On Berry--Esseen bounds for non-instantaneous filters of linear processes

Let $X_n=\sum_{i=1}^{\infty}a_i\epsilon_{n-i}$, where the $\epsilon_i$ are i.i.d. with mean 0 and at least finite second moment, and the $a_i$ are assumed to satisfy $|a_i|=O(i^{-\beta})$ with $\beta >1/2$. When $1/2<\beta<1$, $X_n$ is usually called a long-range dependent or long-memory process. For a certain class of Borel functions $K(x_1,...,x_{d+1})$, $d\ge0$, from ${\mathcal{R}}^{d+1}$ to $\mathcal{R}$, which includes indicator functions and polynomials, the stationary sequence $K(X_n,X_{n+1},...,X_{n+d})$ is considered. By developing a finite orthogonal expansion of $K(X_n,...,X_{n+d})$, the Berry--Esseen type bounds for the normalized sum $Q_N/\sqrt{N},Q_N=\sum_{n=1}^N(K(X_ n,...,X_{n+d})-\mathrm{E}K(X_n,...,X_{n+d}))$ are obtained when $Q_N/\sqrt{N}$ obeys the central limit theorem with positive limiting variance.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ112 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Receiprocity and Downward Wage Rigidity

The employment relationship is to a large extent characterized by incomplete contracts, in which workers have a considerable degree of discretion over the choice of their work effort. This discretion at work kicks in the potential importance of “gift exchange” or reciprocity between workers and employers in their employment relationship. Built on the seminal work of Akerlof (1980), this paper adopts a social norm approach to model reciprocity in labor markets and theoretically derives two versions of downward wage rigidity. The first version explains why employers may adopt a high wage policy far above the competitive level. This version is not a novel finding in the existing literature and is mainly served as a benchmark for later comparison in the current paper. Our main contribution lies in the second version in which not nly may employers adopt a high wage policy far above the competitive level, but one can also account for the asymmetric behavior of wages and explain why employers are hesitant about wage cuts in the presence of negative shocks. We argue that this second and stronger version of downward wage rigidity has moved the efficiency wage theory a step forward.Reciprocity, Downward Wage Rigidity, Social Norm, Efficiency Wage

The Firm as a Community Explaining Asymmetric Behavior and Downward Rigidity of Wages

This paper models the firm as a community à la Akerlof (1980) to account for asymmetric behavior, and in particular, downward rigidity of wages. It is shown that, through social interaction among workers in the firm community, wage cuts can give rise to a large, discontinuous fall in labor productivity (known as “catastrophe”). Furthermore, this large fall in labor productivity will persist or display inertia (known as “hysteresis”) even if the wages are restored to the pre-cut level and beyond. Our catastrophe/hysteresis finding with respect to wage cuts can rationalize the downward rigidity of wage behavior, and is consistent with the interview evidence of fragile worker morale emphasized by Bewley (1999) and others in explaining why employers are sensitive to and refrain from cutting worker pay.Wage rigidity, Firm community, Catastrophe, Hysteresis

Personalized Acoustic Modeling by Weakly Supervised Multi-Task Deep Learning using Acoustic Tokens Discovered from Unlabeled Data

It is well known that recognizers personalized to each user are much more effective than user-independent recognizers. With the popularity of smartphones today, although it is not difficult to collect a large set of audio data for each user, it is difficult to transcribe it. However, it is now possible to automatically discover acoustic tokens from unlabeled personal data in an unsupervised way. We therefore propose a multi-task deep learning framework called a phoneme-token deep neural network (PTDNN), jointly trained from unsupervised acoustic tokens discovered from unlabeled data and very limited transcribed data for personalized acoustic modeling. We term this scenario "weakly supervised". The underlying intuition is that the high degree of similarity between the HMM states of acoustic token models and phoneme models may help them learn from each other in this multi-task learning framework. Initial experiments performed over a personalized audio data set recorded from Facebook posts demonstrated that very good improvements can be achieved in both frame accuracy and word accuracy over popularly-considered baselines such as fDLR, speaker code and lightly supervised adaptation. This approach complements existing speaker adaptation approaches and can be used jointly with such techniques to yield improved results.Comment: 5 pages, 5 figures, published in IEEE ICASSP 201

Unsupervised Spoken Term Detection with Spoken Queries by Multi-level Acoustic Patterns with Varying Model Granularity

This paper presents a new approach for unsupervised Spoken Term Detection with spoken queries using multiple sets of acoustic patterns automatically discovered from the target corpus. The different pattern HMM configurations(number of states per model, number of distinct models, number of Gaussians per state)form a three-dimensional model granularity space. Different sets of acoustic patterns automatically discovered on different points properly distributed over this three-dimensional space are complementary to one another, thus can jointly capture the characteristics of the spoken terms. By representing the spoken content and spoken query as sequences of acoustic patterns, a series of approaches for matching the pattern index sequences while considering the signal variations are developed. In this way, not only the on-line computation load can be reduced, but the signal distributions caused by different speakers and acoustic conditions can be reasonably taken care of. The results indicate that this approach significantly outperformed the unsupervised feature-based DTW baseline by 16.16\% in mean average precision on the TIMIT corpus.Comment: Accepted by ICASSP 201