### ABSTRACTS AND PRESENTATIONS

**Thomas Augustin**,
*Survival Analysis under Generalized Measurement Error
Models*

*abstract**,
presentation*

Survival models provide a very simple but practically highly relevant example of counting
processes with intensities that depend on certain characteristics (covariates) of the units investigated.
This talk considers Cox's proportional hazards model and some accelerated failure time models under
the frequently occurring complication that covariates may be subject to measurement error. For the classical
additive measurement error model, powerful correction methods for unbiased parameter estimation have been
developed in the literature. We examine in detail one of these correction methods, namely the principle
of corrected score functions, aiming at extending it to more complex and "realistic" error models. In this
context, we discuss first ideas to handle internal dependencies, error structures of Berkson type,
and eventually set-valued error models based on the framework of imprecise probabilities.

**Sandor Baran**,
*K-optimal designs for regression models driven by
Ornstein-Uhlenbeck processes and fields*

*abstract,
presentation*

Properties of the K-optimal design minimizing the condition number of the Fisher information
matrix of the unknown parameters of regression models driven by Ornstein-Uhlenbeck processes and sheets
are investigated and the differences compared with the classical D-optimal sampling are highlighted.
The problems of existence of K-optimal designs are studied and the dependence of the two designs on
the covariance parameters of the driving processes are clarified. Finally, a simulation study displaying
the superiority of the K-optimal design for large parameter values of the driving random process is presented.

**Taras Bodnar**,
*Singular Conditional Autoregressive Wishart Model for
Realized Covariance Matrices*

*abstract**
*

*
*Realized covariance matrices are often constructed under the assumption that richness of
intra-day return data is greater than the portfolio size, resulting in non-singular matrix measures.
However, when for example the portfolio size is large, assets suffer from illiquidity issues, or market
microstructure noise deters sampling on very high frequencies, this relation is not guaranteed. Under
these common conditions, realized covariance matrices may obtain as singular by construction. Motivated
by this situation, we introduce the Singular Conditional Autoregressive Wishart (SCAW) model to capture
the temporal dynamics of time series of singular realized covariance matrices, extending the rich
literature on econometric Wishart time series models to the singular case. This model is furthermore
developed by covariance targeting adapted to matrices and a sectorwise BEKK-specification, allowing
excellent scalability to large and extremely large portfolio sizes. Finally, the model is estimated to
a 20 year long time series containing 50 stocks and to a 10 year long time series containing 300 stocks,
and evaluated using out-of-sample forecast accuracy. It outperforms the benchmark models with high
statistical significance and the parsimonious specifications perform better than the baseline SCAW model,
while using considerably less parameters.

*
***Khalifa Es-Sebaiy**,
*Berry-Esseen bounds of second moment estimators for
Gaussian processes observed at high frequency*

*abstract*,
presentation

Let Z be a centered stationary Gaussian process. We study two second moment estimators of
the variance of Z_{0} based on continuous-time and discrete-time observations of Z, using tools from analysis
on Wiener space. We prove that the two estimators are strongly consistent and establish Berry-Esseen bounds
for a central limit theorem. We apply these results to asymptotically stationary Gaussian processes and
estimate the drift parameter for Gaussian Ornstein-Uhlenbeck processes.

**Alexander Ivanov**,
*LSE Consistency of the Symmetric Textured Surface
Parameters*

*abstract*,
presentation

A multivariate trigonometric regression model is considered. Several discrete modifications of
the similar bivariate trigonometric model were studied in detail in the literature on signal and image
processing thanks to multiple applications in the analysis of symmetric textured surfaces. In the lecture
strong consistency of the least squares estimator for amplitudes and angular frequencies is obtained
in such a multivariate model on the assumption that random noise is a homogeneous and Isotropic Gaussian,
specifically, strongly dependent random field on M-dimensional Euclidean space.

**Kestutis Kubilius**,
*Stochastic differential equation with a soft wall*

*abstract*

Recently, much attention has been paid to SDEs driven by fractional Brownian
motion (fBm). In our research we are interested in fractional SDE with a soft wall.
What do we mean by such type of an equation? It has been established that SDE
with reflection can be imagined as equations having a hard wall. Now by introducing
repulsion instead of reflection one gets an SDE with a soft wall. In contrast to the
SDE with reflection, where the process cannot pass the hard wall, the soft wall is
repulsive but not impenetrable. As the process crosses the soft wall boundary, it
experiences the force of a chosen magnitude in the opposite direction. When the
process is far from the wall, the force acts weakly.

We are trying to find conditions under which SDE with a soft wall has a unique
solution and to construct an implicit Euler approximation with a rate of convergence
for this equation. Using the example of the fractional Vasicek process with soft walls,
we illustrate the dependence of the behavior of the solution on the repulsion force.

**Rostyslav Maiboroda**,
*Estimation of concentrations parameters in models of
mixtures with varying concentrations*

*abstract*,
presentation

Finite Mixture Models are useful in statistical analysis of heterogeneous data, in cluster
analysis and pattern recognition. We will consider the model at which the concentrations of mixture
components (mixing probabilities) are different for different observations. The components distributions
are completely unknown, but there is some parametrical model of the concentrations. Least squares and
smoothed empirical likelihood estimators will be discussed for the estimation of these parameters.
Results of simulations will be presented.

**Lutz Mattner**,
*A convolution inequality, yielding a sharper Berry-Esseen
theorem for summands Zolotarev-close to normal*

*abstract*,
presentation

The classical Berry-Esseen error bound, for the normal approximation to
the law of a sum of independent and identically distributed random variables,
is improved by replacing the standardised third absolute moment by a weak norm distance to normality.
We thus sharpen and simplify two results of Ulyanov (1976) and of Senatov (1998), each of them previously optimal,
in the line of research initiated by Zolotarev (1965) and Paulauskas (1969).

Our proof is based on a seemingly incomparable normal approximation theorem of Zolotarev(1986), combined with
our main technical result:

The Kolmogorov (supremum norm of distribution function) distance between a convolution of two laws
and a convolution of two Lipschitz laws is bounded homogeneously of degree 1 in terms of the Wasserstein
distances (L^{1} norms of distribution functions) of the corresponding factors.

**Yuliya Mishura**,
*Statistical estimation in the models with memory*

*abstract*,
presentation

We investigate the mixed fractional Brownian motion with trend, driven by a standard
Brownian motion and a fractional Brownian motion. We develop and compare two approaches to estimation of
all unknown parameters by discrete observations. Also, we consider the model with trend and two
fractional Brownian motions with different Hurst indices.

**Ostap Okhrin**,
*Infinitely stochastic micro reserving** (Jointly with Matúš
Maciak and Michal Pešta)*

*abstract*

Stochastic forecasting and risk valuation are now front burners in a list of applied and
theoretical sciences. In this work, we propose an unconventional tool for stochastic prediction of
future expenses based on the individual (micro) developments of recorded events. Considering a firm,
enterprise, institution, or any entity, which possesses knowledge about particular historical events,
there might be a whole series of several related subevents: payments or losses spread over time.
This all leads to an infinitely stochastic process at the end. The aim, therefore, lies in predicting
future subevent flows coming from already reported, occurred but not reported, and yet not occurred events.
The emerging forecasting methodology involves marked time-varying Hawkes process with marks being other
time-varying Hawkes processes. The estimated parameters of the model are proved to be consistent and
asymptotically normal under simple and easily verifiable assumptions. The empirical properties are
investigated through a simulation study. In the practical part of our exploration, we elaborate a specific
actuarial application for micro claims reserving.

**Kostiantyn Ralchenko**,
*Drift parameters estimation in the Cox–Ingersoll–
Ross model*

*abstract*,
presentation

The talk is devoted to the drift parameters estimation in the Cox–Ingersoll–Ross model.
We prove the strong consistency of the maximum likelihood estimators based on the continuous-time
observations and obtain their rate of convergence in probability. Then we introduce the discrete versions of
these estimators and investigate their asymptotic behavior. In particular we establish the conditions for weak
and strong consistency, asymptotic normality and get the rate of convergence in probability. The quality of
the estimators is illustrated by simulation results.

**Shalabh**,
*Goodness of Fit Statistic in Non-parametric Measurement Error
Model*

*abstract*

The coefficient of determination (R^{2}) is used for judging the goodness of fit in a
multiple linear regression model only when the observations are correctly observed without any
measurement error. In the non-parametric regression model with the presence of measurement errors in the data,
the conventional R^{2} provides invalid results. To avoid this issue, a goodness of fit statistic
for non-parametric multiple measurement error models has been proposed in this talk.

**Sergiy Shklyar**,
*Sufficiency estimator in the inverse exponential regression*

*abstract*

Consider an inverse exponential regression with measurement errors. As the exponential
distribution makes a one-parameter exponential family, and the error-free inverse exponential regression
model is a classical generalized linear model, conditional score methods are applied in the model with
Gaussian errors. Thus, a conditional maximum likelihood ("sufficiency") estimator and conditional-score
estimators are constructed. Conditions for consistency of the sufficiency estimator are provided. This model
and its generalizations can be used in cohort studies.

**Nakahiro Yoshida**,
*Adaptive and non-adaptive estimation for degenerate
diffusion processes*

*abstract*,
presentation

We consider a degenerate system of stochastic differential equations. The first component of
the system has a parameter θ_{1} in a non-degenerate diffusion coefficient and a parameter
θ_{2} in the drift term. The second component has a drift term parameterized by
θ_{3} and no diffusion term. Parametric estimation of the degenerate diffusion system from
time-discrete observations is discussed under ergodicity. Asymptotic normality is proved in three different
situations for an adaptive estimator for θ_{3} with some initial estimators for
(θ_{1},θ_{2}), an adaptive one-step estimator for
(θ_{1},θ_{2},θ_{3}) with some initial estimators for them, and
a joint quasi-maximum likelihood estimator for (θ_{1},θ_{2},θ_{3})
without any initial estimator. The estimators incorporate information of the increments of both components.
By this construction, we show the asymptotic variance of the estimator for θ_{1} is smaller
than the standard one based on the first component only. The convergence of the estimator for
θ_{3} is much faster than the other parameters. The resulting asymptotic variance is smaller
than that of a seemingly natural estimator only using the increments of the second component.
This is a joint work with Arnaud Gloter.