729,368 research outputs found
Conditional fiducial models
The fiducial is not unique in general, but we prove that in a restricted
class of models it is uniquely determined by the sampling distribution of the
data. It depends in particular not on the choice of a data generating model.
The arguments lead to a generalization of the classical formula found by Fisher
(1930). The restricted class includes cases with discrete distributions, the
case of the shape parameter in the Gamma distribution, and also the case of the
correlation coefficient in a bivariate Gaussian model. One of the examples can
also be used in a pedagogical context to demonstrate possible difficulties with
likelihood-, Bayesian-, and bootstrap-inference. Examples that demonstrate
non-uniqueness are also presented. It is explained that they can be seen as
cases with restrictions on the parameter space. Motivated by this the concept
of a conditional fiducial model is introduced. This class of models includes
the common case of iid samples from a one-parameter model investigated by
Hannig (2013), the structural group models investigated by Fraser (1968), and
also certain models discussed by Fisher (1973) in his final writing on the
subject
Conditional Transformation Models
The ultimate goal of regression analysis is to obtain information about the
conditional distribution of a response given a set of explanatory variables.
This goal is, however, seldom achieved because most established regression
models only estimate the conditional mean as a function of the explanatory
variables and assume that higher moments are not affected by the regressors.
The underlying reason for such a restriction is the assumption of additivity of
signal and noise. We propose to relax this common assumption in the framework
of transformation models. The novel class of semiparametric regression models
proposed herein allows transformation functions to depend on explanatory
variables. These transformation functions are estimated by regularised
optimisation of scoring rules for probabilistic forecasts, e.g. the continuous
ranked probability score. The corresponding estimated conditional distribution
functions are consistent. Conditional transformation models are potentially
useful for describing possible heteroscedasticity, comparing spatially varying
distributions, identifying extreme events, deriving prediction intervals and
selecting variables beyond mean regression effects. An empirical investigation
based on a heteroscedastic varying coefficient simulation model demonstrates
that semiparametric estimation of conditional distribution functions can be
more beneficial than kernel-based non-parametric approaches or parametric
generalised additive models for location, scale and shape
Exponential Conditional Volatility Models
The asymptotic distribution of maximum likelihood estimators is derived for a class of exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models. The result carries over to models for duration and realised volatility that use an exponential link function. A key feature of the model formulation is that the dynamics are driven by the score
Exponential conditional volatility models
The asymptotic distribution of maximum likelihood estimators is derived for a class of exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models. The result carries over to models for duration and realised volatility that use an exponential link function. A key feature of the model formulation is that the dynamics are driven by the score.Duration models, Gamma distribution, General error distribution, Heteroskedasticity, Leverage, Score Student's t
Testing Conditional Factor Models
Using nonparametric techniques, we develop a methodology for estimating conditional alphas and betas and long-run alphas and betas, which are the averages of conditional alphas and betas, respectively, across time. The tests can be performed for a single asset or jointly across portfolios. The traditional Gibbons, Ross, and Shanken (1989) test arises as a special case of no time variation in the alphas and factor loadings and homoskedasticity. As applications of the methodology, we estimate conditional CAPM and multifactor models on book-to-market and momentum decile portfolios. We reject the null that long-run alphas are equal to zero even though there is substantial variation in the conditional factor loadings of these portfolios.
Bayesian definition of random sequences with respect to conditional probabilities
We study Martin-L\"{o}f random (ML-random) points on computable probability
measures on sample and parameter spaces (Bayes models). We consider four
variants of conditional random sequences with respect to the conditional
distributions: two of them are defined by ML-randomness on Bayes models and the
others are defined by blind tests for conditional distributions. We consider a
weak criterion for conditional ML-randomness and show that only variants of
ML-randomness on Bayes models satisfy the criterion. We show that these four
variants of conditional randomness are identical when the conditional
probability measure is computable and the posterior distribution converges
weakly to almost all parameters. We compare ML-randomness on Bayes models with
randomness for uniformly computable parametric models. It is known that two
computable probability measures are orthogonal if and only if their ML-random
sets are disjoint. We extend these results for uniformly computable parametric
models. Finally, we present an algorithmic solution to a classical problem in
Bayes statistics, i.e.~the posterior distributions converge weakly to almost
all parameters if and only if the posterior distributions converge weakly to
all ML-random parameters.Comment: revised versio
Geometry and Expressive Power of Conditional Restricted Boltzmann Machines
Conditional restricted Boltzmann machines are undirected stochastic neural
networks with a layer of input and output units connected bipartitely to a
layer of hidden units. These networks define models of conditional probability
distributions on the states of the output units given the states of the input
units, parametrized by interaction weights and biases. We address the
representational power of these models, proving results their ability to
represent conditional Markov random fields and conditional distributions with
restricted supports, the minimal size of universal approximators, the maximal
model approximation errors, and on the dimension of the set of representable
conditional distributions. We contribute new tools for investigating
conditional probability models, which allow us to improve the results that can
be derived from existing work on restricted Boltzmann machine probability
models.Comment: 30 pages, 5 figures, 1 algorith
Conditional Density Models for Asset Pricing
We model the dynamics of asset prices and associated derivatives by
consideration of the dynamics of the conditional probability density process
for the value of an asset at some specified time in the future. In the case
where the price process is driven by Brownian motion, an associated "master
equation" for the dynamics of the conditional probability density is derived
and expressed in integral form. By a "model" for the conditional density
process we mean a solution to the master equation along with the specification
of (a) the initial density, and (b) the volatility structure of the density.
The volatility structure is assumed at any time and for each value of the
argument of the density to be a functional of the history of the density up to
that time. In practice one specifies the functional modulo sufficient
parametric freedom to allow for the input of additional option data apart from
that implicit in the initial density. The scheme is sufficiently flexible to
allow for the input of various types of data depending on the nature of the
options market and the class of valuation problem being undertaken. Various
examples are studied in detail, with exact solutions provided in some cases.Comment: To appear in International Journal of Theoretical and Applied
Finance, Volume 15, Number 1 (2012), Special Issue on Financial Derivatives
and Risk Managemen
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