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47
Polynomial Splines and Their Tensor Products in Extended Linear Modeling
 Ann. Statist
, 1997
"... ANOVA type models are considered for a regression function or for the logarithm of a probability function, conditional probability function, density function, conditional density function, hazard function, conditional hazard function, or spectral density function. Polynomial splines are used to m ..."
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Cited by 140 (14 self)
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ANOVA type models are considered for a regression function or for the logarithm of a probability function, conditional probability function, density function, conditional density function, hazard function, conditional hazard function, or spectral density function. Polynomial splines are used to model the main effects, and their tensor products are used to model any interaction components that are included. In the special context of survival analysis, the baseline hazard function is modeled and nonproportionality is allowed. In general, the theory involves the L 2 rate of convergence for the fitted model and its components. The methodology involves least squares and maximum likelihood estimation, stepwise addition of basis functions using Rao statistics, stepwise deletion using Wald statistics, and model selection using BIC, crossvalidation or an independent test set. Publically available software, written in C and interfaced to S/SPLUS, is used to apply this methodology to...
Hazard Regression
 Journal of the American Statistical Association
, 1995
"... An automatic procedure that uses linear splines and their tensor products is proposed for tting a regression model to data involving a polychotomous response variable and one or more predictors. The tted model can be used for multiple classi cation. The automatic tting procedure involves maximum lik ..."
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Cited by 80 (19 self)
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An automatic procedure that uses linear splines and their tensor products is proposed for tting a regression model to data involving a polychotomous response variable and one or more predictors. The tted model can be used for multiple classi cation. The automatic tting procedure involves maximum likelihood estimation, stepwise addition, stepwise deletion, and model selection by AIC, crossvalidation or an independent test set. A modi ed version of the algorithm has been constructed that is applicable to large data sets, and it is illustrated using a phoneme recognition data set with 250,000 cases, 45 classes and 63 predictors.
Econometric Models of LimitOrder Executions
, 1997
"... Limit orders incur no price impact, however, their execution time is uncertain. We develop an econometric model of limitorder execution times using survival analysis, and estimate it with actual limitorder data. We estimate versions for timetofirstfill and timetocompletion, and for limitsell ..."
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Cited by 19 (1 self)
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Limit orders incur no price impact, however, their execution time is uncertain. We develop an econometric model of limitorder execution times using survival analysis, and estimate it with actual limitorder data. We estimate versions for timetofirstfill and timetocompletion, and for limitsells and limitbuys, and incorporate the effects of explanatory variables such as the limit price, the limit size, the bid/offer spread, and market volatility. We find that execution times are very sensitive to limit price and several other explanatory variables, but not sensitive to limit size. We also show that hypothetical limitorder executions, constructed either theoretically from firstpassage times or empirically from transactions data, are very poor proxies for actual limitorder executions.
MultiPeriod Corporate Failure Prediction with Stochastic Covariates
, 2004
"... We provide maximum likelihood estimators of term structures of conditional probabilities of bankruptcy over relatively long time horizons, incorporating the dynamics of firmspecific and macroeconomic covariates. We find evidence in the U.S. industrial machinery and instruments sector, based on ..."
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Cited by 16 (3 self)
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We provide maximum likelihood estimators of term structures of conditional probabilities of bankruptcy over relatively long time horizons, incorporating the dynamics of firmspecific and macroeconomic covariates. We find evidence in the U.S. industrial machinery and instruments sector, based on over 28,000 firmquarters of data spanning 1971 to 2001, of significant dependence of the level and shape of the term structure of conditional future bankruptcy probabilities on a firm's distance to default (a volatilityadjusted measure of leverage) and on U.S. personal income growth, among other covariates. Variation in a firm's distance to default has a greater relative e#ect on the term structure of future failure hazard rates than does a comparatively sized change in U.S. personal income growth, especially at dates more than a year into the future.
Rate of Convergence for Hazard Regression
 Scand. J. Statist
, 1994
"... The logarithm of the conditional hazard function of a survival time given one or more covariates is approximated by a function having the form of a specified sum of functions of at most d of the variables. Subject to this form, the approximation is chosen to maximize the expected conditional logli ..."
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Cited by 10 (1 self)
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The logarithm of the conditional hazard function of a survival time given one or more covariates is approximated by a function having the form of a specified sum of functions of at most d of the variables. Subject to this form, the approximation is chosen to maximize the expected conditional loglikelihood. Maximum likelihood and sums of tensor products of polynomial splines are used to construct an estimate of this approximation based on a random sample. The components of this estimate possess a rate of convergence that depends only on d and a suitably defined smoothness parameter. KEY WORDS: Conditional hazard function; Maximum likelihood; Tensor product splines. This research was supported in part by a grant from the Graduate School Fund of the University of Washington. y This research was supported in part by National Science Foundation Grant DMS9204247 z This research was supported in part by a Research Council Grant from the University of North Carolina. 1 1. Introducti...
Prediction From Randomly Right Censored Data
, 1999
"... Let X be a random vector taking values in IR d , let Y be a bounded random variable, and let C be a right censoring random variable operating on Y . It is assumed that C is independent of (X; Y ), the distribution function of C is continuous and the support of the distribution of Y is a proper sub ..."
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Cited by 10 (2 self)
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Let X be a random vector taking values in IR d , let Y be a bounded random variable, and let C be a right censoring random variable operating on Y . It is assumed that C is independent of (X; Y ), the distribution function of C is continuous and the support of the distribution of Y is a proper subset of the support of the distribution of C. Given a sample fX i ; minfY i ; C i g; I [Y i C i ] g and a vector of covariates X , we want to construct an estimate of Y such that the mean squared error is minimized. Without censoring, i.e. for C = 1 almost surely, it is wellknown that the mean squared error of suitably defined kernel, partitioning, nearest neighbor, least squares and smoothing spline estimates converges for every distribution of (X; Y ) to the optimal value almost surely, if the sample size tends to infinity. In this paper, we modify the above estimates and show that in the right random censoring model described above the same is true for the modified estimates. AMS classif...
W.F.Elevated and absent pRb expression is associated with bladder cancer progression and has cooperative effects with p53. Cancer Res
 67 CORDONCARDO C., ZHANG Z.F., DALBAGNI G., DROBNJAK M., CHARYTONOWICZ E., HU S.X., XU H.J., REUTER V.E
, 1998
"... This article has been cited by 37 HighWirehosted articles. Access the articles at: ..."
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Cited by 6 (1 self)
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This article has been cited by 37 HighWirehosted articles. Access the articles at:
Measuring lag structure in forecasting models  the introduction of Time Distance
, 1999
"... In modeling series with leading or lagging indicators, it is desirable to begin comparing models in terms of time distance. This paper formalizes the concept of time distance in terms of various metrics, and investigates the behaviors of these metrics. It is shown that under some circumstances, ti ..."
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Cited by 4 (1 self)
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In modeling series with leading or lagging indicators, it is desirable to begin comparing models in terms of time distance. This paper formalizes the concept of time distance in terms of various metrics, and investigates the behaviors of these metrics. It is shown that under some circumstances, time distance metrics indeed perform better in forecasting than standard measures (such as mean squared forecasting errors), and that some timedistance metrics outperform others. Department of Economics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 920930508, USA, email:cgranger@ucsd.edu. This researchwas partially funded by NSF grant SBR9708615. y Center for Basic Research in the Social Sciences, Harvard University, 34 Kirkland Street, Cambridge, MA 02138,USA, email:yjeon@latte.harvard.edu. 1 1 Introduction If one has a pair of time series, x t and y t , their "nearness" is usually measured in terms of their vertical difference z t = x t ; y t , using the abso...