4,959 research outputs found
Efficient estimation of a semiparametric partially linear varying coefficient model
In this paper we propose a general series method to estimate a semiparametric
partially linear varying coefficient model. We establish the consistency and
\sqrtn-normality property of the estimator of the finite-dimensional parameters
of the model. We further show that, when the error is conditionally
homoskedastic, this estimator is semiparametrically efficient in the sense that
the inverse of the asymptotic variance of the estimator of the
finite-dimensional parameter reaches the semiparametric efficiency bound of
this model. A small-scale simulation is reported to examine the finite sample
performance of the proposed estimator, and an empirical application is
presented to illustrate the usefulness of the proposed method in practice. We
also discuss how to obtain an efficient estimation result when the error is
conditional heteroskedastic.Comment: Published at http://dx.doi.org/10.1214/009053604000000931 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Elicitability and backtesting: Perspectives for banking regulation
Conditional forecasts of risk measures play an important role in internal
risk management of financial institutions as well as in regulatory capital
calculations. In order to assess forecasting performance of a risk measurement
procedure, risk measure forecasts are compared to the realized financial losses
over a period of time and a statistical test of correctness of the procedure is
conducted. This process is known as backtesting. Such traditional backtests are
concerned with assessing some optimality property of a set of risk measure
estimates. However, they are not suited to compare different risk estimation
procedures. We investigate the proposal of comparative backtests, which are
better suited for method comparisons on the basis of forecasting accuracy, but
necessitate an elicitable risk measure. We argue that supplementing traditional
backtests with comparative backtests will enhance the existing trading book
regulatory framework for banks by providing the correct incentive for accuracy
of risk measure forecasts. In addition, the comparative backtesting framework
could be used by banks internally as well as by researchers to guide selection
of forecasting methods. The discussion focuses on three risk measures,
Value-at-Risk, expected shortfall and expectiles, and is supported by a
simulation study and data analysis
Some recent developments in microeconometrics: A survey
This paper summarizes some recent developments in rnicroeconometrics with respect to methods for estimation and inference in non-linear models based on cross-section and panel data. In particular we discuss recent progress in estimation with conditional moment restrictions, simulation methods, serniparametric methods, as well as specification tests. We use the binary cross-section and panel probit model to illustrate the application of some of the theoretical results. --
Penalized Likelihood and Bayesian Function Selection in Regression Models
Challenging research in various fields has driven a wide range of
methodological advances in variable selection for regression models with
high-dimensional predictors. In comparison, selection of nonlinear functions in
models with additive predictors has been considered only more recently. Several
competing suggestions have been developed at about the same time and often do
not refer to each other. This article provides a state-of-the-art review on
function selection, focusing on penalized likelihood and Bayesian concepts,
relating various approaches to each other in a unified framework. In an
empirical comparison, also including boosting, we evaluate several methods
through applications to simulated and real data, thereby providing some
guidance on their performance in practice
Semiparametric and Nonparametric Methods in Econometrics
The main objective of this workshop was to bring together mathematical statisticians and econometricians who work in the field of nonparametric and semiparametric statistical methods. Nonparametric and semiparametric methods are active fields of research in econometric theory and are becoming increasingly important in applied econometrics. This is because the flexibility of non- and semiparametric modelling provides important new ways to investigate problems in substantive economics. Moreover, the development of non- and semiparametric methods that are suitable to the needs of economics presents a variety of mathematical challenges. Topics to be addressed in the workshop included nonparametric methods in finance, identification and estimation of nonseparable models, nonparametric estimation under the constraints of economic theory, statistical inverse problems, long-memory time-series, and nonparametric cointegration
Change-point Problem and Regression: An Annotated Bibliography
The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder .
The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis.
Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem.
Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression.
The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression.
The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis
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