## 5 General Discussion and Conclusions
In our experiments, we trained different VTLN models using adults' speech and children's speech from native and non-native speakers (Dutch only) and from three different languages. Each VTLN model exhibited variations in estimated warping factors, impacting ASR performance to varying degrees. Notably, when the VTLN model estimated warping factors that were distinct for adults and children, this generally led to improved recognition performance, particularly for younger children. In line with our no children's speech and text data scenario, we trained a VTLN model on adults' speech only, which showed significant improvements over baseline for all native children and teenager speaker groups for all three languages when applied in isolation and in combination with SP and SpecAug. Not surprisingly, training the VTLN model (also) on children's speech further improved performance. This is as expected as the VTLN model was trained on the same database as the children's speech database, thus reducing database mismatch and providing the target speech to the VTLN model for training. This scenario is nevertheless realistic as, although often both speech and transcribed text are not available for acoustic model and language model training, children's speech audio alone is more readily available. Using VTLN trained with in-domain children's speech is likely thus the best solution; however, using the VTLN model trained with adults' or any other children's speech is a good alternative solution. This is in line with our previous findings [67], which indicated that VTLN models trained on Dutch improved the performance of Mandarin Chinese children's speech recognition, demonstrating the generalizability of the VTLN warp factors across languages. Overall, the best results were obtained when the VTLN model was trained on training data that consisted of speech from all three languages, all ages, and all speech types. This shows that the more variable the training data are, the better the VTLN warping factors are estimated, resulting in improved recognition performance of children's speech. The impact of VTLN varied depending on where VTLN was applied in the automatic speech recognition process. We explored its effects when applied during both training and testing and only during testing. The approach of using VTLN during training and testing can only be applied when the model can be retrained, which is not always the case. The results show that applying VTLN only during testing gave improvements for all languages over the baseline results. Thus, even when a model cannot be retrained, applying VTLN will help children's speech recognition performance. For Dutch, applying VTLN both during training and testing gave the best results, while for German and Mandarin this condition gave slightly worse results than the test-only condition. The difference between the languages is that for Dutch, the VTLN model was trained on adults' speech with a wide variety of speech styles (including read speech, lecture recordings, broadcast data, and spontaneous conversations), while for German and Mandarin only read adults' speech was used. The results of Experiment 3 showed that the VTLN model trained on a variety of languages, speech styles, and age groups outperformed the VTLN models that were trained with less diverse data. Likewise, we hypothesize that the more diverse adult Dutch training data for the VTLN model training yielded better warping factors than the less diverse adults' speech data for German and Mandarin. This led to better normalized features, which could be learned during training, while these same normalized features were available during testing, leading to a matched train-test scenario and improved recognition performance. Importantly, the performance for adults' speech does not degrade when VTLN is applied. The age and gender analyses on Dutch children's and teenagers' speech showed that WERs are higher for younger children and then become gradually constant with age, as shown in earlier studies that use hybrid ASR systems [6].