The solution of the Kolmogorov backward equation is expressed as a functional integral by means of the Feynman–Kac formula. The expectation value is approximated as a mean over trajectories. In order to reduce the variance of the estimate, importance sampling is utilized. From the optimal...

We propose a Bayesian method to select groups of correlated explanatory variables in a linear regression framework. We do this by introducing in the prior distribution assigned to the regression coefficients a random matrix <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$G$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>G</mi> </math> </EquationSource> </InlineEquation> that encodes the group structure. The groups can thus be...</equationsource></equationsource></inlineequation>

We deal with sampling by variables with two-way protection in the case of a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$N\(\mu ,\sigma ^2)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>N</mi> <mspace width="0.222222em"/> <mo stretchy="false">(</mo> <mi mathvariant="italic">μ</mi> <mo>,</mo> <msup> <mi mathvariant="italic">σ</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> distributed characteristic with unknown <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\sigma $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">σ</mi> </math> </EquationSource> </InlineEquation>. The LR sampling plan proposed by Lieberman and Resnikoff (JASA 50: 457<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$${-}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mo>-</mo> </math> </EquationSource> </InlineEquation>516, <CitationRef CitationID="CR9">1955</CitationRef>) and the BSK...</citationref></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

The purpose of this paper is to jointly monitor the mean vector and the covariance matrix of multivariate nonlinear times series. The underlying target process is assumed to be a constant conditional correlation process Bollerslev (Rev Econ Stat 72:498–505, <CitationRef CitationID="CR5">1990</CitationRef>) or a dynamic conditional...</citationref>

Robust Bayesian methodology deals with the problem of explaining uncertainty of the inputs (the prior, the model, and the loss function) and provides a breakthrough way to take into account the input’s variation. If the uncertainty is in terms of the prior knowledge, robust Bayesian analysis...

The behaviour of market agents has been extensively covered in the literature. Risk averse behaviour, described by Von Neumann and Morgenstern (Theory of games and economic behavior. Princeton University Press, Princeton, <CitationRef CitationID="CR16">1944</CitationRef>) via a concave utility function, is considered to be a cornerstone...</citationref>

In an asset return series, there is a conditional asymmetric dependence between current return and past volatility depending on the current return’s sign. To take into account the conditional asymmetry, we introduce new models for asset return dynamics in which frequencies of the up and down...

This article is concerned with the estimating problem of heteroscedastic partially linear errors-in-variables models. We derive the asymptotic normality for estimators of the slope parameter and the nonparametric component in the case of known error variance with stationary <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\alpha $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">α</mi> </math> </EquationSource>...</equationsource></equationsource></inlineequation>

In this paper, we investigate a nonparametric estimation of the conditional density of a scalar response variable given a random variable taking values in separable Hilbert space. We establish under general conditions the uniform almost complete convergence rates and the asymptotic normality of...

Widely spread tools within the area of Statistical Process Control are control charts of various designs. Control chart applications are used to keep process parameters (e.g., mean <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mu $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">μ</mi> </math> </EquationSource> </InlineEquation>, standard deviation <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\sigma $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">σ</mi> </math> </EquationSource> </InlineEquation> or percent defective <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>p</mi> </math> </EquationSource> </InlineEquation>) under surveillance...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>