varying a robustness parameter and graphing the curves traced out by the estimates and confidence intervals.     

The Bias in Price Elasticity Estimates Under Homothetic Separability: Implications for Analysis of Peak-Load Electricity Pricing

This article demonstrates that the assumption of a homothetically separable utility function places a priori restrictions on the parameters of the demand system. If these restrictions are unwarranted, an open question if they are not explicitly tested, they will lead to biased price elasticity estimates. In particular, we show that the uncompensated own-price elasticities must be smaller than the negative of the expenditure shares; that is, the price elasticity of peak electricity demand must be less than the negative of the share of expenditure devoted to peak electricity. This finding is probably not new to economists familiar with consumer demand analysis. Nevertheless, many recent studies of consumer demand for electricity under time-of-day rates explicitly impose this restriction. The resulting price elasticity estimates are usually quite large in absolute value (.5 to .8); but they are the product of restrictive a priori assumptions as well as information embodied in the sample data. The results of two analyses of time-of-day experiments, where the researchers imposed the untested assumption of homothetic separability, are examined more closely. We find that the reported price elasticities are strongly influenced by that a priori assumption. A Monte Carlo experiment demonstrates that using this model will lead to the reported price elasticities even if the consumption data are perfectly random with respect to price.     

The Estimation of Food Expenditures From Household Budget Data in the Presence of Bulk Purchases

The aim of this article is the estimation of annual food expenditures with limited information about bulk purchases with data from a Spanish household-budget survey for 1990—1991. Three alternatives are compared. The first, currently used for official purposes, does not use all the information. The second uses all the available information in a rough way. The third assumes a formal model for the unknown frequency of purchases. The three alternatives are compared by a regression model that should be homogeneous with respect to the dummy variables that represent the partial information of the groups and should show a distinct pattern of outliers under each alternative. Finally, we study the effect of the official and the best alternative on food inflation and inequality measures. We find that they lead to similar inflation rates but to different inequality estimates.     

Determining the Number of Primitive Shocks in Factor Models

Personal consumption expenditures (PCE) in the National Income and Product Accounts are often used to investigate whether the time series properties of consumption are consistent with the permanent-income/life-cycle hypotheses. In this article, I address the issue of the general quality of the PCE data and its definitional consistency with the typical model of the intertemporal allocation of consumption. I find that, in terms of the population coverage and the consumption concept, the raw PCE data are unsuitable for the analysis of the permanent-income/life-cycle hypotheses. More fundamentally, adjustments to the data to provide greater consistency with the theory alter critical conclusions concerning the time series properties of consumption.     

Spurious Instrumental Variables

Spurious regression phenomenon has been recognized for a wide range of Data Generating Processes: driftless unit roots, unit roots with drift, long memory, trend and broken-trend stationarity, etc. The usual framework is Ordinary Least Squares. We show that the spurious phenomenon also occurs in Instrumental Variables estimation when using non stationary variables, whether the non stationarity component is stochastic or deterministic. Finite sample evidence supports the asymptotic results.     

Sequential Comparison of d Populations and Related Tables

The paper deals with the numerical solution of the likelihood equations for incomplete data from exponential families, that is for data being a function of exponential family data. Illustrative examples especially studied in this paper concern grouped and censored normal samples and normal mixtures. A simple iterative method of solution is proposed and studied. It is shown that the sequence of iterates converges to a relative maximum of the likelihood function, and that the convergence is geometric with a factor of convergence which for large samples equals the maxi-mal relative loss of Fisher information due to the incompleteness of data. This large sample factor of convergence is illustrated diagrammaticaily for the examples mentioned above. Experiences of practical application are mentioned.     

Principal component analysis of canine hip dysplasia phenotypes and their statistical power for genome-wide association mapping

The aims of this study were to undertake principal component analysis (PCA) of hip dysplasia (HD) and to examine the power of the principal components (PCs) in genome-wide association studies. A cohort of 278 dogs for PCA and that of 369 dogs for genotyping were used. The distraction index (DI), the dorsolateral subluxation (DLS) score, the Norberg angle (NA), and the extended-hip radiographic (EHR) score were used for the PCA. One thousand single-nucleotide polymorphisms (SNPs) (of 23,500) were used to simulate genetic locus sharing between the HD phenotypes and 1000 SNPs were used to calculate the genetic mapping power of the PCs. The DI and the DLS score (first group) reflected hip laxity and the NA and the EHR score (second group) reflected the congruency between the femoral head and acetabulum. The average hip measurements of the two groups reflected in the first PC captured 55% of total radiographic variation. The first four PCs captured 90% of the total variation. The PCs had higher statistical mapping power to detect pleiotropic quantitative trait loci (QTL) than the raw phenotypes. The PCA demonstrated for the first time that HD can be reduced mathematically into simpler components essential for its genetic dissection. Genes that contribute jointly to all four radiographic hip phenotypes can be detected by mapping their first four PCs, while those contributing to individual phenotypes can be mapped by association with the individual raw phenotype.     

Density estimation with distribution element trees

The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient methods are needed. We propose a new method that is based on a decomposition of the unknown distribution in terms of so-called distribution elements (DEs). These elements enable an adaptive and hierarchical discretization of the sample space with small or large elements in regions with smoothly or highly variable densities, respectively. The novel refinement strategy that we propose is based on statistical goodness-of-fit and pairwise (as an approximation to mutual) independence tests that evaluate the local approximation of the distribution in terms of DEs. The capabilities of our new method are inspected based on several examples of different dimensionality and successfully compared with other state-of-the-art density estimators.