In a sailboat race, the navigator’s attempts to plot the fastest possible course are hindered by shifty winds. We present mathematical models appropriate for this situation, which use statistical analysis of wind fluctuations and are amenable to stochastic optimization methods. We describe the...

We propose a non-linear density estimator, which is locally adaptive, like wavelet estimators, and positive everywhere, without a log- or root-transform. This estimator is based on maximizing a non-parametric log-likelihood function regularized by a total variation penalty. The smoothness is...

We consider Taylor’s stochastic volatility model (SVM) when the innovations of the hidden log-volatility process have a Laplace distribution (ℓ <Subscript>1</Subscript> exponential density), rather than the standard Gaussian distribution (ℓ <Subscript>2</Subscript>) usually employed. Recently many investigations have employed ℓ <Subscript>1</Subscript>...</subscript></subscript></subscript>

We consider the problem of estimating the volatility of a financial asset from a time series record of length T. We believe the underlying volatility process is smooth, possibly stationary, and with potential abrupt changes due to market news. By drawing parallels between time series and...

We consider Taylor's stochastic volatility model when the innovations of the hidden log-volatility process have a Laplace distribution (l1 exponential density), rather than the standard Gaussian distribution (l2) usually employed. Using a distribution with heavier tails allows better modeling of...

Time series of financial asset values exhibit well known statistical features such as heavy tails and volatility clustering. Strongly present in some series, nonstationarity is a feature that has been somewhat overlooked. This may however be a highly relevant feature when estimating extreme...

The proposed smooth blockwise iterative thresholding estimator (SBITE) is a model selection technique defined as a fixed point reached by iterating a likelihood gradient-based thresholding function. The smooth James--Stein thresholding function has two regularization parameters λ and ν, and a...

For the problem of estimating a sparse sequence of coefficients of a parametric or non-parametric generalized linear model, posterior mode estimation with a Subbotin("λ","ν") prior achieves thresholding and therefore model selection when "ν"   is an element of    <b>[0,1]</b> for a class...

Whether doing parametric or nonparametric regression with shrinkage, thresholding, penalized likelihood, Bayesian posterior estimators (e.g., "ridge regression, lasso, principal component regression, waveshrink" or "Markov random field"), it is common practice to rescale covariates by dividing...