arXiv subjects

Alexandra Chronopoulou

Publications and source records attributed to Alexandra Chronopoulou.

26 records · Page 2Linked to original sources

arXiv2018

A Customer Choice Model with HALO Effect

In this paper, we propose an extension to the multinomial logit (MNL) model, the Halo MNL, that takes into account the interaction effects among products in an assortment. In particular, this model incorporates pairwise interactions of items in an effort to describe positive/negative effects among products that are present/absent in the assortment. Furthermore, we are interested in establishing sufficient conditions for identifiability, in order to build robust estimation methods. Under strict identifiability conditions, we use maximum likelihood to estimate the model parameters for which we derive closed formulas. We also perform simulation experiments, in order to numerically evaluate our method, study the accuracy of the estimators and compare it with the MNL. Last, we fit our model in the Hotel Chain dataset in Bodea et al., and we compare it with MNL in terms of efficiency, accuracy and robustness. We conclude that for rich enough datasets the model that includes interaction effects performs better in terms of how well it fits the data.

stat.AP↗

arXiv2018

NTUA-SLP at SemEval-2018 Task 1: Predicting Affective Content in Tweets with Deep Attentive RNNs and Transfer Learning

In this paper we present deep-learning models that submitted to the SemEval-2018 Task~1 competition: "Affect in Tweets". We participated in all subtasks for English tweets. We propose a Bi-LSTM architecture equipped with a multi-layer self attention mechanism. The attention mechanism improves the model performance and allows us to identify salient words in tweets, as well as gain insight into the models making them more interpretable. Our model utilizes a set of word2vec word embeddings trained on a large collection of 550 million Twitter messages, augmented by a set of word affective features. Due to the limited amount of task-specific training data, we opted for a transfer learning approach by pretraining the Bi-LSTMs on the dataset of Semeval 2017, Task 4A. The proposed approach ranked 1st in Subtask E "Multi-Label Emotion Classification", 2nd in Subtask A "Emotion Intensity Regression" and achieved competitive results in other subtasks.

cs.CL↗

arXiv2017

Sequential Monte Carlo for fractional Stochastic Volatility Models

In this paper we consider a fractional stochastic volatility model, that is a model in which the volatility may exhibit a long-range dependent or a rough/antipersistent behavior. We propose a dynamic sequential Monte Carlo methodology that is applicable to both long memory and antipersistent processes in order to estimate the volatility as well as the unknown parameters of the model. We establish a central limit theorem for the state and parameter filters and we study asymptotic properties (consistency and asymptotic normality) for the filter. We illustrate our results with a simulation study and we apply our method to estimating the volatility and the parameters of a long-range dependent model for S&P 500 data.

stat.ME↗

arXiv2015

Maximum likelihood estimation for small noise multiscale diffusions

We study the problem of parameter estimation for stochastic differential equations with small noise and fast oscillating parameters. Depending on how fast the intensity of the noise goes to zero relative to the homogenization parameter, we consider three different regimes. For each regime, we construct the maximum likelihood estimator and we study its consistency and asymptotic normality properties. A simulation study for the first order Langevin equation with a two scale potential is also provided.

math.ST↗

arXiv2012

Optimal sequential change-detection for fractional diffusion-type processes

We consider the problem of detecting an abrupt change in the distribution of a sequentially observed stochastic process. We establish the optimality of the CUSUM test with respect to a modified version of Lorden's criterion for arbitrary processes with continuous paths and apply this general result to the special case of fractional diffusion-type processes. As a by-product, we show that the CUSUM test optimizes Lorden's original criterion when a fractional Brownian motion with Hurst index H adopts a polynomial drift term with exponent H + 1/2 after the change.

math.ST↗

arXiv2011

On inference for fractional differential equations

Based on Malliavin calculus tools and approximation results, we show how to compute a maximum likelihood type estimator for a rather general differential equation driven by a fractional Brownian motion with Hurst parameter H>1/2. Rates of convergence for the approximation task are provided, and numerical experiments show that our procedure leads to good results in terms of estimation.

math.PR↗

arXiv2010

Self-similarity parameter estimation and reproduction property for non-Gaussian Hermite processes

We consider the class of all the Hermite processes $(Z_{t}^{(q,H)})_{t\in \lbrack 0,1]}$ of order $q\in \mathbf{N}^{\ast}$ and with Hurst parameter $% H\in (\frac{1}{2},1)$. The process $Z^{(q,H)}$ is $H$-selfsimilar, it has stationary increments and it exhibits long-range dependence identical to that of fractional Brownian motion (fBm). For $q=1$, $Z^{(1,H)}$ is fBm, which is Gaussian; for $q=2$, $Z^{(2,H)}$ is the Rosenblatt process, which lives in the second Wiener chaos; for any $q>2$, $Z^{(q,H)}$ is a process in the $q$th Wiener chaos. We study the variations of $Z^{(q,H)}$ for any $q$, by using multiple Wiener -Itô stochastic integrals and Malliavin calculus. We prove a reproduction property for this class of processes in the sense that the terms appearing in the chaotic decomposition of their variations give rise to other Hermite processes of different orders and with different Hurst parameters. We apply our results to construct a strongly consistent estimator for the self-similarity parameter $H$ from discrete observations of $Z^{(q,H)}$; the asymptotics of this estimator, after appropriate normalization, are proved to be distributed like a Rosenblatt random variable (value at time $1$ of a Rosenblatt process).with self-similarity parameter $1+2(H-1)/q$.

math.PR↗

arXiv2009

Variations and Hurst index estimation for a Rosenblatt process using longer filters

The Rosenblatt process is a self-similar non-Gaussian process which lives in second Wiener chaos, and occurs as the limit of correlated random sequences in so-called \textquotedblleft non-central limit theorems\textquotedblright. It shares the same covariance as fractional Brownian motion. We study the asymptotic distribution of the quadratic variations of the Rosenblatt process based on long filters, including filters based on high-order finite-difference and wavelet-based schemes. We find exact formulas for the limiting distributions, which we then use to devise strongly consistent estimators of the self-similarity parameter $H$. Unlike the case of fractional Brownian motion, no matter now high the filter orders are, the estimators are never asymptotically normal, converging instead in the mean square to the observed value of the Rosenblatt process at time 1.

math.PR↗