Thomas W. Sager

Statistical profile estimation in database systems

A statistical profile summarizes the instances of a database. It describes aspects such as the number of tuples, the number of values, the distribution of values, the correlation between value sets, and the distribution of tuples among secondary storage units. Estimation of database profiles is critical in the problems of query optimization, physical database design, and database performance prediction. This paper describes a model of a database of profile, relates this model to estimating the cost of database operations, and surveys methods of estimating profiles. The operators and objects in the model include build profile, estimate profile, and update profile. The estimate operator is classified by the relational algebra operator (select, project, join), the property to be estimated (cardinality, distribution of values, and other parameters), and the underlying method (parametric, nonparametric, and ad-hoc). The accuracy, overhead, and assumptions of methods are discussed in detail. Relevant research in both the database and the statistics disciplines is incorporated in the detailed discussion.

Characterization of a Ranked-Set Sample with Application to Estimating Distribution Functions

Abstract Ranked-set sampling has been shown to provide improved estimators of the mean and variance when actual measurement of the observations is difficult but ranking of the elements in a sample is relatively easy. This result holds even if the ranking is imperfect. In this article, we provide a characterization of a ranked-set sample that makes the source of this additional information intuitively clear. It is applied to show that the empirical distribution function of a ranked-set sample is unbiased and has greater precision than that from a random sample. The null distribution of a Kolmogorov-Smirnov statistic based on this empirical distribution function is derived for the case in which perfect ranking is possible. It is seen to be stochastically smaller than the usual Kolmogorov-Smirnov statistic based on a simple random sample, resulting in a smaller simultaneous confidence interval for the cumulative distribution function.

The Relations Among Asset Risk, Product Risk, and Capital in the Life Insurance Industry

This paper explores the relation between capital and risk in the life insurance industry in the period after the adoption of life risk-based capital (RBC) regulation. To examine this issue, we use a simultaneous-equation partial-adjustment model. Three equations express the interrelations among capital and two measures of risk: product risk and asset risk. The asset-risk measure used in this paper reflects credit or solvency risk as in RBC. Product risk assessment for life insurance products is rationalized by transaction-cost economics - contractual uncertainty. A significant finding is that for life insurers the relation between capital and asset risk is positive. This agrees with prior studies for the property/casualty insurance industry and some banking studies. But the relation between capital and product risk is negative. This is consistent with the hypothesized impact of guarantee funds in other studies. The contrast between the positive relation of capital to asset risk and the negative relation of capital to product risk underscores the importance of distinguishing these two components of risk.

Capital and Risk Revisited: A Structural Equation Model Approach for Life Insurers

The role of risk in the capital structure decision of firms is a vast topic in finance. Commonly, models of the interrelationship between risk and capital enumerate as many risk factors as possible by appropriate proxies, with the goal of detailing their individual effects. In this study of the life insurance industry for 1994 through 2000, we take a broader, holistic view of enterprise risk, identifying two groups of insurer risk factors that arise from the major activities of life insurers: investing and underwriting. We call the group of risk factors associated with investing asset risk, and the group associated with underwriting product risk. After specifying other important determinants of capital structure as controls, we allow all other risk factors to find expression in residual error. Within this framework, our focus is to compare two candidate measures for the role of proxy for asset-related risks. One measure, called regulatory asset risk (RAR), derives from the regulatory tradition of concern with solvency and is related to the C-1 component of risk-based capital. The other measure, called opportunity asset risk (OAR), is motivated by traditional finance concerns with market risk and reflects volatility of returns. Product-related risks are proxied by underwriting exposures in different product lines. We employ structural equation modeling (SEM), which uses longitudinal factor analysis. SEM is an innovative technique for such studies, in dealing effectively with multiple structural equations, autocorrelated panel data, unobserved underlying factors, and other issues that are not simultaneously addressed in other methodologies. We find that RAR and OAR are not equivalent proxies for asset risks. Although overlapping to some extent, each illuminates different aspects of the asset risk-capital interrelationship. In particular, RAR does not seem to affect the capital structure decision of small firms, although OAR does. We interpret this to suggest that small firms as a whole are not as sensitive in their capital decisions to the proxy of regulatory concerns as to the proxy of market opportunity. This contrasts with large insurers, for whom both RAR and OAR have significant effects on capital that comport with the finite risk hypothesis. More detailed analysis suggests that the lack of effect of RAR for small insurers may result from RARs proxying some factors that induce finite risk for part of the small insurer sample, and other factors that favor the excessive risk hypothesis.

An Iterative Method for Estimating a Multivariate Mode and Isopleth

Abstract An iterative procedure for estimating the mode and isopleths of a multivariate distribution is presented. The mode is estimated by selecting a point from the final set in a nested decreasing sequence of convex sets, each one of which is iteratively the smallest closed, convex subset containing a certain proportion of its predecessors data points. An isopleth is estimated by the boundary of the convex subset corresponding to a fixed number of iterations (independent of n). The method gives rise to a natural density estimator. The estimators are shown to converge almost surely, and convergence rates for the univariate isopleth estimator are presented. Applications to air pollution and health sciences are noted.

Factor analysis of trends in Texas acidic deposition

Abstract Precipitation chemistry data collected between 1980 and 1987 for 11 NADP/NTN sites in Texas have been analyzed using factor analysis and a trend analysis of monthly averages. Factor analysis identified four major factors which differed significantly from site to site: (1) a Gulf factor of Na+, Cl-, and Mg2+; (a) a soil factor of Ca2+, K+, Na+, and Mg2+; (3) an acid factor of H+, NO−3, and SO44−; and (4) an aged aerosol factor of NO3−, SO42−, and NH4+. At Longview, the acid and Gulf factors accounted for 18 and 46%, respectively, of the variation of the data. A trend analysis was performed on the logarithm of the monthly averages at the Longview and Victoria sites, the two sites with the largest and most complete data. Results suggest that hydrogen ions have been increasing at both sites, while calcium ions have been decreasing.

Industry Segmentation and Predictor Motifs for Solvency Analysis of the Life/Health Insurance Industry

This paper contributes one principal idea to the methodology of solvency studies for the life insurance industry. The idea is grouping, which is applied in two different ways. First, companies are grouped into industry segments by insurer specialization or by size. Second, predictor variables are grouped into thematically related motifs. The primary benefits of grouping are improved solvency prediction and improved interpretation of predictors. Improved prediction results from industry segmentation; improved interpretation from predictor motifs. The models are developed by the technique of cascaded logistic regression, which forecasts solvency status on the basis of motifs, rather than of individual variables. A key finding is that the segments differ in their significant motifs in anticipated ways. For example, investment motifs are important for solvency in the Life and Annuities segments, but not in the Health segment. A similar pattern characterizes the difference between large and small insurers. The study covers the 1990 through 1992 time period, when there were a historically high number of troubled companies.

A Semiparametric Stochastic Spline Model as a Managerial Tool for Potential Insolvency

This study introduces a flexible nonlinear semiparametric spline model, new to solvency studies, as a tool for managerial discretion and regulatory oversight. The model has a linear component and a nonlinear component that uses stochastic splines. The study focuses on the functional relationship between regressors and the probability of financial distress as an object for managerial action. Leverage plots are provided to analyze the potential effect of decisions to modify firm levels of financial variables. If the true relationship between regressors and the response is not linear, then managerial efforts to rectify deteriorating financial conditions can be misinformed by reliance on a linear solvency model. The leverage plots adjust to the firms position within the industry and its specific levels of various financial variables. A five-regressor semiparametric spline model is shown to yield insights into the behavior of the risk of financial distress probabilities that linear parametric models suppress. The model also classifies and validates well in comparison with recent insolvency studies and as well as parametric logit and probit models on the same data.

Estimating modes and isopleths

Recent years have witnessed a renewal of interest in estimating the mode and in related multivariate mapping problems. In part, this renaisance may be attributed to the Phillosopoicdi Success of nonparametrics in challenging the dominant (Fisherian) parametric world-view. But the main reason is the recent advent of powerful mathematical tools and computational machinery that render these problems much more tractable. In surveying the mode, this paper has several objectives: (1) to place the development of modal estimation in historical perspective, noting the statistical currents that stimulated and retarded its progress; (2) to present all the methods for estimating the mode that have been studied in the literature; (3) to summarize the mathematical results, including consistency and asymptotic distributions; (4) to evaluate critically the extant simulation studies; (5) to note areas of cross-fertilization with other disciplines and with other areas of statistics, such as density estimation, cartography,...

Table for the asymptotic distribution of univariate mode estimators

Previous theoretical studies have connected the asymptotic distribution of various univariate mode estimators to the distribution of the location of the minimum/maximum of the two—sided Wiener—Levy process with square drift. In this paper, an empirical distribution for the latter is obtained through simulation. The tabulated probabilities of this distribution are useful in making inferences about the mode. Illustrative examples of confidence intervals for the mode are provided using real data